Int. J. Production Economics 79 (2002) 231–260
New product warranty: A literature review
D.N.P. Murthya,b,*, I. Djamaludina,1
b
a
Department of Mechanical Engineering, The University of Queensland, St. Lucia, Qld. 4072, Australia
Department of Quality and Production Engineering, Norwegian University of Science and Technology, Trondheim, Norway
Received 12 September 2001; accepted 2 April 2002
Abstract
Warranty is an important element of marketing new products as better warranty signals higher product quality and
provides greater assurance to customers. Servicing warranty involves additional costs to the manufacturer and this cost
depends on product reliability and warranty terms. Product reliability is influenced by the decisions made during the
design and manufacturing of the product. As such warranty is very important in the context of new products. Product
warranty has received the attention of researchers from many different disciplines and the literature on warranties is
vast. This paper carries out a review of the literature that has appeared in the last ten years. It highlights issues of
interest to manufacturers in the context of managing new products from an overall business perspective. r 2002
Elsevier Science B.V. All rights reserved.
Keywords: New products; Product warranty; Manufacturing; Management
1. Introduction
Modern manufacturing is characterised by (i)
rapidly changing technologies, (ii) global markets,
(iii) fierce competition, (iv) often nearly identical
products due to common components and technology being used and, (v) better educated and
more demanding customers. This has posed
serious challenges for buyers, manufacturers and
policy makers at national and regional levels.
In the purchase decision of a product, buyers
typically compare characteristics of comparable
models of competing brands. When competing
brands are nearly identical, it is very difficult, in
*Corresponding author.
E-mail address: [email protected] (D.N.P. Murthy).
1
This was formerly this author’s affiliation.
many instances, to choose a particular product
solely on the basis of the product related
characteristics such as product price, special
features, perceived product quality and reliability,
financing offered by the manufacturer and so on.
In such situations, post-sale factors – warranty,
parts availability and cost, service, maintenance,
and so forth – take on added importance in
product choice (see Lele [1], Lele and Karmarkar
[2], Ives and Vitale [3,4], and Ritchken et al. [5]).
Of these, warranty is one that is known (or at least
potentially known) to the buyer at the time of
purchase.
In the case of new products, another feature is
that each new generation is more complex than the
earlier generation it replaces. Often customers are
uncertain about new product performance. Here
warranties play an important role in providing
0925-5273/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 5 2 7 3 ( 0 2 ) 0 0 1 5 3 - 6
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D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
product assurance to customers and different types
of warranties are offered depending on the product
and the buyer.
The notion of post-sale support is becoming an
important feature of any product sale. In this
context, warranty (and extended warranty) is an
element of post-sale support and manufacturing
business needs to view it as part of the post-sale
service strategy. A warranty of any type, since it
involves an additional service associated with a
product, will lead to potential costs beyond those
associated with the design, manufacture and sale
of the product. These costs, in fact, are unpredictable future costs, which typically range from 2%
to as much as 15% of net sales McGuire [6]. As a
result, warranty has a significant impact on the
total profits for a manufacturing business. Similarly, for businesses where new products purchased
constitute a major component of their total
operating budget ineffective management of warranties can have a significant impact on the total
operating costs.
As a result, product warranty plays an increasingly important role in consumer and commercial
transactions. The use of warranties is widespread
and they serve many purposes. These include
protection for manufacturer and buyer, signalling
of product quality, an important element of
marketing strategy, assuring buyers against items
which do not perform as promised and play an
important role in the dispute resolution between
buyer and manufacturer. These in turn pose
serious challenges to legislators in terms of
formulating sensible warranty policy legislation
that will protect the societal (buyers and manufacturers) interests. In the USA, the Congress
passed the Magnusson Moss Act and recently the
European Union (EU) passed new legislation
requiring all a two-year warranty for all products.
The concept of warranty has been around for
almost as long as there has been trade and there
have been many representations of warranty
throughout history. It has existed in some form
or another from the early civilisations (Babylonian, Assyrian, and Egyptian Eras, Ancient Hindu
and early Islamic periods), through the European
Period (Roman Era, Germanic, Jewish, and early
English periods, and the early Russian Era), the
Middle Ages, the Industrial Revolution and
beyond. Until the sixteenth century, the general
purpose of warranty was to protect the buyer from
fraud and faulty workmanship. When trade policy
reversed around the dawn of the industrial
revolution to favour the manufacturer, it was not
a pressing issue since products were still produced
locally by people known personally to buyers.
Products were still relatively simple and easily
evaluated, and any dissatisfaction was addressed
directly to the manufacturer, with word of mouth
travelling fast in local and tight knit communities.
As communities grew, so did the acceptance of
caveat emptor or ‘‘let the buyer beware’’. For
further details of warranty evolution over this long
period, see Loomba (PWH, Chapter 2)2
Late in the nineteenth century, standardised
product warranties became more common,
although many were extremely limited in coverage.
As deceit became more widespread, consumers
began to see warranties as indicators of poor
quality, with manufacturers offering contracts
with no intention of honouring them, and no legal
incentive to do so. This was the basis of the
exploitation theory of warranty. According to this
theory, the warranty terms are developed for the
manufacturer’s benefit, while the consumer has
few rights and bears the risks. Buyers who believe
this theory often feel that if a product is sold, it
should last a certain amount of time, and the
warranty is seen to serve the manufacturer by
adding to the price of the product; i.e., by offering
a service which should be provided anyway.
Because a warranty is offered, it is reasoned, these
buyers feel that the manufacturer does not have
confidence in its own product.
In 1914, to counter this trend, the Federal Trade
Commission (FTC) was established, which set
forth codes to govern the sale of goods. By 1952,
all but one state in the United States had
introduced the Uniform Commercial Code
(UCC) which specified the obligations of those
parties involved in the sale of goods. This code
also covers both explicit and implied warranties.
2
Two books that will be cited often are Warranty Cost
Analysis [26] and Product Warranty Handbook [186] and these
will be referred to as WCA and PHW respectively in the paper.
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
Before 1975, consumers were still at the mercy
of manufacturers for several reasons. Warranties
did not provide notice of consumer rights,
disclaimers were couched in legal jargon, administration of warranty was confusing and ineffective, remedies were impractical for defective items,
and excessive and unjustified claims often resulted
from consumer frustration and hostility (Burton,
PWH, Chapter 28).
The Magnuson–Moss Warranty Act aimed to
provide American consumers with information,
improve the quality of warranties and to provide
procedures for consumer remedies. The readability
of warranties has been found to have increased
slightly, however the act’s standard of ‘‘simply and
readily understood’’ is still a fair distance off
(Burton, PWH, Chapter 28). Another aim of the
act was to ensure that warranty was a good
indicator of reliability, leading to the signal theory
of Warranty.
As products become more complex, and less
easily evaluated by consumers, warranties are used
to indicate the product’s performance and reliability. The product performance and the warranty
terms together determine the costs incurred by the
manufacturer, so it follows that a longer warranty
period will result in more costs unless the product
performance is of a correspondingly higher quality. This theory [7] proposes that if a manufacturer
offers a better warranty than a competitor, then
the reliability of the product should also be better
to reduce costs associated with warranty claims.
Due to this signalling characteristic, warranty is an
important product feature and can be used by
marketing to promote sales.
More recently, warranty has been viewed as
both an insurance policy and a repair contract.
This has given rise to a third theory of warranty,
the investment theory. Under this theory, the
warranty is seen as an investment by the buyer to
reduce the risk of early failure. Manufacturers are
insured against having to rectify problems caused
by inappropriate use while the buyer is covered for
repair costs of premature failures. The aim is to
extend the useful life of the product by specifying
responsibilities of the manufacturer and the buyer.
Blischke’s [8] was the first review paper on
warranties and it dealt with mathematical models
233
for warranty cost analysis. The three-part review
paper (Product Warranty Management – I–III;
Blischke and Murthy [9], Murthy and Blischke
[10,11]) proposed a taxonomy for new product
warranties and discussed various issues. Since then
the literature on warranties (for both new and used
products) has grown considerably with two review
papers, three books and many journals and
conference papers. The review paper by Chukova
et al. [12], is a translation of a paper in Russian
and deals with warranty analysis and contains
references to papers that have appeared in the East
European journals. A more recent review paper by
Thomas and Rao [13] deals with warranty
economic models, discusses some warranty management issues and suggests few topics for future
research.
In this paper we review the literature that has
appeared over the last 10 years. It builds on the
1992 review paper by the first author. The review
looks at all different aspects of warranties for new
products.3 The main thrust is on issues that are of
high relevance to manufacturer from a product life
cycle perspective. Our scope and focus is broader
than that in Thomas and Rao [13].
The outline of the paper is as follows. Section 2
discusses warranties in a general and highlights the
concept and role of warranties. Section 3 deals
with the framework used for reviewing the
literature on warranties since 1990. It involves six
key elements. These are discussed in the next six
sections (Sections 4–9). Section 10 deals briefly
with topics not covered in the earlier sections.
2. Warranties: An overview
2.1. Warranty concept
A warranty is a manufacturer’s assurance to a
buyer that a product or service is or shall be as
represented. It may be considered to be a
contractual agreement between the buyer and
3
The authors have been reasonably thorough in their search
of the literature on warranty for the period 1990 onwards. The
search was confined to journals and conference papers and
books in English.
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D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
manufacturer entered into upon the sale of the
product or service. A warranty may be implicit or
it may be explicitly stated.
In broad terms, the purpose of a warranty
is to establish liability among the two parties
(manufacturer and buyer) in the event that
an item fails. An item is said to fail when it is
unable to perform satisfactorily its intended
function when properly used. The contract specifies both the performance that is to be expected
and the redress available to the buyer if a failure
occurs.
In this paper, we consider warranties for both
new and used products. New products can be
divided into the following three categories:
1. Consumer durables (e.g., household appliances, cars) bought by individual households
as a single item.
2. Industrial and commercial products bought
by businesses for the production of services
(e.g., equipment used in a hospital to provide
medical care, aircraft’s used by airline operators) or products (e.g., components bought by
a manufacturer). These are bought either
individually (e.g., a single X-ray machine
bought by a hospital) or as a batch of L
(L > 1) items (e.g., batteries bought by a car
manufacturer, fleet of trucks bought by a car
rental agency). One needs to differentiate
‘‘standard’’ off-the-shelf products from ‘‘custom-built’’ products built to buyer’s specifications.
3. Government acquisitions (e.g., new fleet of
tanks or jet fighters) involving new and
evolving technologies. As such, they are
characterised by a high degree of uncertainty
in the product development process. (Note: A
government is also a large buyer of ‘‘standard’’ industrial and commercial products but
these do not involve product development as
part of the warranty.)
Used products can be either consumer durables
or industrial and commercial products and these
are in general bought individually although some
times they can also be bought in lots.
Another related concept is that of an ‘‘extended
warranty’’ or a ‘‘service contract’’. The difference
between a warranty and a service contract is that
the latter is entered into voluntarily and is
purchased separately – the buyer may even have a
choice of terms, whereas a warranty is part of
product purchase and integral to the sale.
2.2. Role of warranty
Warranties are an integral part of nearly all
commercial and many government transactions
that involve product purchases. The buyer (individual, corporation, or government agency)
point of view of a warranty is different from that
of the manufacturer (or distributor, retailer, and
so forth). Another is the societal point of view and
this includes legislators, consumer affairs groups,
the courts, and public policy decision-makers.
2.2.1. Buyer’s point of view
From the buyer’s point of view, the main role of
a warranty in these transactions is protectional – it
provides a means of redress if the item, when
properly used, fails to perform as intended or as
specified by the seller. Specifically, the warranty
assures the buyer that a faulty item will either be
repaired or replaced at no cost or at reduced cost.
A second role is informational. Many buyers infer
that a product with a relatively longer warranty
period is more reliable and long lasting than one
with a shorter warranty period.
2.2.2. Manufacturer’s point of view
One of the main roles of warranty from the
manufacturer’s point of view is also protectional.
Warranty terms may, and often do, specify the use
and conditions of use for which the product is
intended and provide for limited coverage or no
coverage at all in the event of misuse of the
product. The manufacturer may be provided
further protection by specification of requirements
for care and maintenance of the product. A second
important purpose of warranties for the manufacturer is promotional. Since buyers often infer a
more reliable product when a long warranty is
offered, this has been used as an effective
advertising tool. This is often particularly important when marketing new and innovative products,
which may be viewed with a degree of uncertainty
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
by many potential consumers. In addition, warranty has become an instrument, similar to
product performance and price, used in competition with other manufacturers in the marketplace.
2.2.3. Warranty in government contracting
In simple transactions involving consumer or
commercial goods, a government agency may be
dealt with in basically the same way as any other
customer obtaining the standard product warranty
for the purchased item. Often, however, the
government, as a large entity wielding substantial
power as well as a very large consumer, will be
dealt with considerably differently, with warranty
terms negotiated at the time of purchase rather
than specified unilaterally by the seller. The role of
warranty in these transactions is usually primarily
protectional for both parties.
In some instances, particularly in the procurement of complex military equipment, warranties of
a certain type play a very different and important
role, that of an incentive to the seller to increase
the reliability of the items after they are put into
service. This is accomplished by requiring that the
contractor service the items in the field and make
design changes as failures are observed and
analysed. The incentive is an increased fee paid
to the contractor if it can be demonstrated that the
reliability of the items has, in fact, been increased.
Warranties of this type are called Reliability
Improvement Warranties (RIW).
2.3. Warranty study
Because of this diversity of purpose, product
warranty has received the attention of researchers
from many diverse disciplines. Warranties have
been studied from many different perspectives and
they deal with different issues as illustrated by the
following list.
1. Historical: Origin and use of the notion.
2. Legal: Court action, dispute resolution, product liability.
3. Legislative: Magnusson–Moss Act; Federal
Trade Commission, warranty requirements in
government acquisition (particularly military)
in the USA and the latest EU legislation.
235
4. Economic: Market equilibrium, social welfare.
5. Behavioural: Buyer reaction, influence on
purchase decision, perceived role of warranty,
claims behaviour.
6. Consumerist: Product information, consumer
protection.
7. Engineering: Design, manufacturing, quality
control, testing.
8. Statistics: Data acquisition and analysis, databased reliability analysis.
9. Operations Research: Cost modelling, optimisation.
10. Accounting: Tracking of costs, time of accrual.
11. Marketing: Assessment of consumer attitudes,
assessment of the marketplace, use of warranty as a marketing tool, warranty and sales.
12. Management: Integration of many of the
previous items, determination of warranty
policy, warranty servicing decisions.
13. Societal: public policy issues.
The bibliography by Djamaludin et al. (PWH,
Chapter 33) lists over 1500 papers dealing with the
above issues and since then the list has increased
significantly.
3. Framework for review
Warranties are offered with the sale of products,
services, software and live stock. Bulk of the
literature deals with product warranty and in this
paper we confine our attention to such warranties.
Our review of this literature deals with the
following topics:
1.
2.
3.
4.
5.
6.
Warranty
Warranty
Warranty
Warranty
Warranty
Warranty
policies.
cost analysis.
and engineering.
and marketing.
and logistics.
management.
Engineering deals with issues prior to the sale
(such as product concept, design and development,
manufacturing), marketing deals with issues related to the sale and logistic deals with post-sale
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
236
issues (such as servicing, spares etc). In the context
of product life cycle, these three are sequentially
linked. Management deals with decision making at
strategic and operational levels. This requires
taking into account the interactions between
engineering, marketing and post-sale support
elements of the manufacturing firms. As a result,
the logical connections between the six topics of
warranty reviewed in this paper are as shown in
Fig. 1.
Our focus is on both qualitative and quantitative models so that the review would be of
greater interest to a wider group of researchers
involved with different issues in manufacturing.
We omit giving any mathematical details and
interested readers can find them in the references
cited.
These six different topics are reviewed separately in the next six sections. Other topics are
briefly reviewed in a later section.
As mentioned earlier, this review does not deal
with software warranties or warranties associated
with live stock and veterinary sales. Interested
readers can find more details of software warranty
in Gomulkiewicz [14], Zhang and Pham [15],
Kimura et al. [16], Pham and Zhang [17] and
Sahin and Zahedi [18], and of warranties relating
to live stock and veterinary sales in Emswiller [19]
and Hannah [20]. Vlatas [21] discusses warranty in
the context of commercial lease.
The market for second-hand products has
been increasing Genesove [22]. As a result,
WARRANTY MANAGEMENT
WARRANTY POLICIES
WARRANTY COST ANALYSIS
WARRANTY
AND
ENGINEERING
WARRANTY
AND
MARKETING
WARRANTY
AND
LOGISTICS
Fig. 1. Frame work for review.
warranties for second-hand product has
become an important issue for certain products
(such as cars). We do not deal with this
topic. Interested readers should consult Chattopadhyay [23], Murthy and Chattopadhyay [24],
Chattopadhyay and Murthy [25, 183] for more on
this topic.
4. Warranty policies
Many different types of warranty policies for
new products have been proposed and studied.
Blischke and Murthy [9] proposed a taxonomy
to integrate these policies. The policies are
grouped into three categories (Types A, B and C)
and the details of the different policies can be
found in above reference and also in WCA
(Chapter 2).
The Type A policies (single item sale and
not involving product development) can be divided into one- and two-dimensional policies. In
the two-dimensional policies, the warranty is
characterised by a region in the two-dimensional
plane where one axis represents age and the other
usage. Blischke and Murthy [9,26] define four
different shapes for the warranty regions. Singpurwalla and Wilson [27] suggest many other
shapes.
Under a non-renewing warranty, the terms
of the warranty do not change during the
warranty period. As a result, if an item fails
during the warranty period, it is rectified by the
dealer and returned to the buyer without any
changes to the original warranty terms. Under a
renewing warranty, the warranty terms can
change, for example, after failure, the item is
returned with a new warranty either identical to,
or different from, the original warranty terms.
Each of these can be further subdivided into two
sub-groups – simple policies and combination policies. The two simple policies are the free
replacement warranty (FRW) and the pro-rata
warranty (PRW). Combination warranties involve
different FRW or PRW terms over different
periods of the warranty. For more details, see
WCA.
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
5. Warranty cost analysis
For products sold with warranty the manufacturer incurs additional cost resulting from the
servicing of claims under warranty. Warranty
claims occur due to item failures (real or
perceived). An item is said to have failed when it
is unable to perform its function in a satisfactory
manner. Item failures are influenced by several
factors. These include the engineering decisions
during design and manufacture that determine the
inherent reliability of the product, the usage
intensity and environment and the maintenance
effort expended by buyers.
Blischke and Murthy [26] define several costs of
interest to manufacturers and buyers. They include
the following:
1. Warranty cost per unit sale.
2. Warranty cost over the lifetime of an item (Life
cycle cost – LCC-I): This is buyer oriented and
includes elements such as purchase cost,
maintenance and repair costs following expiration of the warranty coverage, operating
costs and disposal costs.
3. Warranty costs over the product life cycle (Life
cycle cost – LCC-II): This is dependent on the
interval over which buyers purchase the
product. This life cycle begins with the launch
of the product onto the marketplace and ends
when it is withdrawn.
4. Cost per unit time: This is useful for managing
warranty servicing resources such as parts
inventories, labour and costs over time with
dynamic sales.
The costs clearly are different for buyer
and manufacturer. These costs are random variables, since claims under warranty and the cost to
rectify each claim are uncertain. The warranty
cost per unit sale is important in the context
of pricing the product. The sale price must exceed
the manufacturing cost plus the warranty cost or
the manufacturer incurs a loss. On average,
warranty cost per item decreases as reliability
increases. When a buyer has the option of
choosing between different warranty policies, then
this cost is of relevance. The life cycle cost of a
product is relevant to both buyer and manufac-
237
turer in the context of complex and expensive
products.
5.1. One-dimensional warranties
The first step in the warranty cost analysis is the
modelling of failures and the costs of rectification
actions over the warranty period (or the life of the
product in the case of life cycle costs).
5.1.1. Modelling failures
Failures over the warranty period can be
modelled either at the component level or at the
product (or item) level.
Component level modelling: Here the item is
characterised in terms of its components and
failure of each component modelled separately.
The modelling of first failure needs to be treated
different from that for subsequent failures. It
depends on whether the component is repairable
or not, the type of repair action used in the case of
repairable item and, the type of item (used or new)
used in the case of replacement of a failed item.
The time to first failure is modelled by a
probability distribution function. The type of
formulation needed for modelling subsequent
failure depends on the nature of rectification
(repair or replace) action. When every failure
results in a replacement by a new item and the
replacement times are negligible then the formulation is a renewal process. If all failures are
minimally repaired and the repair times are
negligible then the formulation is a point process
formulation with specified intensity function. For
further details, see Blischke and Murthy (WCA,
Chapter 2) or Murthy (PWH, Chapter 3).
When the rectification can involve either minimal repair or replacement by new, then the
formulation needed is more complex and is given
by the G-Renewal process (see, Kijima and Sumita
[28]).
System (product) level modelling: Here the item
state is modelled as a binary variable (working or
failed) and failures over time are modelled by a
non-stationary Poisson process formulation with
an intensity function LðtÞ: It is an increasing
function of t implying more failures (in a
probabilistic sense) as the item ages.
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5.1.2. Modelling rectification costs
The cost of each rectification is comprised of
several cost elements (handling, material, labour,
facilities, etc). Often it is modelled by a single
variable which is the aggregate of the different
costs. In general the aggregate cost is a random
variable and needs to be modelled by a probability
distribution function.
5.1.3. Cost analysis
Most analysis is based the following simplifying
assumptions:
*
*
*
*
*
All buyers are alike in their usage.
All items are statistically similar.
Whenever a failure occurs, it results in an
immediate claim.
All claims are valid.
The time to rectify a failed item (either through
repair or replacement) is sufficiently small in
relation to the mean time between failures so
that it can be approximated as being zero.
The manufacturer has the logistic support
(spares and facilities) needed to carry out the
rectification actions without any delays.
The product life cycle, L; is modelled as a
deterministic variable. One can easily relax this
assumption and treat it as a random variable with
a specified distribution.
All the model parameters (cost and of the
various distributions involved) are known.
Bulk of the literature deals with expected
warranty costs and few deal with higher
moments or characterisation through a distribution function. Blischke (PWH, Chapter 8) discusses the statistical techniques for warranty cost
analysis.
Free replacement warranties: Blischke and
Murthy (WCA, Chapter 4) and Blischke (PWH,
Chapter 10) deal with expected warranty costs for
both repairable and non-repairable products.
Kaminsky and Krivstov [29] deal with the case
where failures are modelled by a G-Renewal
process. Sahin and Polatoglu [30], Polatoglu and
Sahin [31] and Sahin and Polatoglu [32] derive the
probability distribution for warranty cost and
some related variables.
Pro-rata warranties: Blischke and Murthy
(WCA, Chapter 5) and Patankar and Mitra
(PWH, Chapter 11) deal with the expected cost
analysis. Menzefricke [33,34] deal with both the
mean and variance of total warranty cost. Sahin
and Polatoglu [30], Polatoglu and Sahin [31] and
Sahin and Polatoglu [32] derive the probability
distribution for warranty cost and some related
variables.
Combination warranties: The expected warranty
cost analysis for a variety of combination policies
can be found in Blischke and Murthy (WCA,
Chapter 6) and Blischke (PWH, Chapter 12).
Bohoris and Young [35] deal with the warranty
cost analysis of a hybrid warranty.
Simulation approach: The warranty cost analysis
requires solving complicated renewal functions.
An alternate approach is to obtain estimates of the
costs through simulation. Hill et al. [36] and
Murthy et al. [37] deal with this topic.
Extended warranties: The warranty that is an
integral part of product sale is called the base
warranty. It is offered by the manufacturer at no
additional cost and is factored into the sale price.
Extended warranty provides additional coverage
over the base warranty and is obtained by the
buyer by paying a premium. Extended warranties
are optional warranties which are not tied to the
sale process and can be either offered by the
manufacturer or a third party (for example, several
credit card companies offer extended warranties
for products bought using their credit cards and
some large merchants offer extended warranties).
The expected cost to the provider of extended
warranties can be calculated using models similar
to those for the cost analysis of base warranties.
The cost of extended warranty is related to
product reliability and usage intensity. The reasons for purchase of extended warranties have
been analysed extensively in the marketing literature. Padmanabhan (PWH, Chapter 18) discusses
alternate theories and the design of extended
warranty policies.
Padmanabhan and Rao [38] examine extended
warranty with heterogeneous customers with
different attitude to risk and captured through a
utility function. Patankar and Mitra [39] consider
the case where items are sold with pro-rata
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
warranty where the customer is given the option of
renewing the initial warranty by paying a premium
should the product not fail during the initial
warranty period.
Mitra and Patankar [40] deal with model where
the product is sold with a rebate policy and the
buyer has the option to extend the warranty
should the product not fail during the initial
warranty period.
Yeh and Peggo [41] look at extended warranty
policies with different options for consumers.
Rinsaka and Sandoh [42] deal with the extension
of the warranty period.
Service contracts: A service contract is similar to
an extended warranty. Bulk of the literature on
service contracts is mainly qualitative. Murthy and
Asgharizadeh [43] and Murthy [44] deal with the
modelling and analysis of service contracts using a
game-theoretic approach.
5.1.4. Related issues and models
In this section we briefly review the literature
dealing with some other models and issues related
to warranty cost analysis.
Intermittent usage: When components are used
intermittently, Murthy [45] proposed a model
formulation where the failure rates are different
depending on whether the item is in use or idle.
Murthy [46] deals with a model when the usage is
for short periods so that it can be modelled as a
point process formulation and the item can be
either in working or failed state when put into use
mode. Some systems (such as defence missiles) are
dormant for a long period before being put into
use. For an analysis of warranties for dormant
system, see Gomez [47].
Multi-component systems: Chukova and Dimitrov (PWH, Chapter 22) discuss warranty analysis
for complex systems.
Varying usage: Varying usage in the context of
two-dimensional warranties has received considerable attention. Kim et al. [48] deal with varying
usage for one-dimensional warranties.
Warranty execution: Most of the models discussed earlier assume that the buyer executes a
warranty claim whenever a failure occurs. When
this is not the case, the analysis needs to be
modified. Patankar and Mitra [49] model the non-
239
execution through a probability that increases the
warranty period remaining decreases. See also,
Patankar and Mitra (PWH, Chapter 17).
Sensitivity studies: For the same mean and
variance for failure distribution, the expected
warranty costs vary significantly with form of the
distribution. Blischke and Vij [50] study this issue
and this highlight the need to have good data to
model the failure distributions properly.
Phase type distributions: The cost analysis of free
replacement warranties for non-repairable product
involves solving the renewal function associated
the failure distribution for the product. In general,
it is not possible to derive analytical expressions
for the renewal function. Phase type distributions
provide the flexibility to approximate any arbitrary distribution and offer some computational
advantages. For more on this, see Kao and Smith
[51,52] and Rao [53].
Maintenance: Bulk of the cost analysis deals
with failures over the warranty period and
corrective actions to rectify the failures. Preventive
maintenance actions are actions taken to reduce
the occurrence of failures. A variety of models
have been proposed. These include Chun and Lee
[54], Chun [55], Jack and Dagpunar [56], Dagpunar and Jack [57], Sahin and Polatoglu [58] and
Monga and Zuo [59]. Djamaludin et al. [184]
reviews this literature and develops a framework
to study warranty and maintenance. Gi et al. [60]
deals with maintenance following the expiration of
warranty. Yeh and Lo [61] deals with a model
where preventive maintenance reduces the age of
the system. The age reduction at each preventive
maintenance action is a decision variable to be
optimally selected along with the number and time
instants at which maintenance actions are carried
out.
Data driven models: The models discussed so far
assume a failure model (either at component or
system level) and then obtain estimates for number
of failures over the warranty period. These models
can be called as ‘‘theoretical’’ models. As highlighted by Blischke and Vij [50], the distributional
assumptions have a significant impact on the
expected values of failures and costs. An alternate
approach is to build models based on failure data
and these can be called ‘‘empirical’’ models.
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The empirical models require the analysis of
warranty data (failures and costs over the warranty period). This topic has received some
attention in the literature, see for example,
Robinson and McDonald [62], Kalbfleisch et al.
[63], Kalbfleisch and Lawless [64] and PWH;
Chapter 9; Lawless [65], Lawless and Kalbfleisch
[66], Hu and Lawless [67,68], Escobar and Meeker
[69]. Complicating issues include the data being
truncated, delay in failure reporting etc.
The warranty claims over time occur according
to a point process and depends on the reliability of
the product and the sales over time. The failure
data is incomplete (due not censoring) and often
grouped or aggregated. The sales information
might be either incomplete or aggregated. These
raise several interesting and challenging problems
for modelling and estimation. Suzuki and his
associates have looked at some of these problems
and for further details, see Suzuki [70], Karim et al.
[71–73]; Suzuki et al. [74], Wang and Suzuki
[75,76] and Suzuki et al. [77].
An alternative approach to modelling the
aggregate claims over time is based on time series
models. Linear dynamic models based on Kalman
filtering approach have been studied by Wasserman [78], Singpurwalla and Wilson [27] and Chen
et al. (PWH, Chapter 31). Wasserman and
Sudjianto [79] discuss the time series approach
and compare it with two other approaches (static
predictive models and non-parametric models).
They also discuss the use of artificial intelligence
and neural networks in the modelling process.
Finally, for some discussion on the data
acquisition system, see Jauw and Vassilou [80]
where they discuss the system at Amway.
5.2. Two-dimensional policies
The two-dimensional warranties have received a
lot less attention relative to the one-dimensional
case.
5.2.1. Modelling failures
Here item failures are points on a plane with one
axis representing age ðtÞ and the other representing
usage ðxÞ: Two different approaches have been
used to modelling item failures. The first is to
model item failure by a two-dimensional distribution function. In this case failures are modelled by
a two-dimensional point process formulation (see,
Iskandar [81], Murthy et al. [82] and Hunter
(PWH, Chapter 7)). The second approach involves
modelling usage as a function of time so that
failures are effectively modelled by a one-dimensional point process formulation. Iskandar [81]
suggests a linear model for usage given by xðtÞ ¼
Lt where L is the usage rate and is modelled as a
random variable to model the varying usage across
the consumer population. Moskowitz and Chun
[83] also use a one-dimensional approach between
usage and age. They model the failures by a
Poisson process with intensity function being a
linear function of age and usage.
Singpurwalla and Wilson [27] follow a different
approach. Conditional on the total usage, the time
to failure is modelled by a univariate distribution
function. The total usage as a function of age is
modelled by another univariate distribution.
Combining these two, they derive a two-dimensional distribution for failure involving both age
and usage. See also, Singpurwalla and Wilson [84].
Singpurwalla [85] deals with modelling the survival
under multiple time scales in dynamic environments with the usage rate changing dynamically.
Gertsbakh and Kordonsky [86] and Ahn et al.
[87] reduce the usage and time to a single scale.
The former uses a linear relationship and the latter
has a linear relationship after log transformation.
5.2.2. Cost analysis
A two-dimensional warranty is characterised by
a region in a two-dimensional plane. Different
shapes for the region characterise different policies
and many different shapes have been proposed
(see Blischke and Murthy (WCA, Chapter 8) and
Singpurwalla and Wilson [84]).
Free replacement warranties: The expected warranty costs for a variety of policies can be found in
Moskowitz and Chun [83] and PWH; Chapter 13;
Singpurwalla and Wilson [84], Blischke and
Murthy (WCA, Chapter 8), Murthy et al. [88]
and Chun and Tang [89]. Kim and Rao [90] deal
with the cost analysis based on a bivariate
exponential distribution.
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Pro-rata warranties: The expected warranty cost
analysis for a variety of policies can be found in
Iskandar [81], Blischke and Murthy (WCA,
Chapter 8), Wilson and Murthy (PWH, Chapter
14) and Chun and Tang [89]. Patankar and Mitra
[49] and Eliashberg et al. [91] deal with warranty
reserve problem.
Combination warranties: The expected warranty
cost analysis for combination policies can be
found in Iskandar et al. [92] and Wilson and
Murthy (PWH, Chapter 14).
5.3. Fleet warranties
These are also referred to as cumulative
warranties. Berke and Zaino [93] and Zaino and
Berke [94] and Blischke and Murthy [26] deal with
the warranty cost analysis for a variety of such
policies. Yeh and Chen [95] deals with economic
ordering quantities for items bought in lots with a
cumulative free-replacement warranty.
6. Warranty and engineering
The warranty costs depend on the reliability of
the product and this in turn is influenced by the
decisions made during the design and manufacturing stages. By improving product reliability, the
expected warranty cost can be reduced. The
reliability of a product can be improved during
design stage through development and the degradation in reliability during manufacturing can be
controlled through better quality control. Both of
these involve additional costs and are worthwhile
only if the reductions in the expected warranty
costs exceed the additional costs incurred. The
warranty and engineering literature deals with
these issues.
6.1. Warranty and design
6.1.1. Reliability improvement during design
There are basically two approaches to improving product reliability. These are (i) using redundancy and (ii) reliability growth through
development programme.
241
6.1.1.1. Redundancy. Here one or more components are replicated to improve the reliability of
the product. As such, for a component that is
replicated we have a module of kðX2Þ components
instead of a single component. The three different
types of redundancy that have been used are (i) hot
standby, (ii) cold standby and (iii) warm standby.
In the hot standby all k replicates are connected in
parallel and in use so that the module failure time
is the largest of the k component failure times. In
cold standby, only one component is in use at any
given time. When it fails, it is replaced by a
working component (if available) through a
switching mechanism. If the switch is perfect and
components do not degrade when not in-use, then
the module failure time is the sum of the k
component failure times. In warm standby the
failure distribution of the non-failed components
(in partially energised state as opposed to fully
energised state when put into operation) have a
failure distribution which is different from that in
fully energised state. As a result, a component in
partially energised state can fail before it is put
into use. For further details, see Hussain [96] and
Blischke and Murthy [97].
For all three types of redundancy the module is
more reliable than a single component. The
reliability increases with k; the number of replicates in a module. However, this is achieved at a
cost for the cost of a module depends on the
number of replicates used and the type of
redundancy (as both cold and warm standby
redundancies involve a switching mechanism).
6.1.1.2. Reliability growth. This involves research
and development (R&D) effort where the product
is subjected to an iterative process of test, analyse
and fix cycles. During this process, an item is
tested for a certain period of time or until a failure
occurs. Based on the analysis of the test run and
failure mode, design and/or engineering modifications are made to improve the reliability. The
process is repeated resulting in reliability improvement (or growth) of the product. The reliability
growth models can be broadly grouped into two
groups – continuous and discrete models. Fries and
Sen [98] give a comprehensive review of the
discrete models and a discussion of continuous
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time models can be found in Blischke and Murthy
[97].
In continuous time models, the improvement in
reliability is modelled through a parameter ðyÞ of
the distribution which decreases with development. Most models are deterministic, where the
reliability improvement is a deterministic function
of the development. In real life, the reliability
improvement at the end of the development period
is uncertain. As a result, the reliability achieved at
the end of the development period is uncertain.
Hussain and Murthy [99] propose a model
where the outcome of the development process is
uncertain. Their model is as follows. As the
development programme continues, y decreases
thereby improving the reliability of the product
* after a development period of
but the outcome yðtÞ
t is uncertain. Let y0 denote the initial value of y;
that is, the value before the development programme is initiated, and let ym be the limiting
minimum value after development for an infinite
* is given by yðtÞ
* ¼ y0 ðy0 ym ÞZt : Zt is
time. yðtÞ
a random variable which is a function of the
development time t and given by Zt ¼
½1 expðrtÞY ; where Y A½0; 1 is a random
variable distributed according to a beta distribution with parameters a and b: This implies that
*
conditional on Y ; E½Zt increases and E½yðtÞ
decreases as t increases.
6.1.2. Optimal reliability and warranty
Murthy [100] deals with optimal reliability
choice for products sold with warranty. Murthy
and Hussain [101] and Murthy (PWH, Chapter 21)
examine optimal hot and cold standby redundancy
to achieve an optimal tradeoff between manufacturing cost and expected warranty cost. Hussain
[96] looks at all three types of redundancy and
optimal choice between redundancy and no
redundancy.
Vintr [102] looks at two cases for optimal
reliability for products sold with warranty. In the
first, the warranty period is specified and optimal
reliability is determined to minimise the manufacturer’s cost. In the second, the warranty period is a
decision variable to be selected optimally.
Majeske and Herrin [103] deal with design
changes and their impact on warranty costs.
Monga and Zuo [59] look at system design taking
into account maintenance and warranty. Goering
and Read [104] look at reliability in the microeconomics context.
For a more detailed discussion on reliability and
warranty, see Murthy and Blischke [105].
6.2. Warranty and manufacturing quality
6.2.1. Quality variations
Due to variability in manufacturing process,
some of the items do not conform to design
specifications and these are termed ‘‘non-conforming’’ in contrast to the remaining which are termed
‘‘conforming’’. The reliability characteristics of a
non-conforming item are inferior to a conforming
item. We call this as ‘‘manufacturing quality’’ and
higher quality implies fewer non-conforming items
being produced in a probabilistic sense. The
probability that an item produced is conforming
or non-conforming depends on the state of the
manufacturing process. In the simplest characterisation, the state can be modelled as being either
in-control or out-of-control. When the state is incontrol, all the assignable causes are under control
and, although non-conformance cannot be
avoided entirely, the probability that an item
produced is non-conforming is very small. When
the state changes to out-of-control, this probability increases significantly. The manufacturing
process starts in-control and after a random length
of time it changes to out-of-control.
One needs to differentiate two types (called TN1
and TN2) of non-conforming items. A TN1 nonconforming item has distribution F ðxÞ ¼ 1 for
x > 0: This implies that the item is non-functional
and is detected immediately after it is put in use.
Such type of non-conformance is usually due to
defects in assembly (e.g., dry solder joint). For a
TN2 non-conforming item, the mean to first
failure is greater than zero and hence cannot be
detected easily as a TN1 non-conforming item.
For further details, see Djamaludin [106].
Many different models for quality variation
have been proposed. A review of these can be
found in Murthy and Djamaludin [107].
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
6.2.2. Quality control and warranty
The occurrence of non-conforming items during
manufacturing can be controlled using one or
more of the following approaches – weeding, prevention and process improvement. The first two
are ‘‘on-line’’ approaches and the third one is an
‘‘off-line’’ approach.
6.2.2.1. Weeding out non-conforming items through
inspection. The aim of inspection is to weed out
non-conforming items before they are released for
sale. This requires testing the items produced. For
TN1 non-conformance, testing takes very little
time, since a non-conforming item is detected
immediately after it is put into operation. In
contrast, the detection of non-conforming items
for TN2 non-conformance involves testing for a
significant length of time.
In life testing the testing is often terminated
before all the items fail. These lead to two types of
censoring – Types I and II, respectively. In Type I
censoring, all items in the sample are tested for a
fixed period of time T; and in Type II censoring,
the testing is terminated when a specified number
of items on the test fail. Note that in Type I
censoring, the number of failed items at the end of
the testing period is a random number and in Type
II censoring, the total duration of testing is a
random variable. Another issue is the level of
testing. It can be either 100% or less than 100%.
For TN1 non-conformance, Chen [108] examines various inspection schemes such as single,
double and sequential sampling plans, using a
model proposed by Balcer and Sahin [109] to
calculate the expected warranty cost, and studies
the effect of inspection scheme on the total cost.
For TN2 non-conformance, Murthy et al. [110]
study the optimal testing period (with Type I
censoring) for items sold with warranty. They
consider three different warranty policies and
determine conditions to determine if testing is the
optimal strategy or not. Kwon [111] deals with a
method to find the optimal sampling plans that
minimise the expected average cost per lot for
items sold with pro-rata warranty (PRW).
6.2.2.2. Burn-in. Burn-in is used for weeding out
Type II non-conforming items. Burn-in involves
243
testing items for a period t: Those that fail during
testing are scrapped. The rationale for this is that
non-conforming items are more likely to fail than
conforming items and hence are weeded out. As t
increases, probability that an item released is
conforming increases, and hence the outgoing
quality is improved. However, this is achieved at
the expense of the useful life of conforming items
released being reduced by an amount t: Burn-in
costs money and the optimal burn-in achieves a
tradeoff between the burn-in cost and the resulting
reduction in the expected warranty cost. Blischke
and Murthy (WCA, Chapter 10), Murthy (PWH,
Chapter 23), Mi [112,113] discuss the optimal
burn-in period for different warranty policies.
6.2.2.3. Environmental stress screening (ESS). Coleman [114] suggests the use ESS to improve
product reliability. The screening process can be
applied at various stages during production e.g.
component, assembly or on a complete system. The
type of stress used depends on the type of faults to be
detected, and should be selected for maximum
effectiveness on weak unit without causing damage
to good units. The ESS facilities usually represent a
significant capital investment and increased operating
costs which its benefit can only be justified if the field
servicing and repair costs are high.
Kar and Nachlas [115] study a net-profit
model to optimally select the warranty period,
burn-in and stress variables to minimise the
expected net-profit. Pohl and Dietrich [116]
deal with the optimal screening duration and
develop a three level environmental stress screening (ESS) model for a complex electronic system
(an electronic printed circuit board). Pohl and
Dietrich [117] deal with a model that is an
extension of their earlier model. Here the detection
of failures is imperfect so that a failed item may
escape to the next level of assembly before being
detected.
6.2.2.4. Preventing occurrence of non-conforming
items. For batch production, the fraction of
non-conforming items is a function of the lot size.
This increases with lot size as the likelihood of
items being produced with the state being out-ofcontrol increases. As a result, the lot size can be
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used to control the occurrence of non-conforming
items.
Djamaludin et al. [118] study the quality of
product warranted is controlled through lot sizing.
Djamaludin et al. [119] deal with a model similar
to that in Djamaludin et al. [118], except that it
also involves testing a fraction of items in some
lots. Djamaludin et al. [120] deal with model
similar to that in Djamaludin et al. [119], except
that at the end of production of a lot, the process
state is not known. They consider three different
warranty policies (i) FRW for repairable product,
(ii) PRW for non-repairable product and (iii)
FRW for non-repairable product.
Yeh and Lo [121] use lot size and burn-in to
control quality for products sold with free
replacement policy. They determine the optimal
burn-in and lot size to achieve a balance between
quality control and warranty costs. Yeh et al. [122]
extend the results of Djamaludin et al. [118] to
include inventory holding costs under the assumption that the demand rate and production rates are
constants. For a different model formulation, see
Chen et al. [123].
6.2.2.5. Release without testing. Murthy et al. [82]
deal with the case where the manufacturer is
unable to carry out life testing before releasing the
items for sale. As a result, both conforming and
non-conforming items are released for sale. Since
non-conforming items have a higher failure rate,
they tend to fail early and this affects consumer
satisfaction. One way of overcoming this is
through a consumer incentive warranty policy.
Under this policy, should the first failure occur
within a period T (TpW ) the customer is offered
the following two options. Option 1 is a total
refund (money back guarantee) and Option 2 is a
new replacement item with a new warranty
identical to the original warranty and a lump
sum Cls as compensation for the inconvenience
caused due to the early failure. All failures beyond
T and within warranty are repaired minimally at
no cost to the consumer.
6.2.3. Process improvement
The design of the manufacturing process has a
significant impact on pin ; the probability that an
item is conforming when the process is in-control.
Ideally, one would like to have this probability
one, so that no item produced is non-conforming.
This involves proper design of experiment to
determine the optimal settings for the various
controllable factors.
6.3. Warranty, design and manufacturing
When component quality is uncertain then use
of redundancy as a way of improving reliability
also offers the option of testing to weed out nonconforming items. The testing can be done either
at component or module level. As such, the models
involve both design and manufacturing integrated
with warranty.
Hussain and Murthy [124,99,125] deal with
redundancy decisions when there are variations
in the quality of components and examine testing
at component and module level for weeding out
non-conforming items.
Majeske et al. [126] deals with evaluating
product and process design changes with warranty
data, and Majeske and Herrin [103] deals with
determining the warranty benefits with design
changes, in the context of the audio system for
an automobile.
For a review, see Murthy and Djamaludin [185].
7. Warranty and marketing
The consumer buying process (for both consumer durables and industrial and commercial
products) is a multi-stage process. In a simplified
characterisation it involves the following stages:
*
*
*
*
Recognition of the need for the product.
Obtaining information regarding the different
product brands.
Evaluating the different brands to decide on the
brand to purchase in terms of price, performance, assurance, post-sale support etc.
Final purchase.
To help the process, manufacturers need to
promote their brand and provide the information
to help consumers in the decision-making process.
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
As discussed earlier, warranties (and extended
warranties) serve both promotional and protectional roles.
The literature on warranty and marketing can be
grouped into several categories as indicated below:
(1) Warranty and consumer behaviour
(2) Product price and sales for warranted products
(3) Warranty and market outcome
(4) Warranty as a marketing strategy
7.1. Warranty and consumer behaviour
The behaviour of consumers depends on the
type of product since the purchase process for
consumer durables is totally different from that for
industrial and commercial products. Discussion on
how warranty is viewed during the purchase
decision making process and post purchase responses of dissatisfied buyers can be found in
Kelley (PWH, Chapter 16). Of particular relevance
are the empirical studies that show that warranties
have a significant impact on consumer product
choice and that they would pay a premium for
products with better warranty terms.
Boulding and Kirmani [127] carry out an
experimental investigation to answer the question – do consumers perceive warranties as signals
of quality? The results indicate that consumer
responses to warranties are consistent with the
behavioural assumptions of signalling theory of
warranty. Agrawal et al. [128] study warranty as a
source of information regarding product reliability
in the context of household appliances.
One anticipated outcome of the Magnusson–
Moss Warranty Act was to make warranties ‘‘easy
to read and understand’’. Moore and Shuptrine
[129] look at this issue by examining 121 warranties and conclude that the readability level
requirements are well beyond most Americans
and that the thrust has been away from full
warranty to limited warranty.
Blair and Innis [130] examine the effects of
product knowledge on the evaluation of warranted
brands. Lassar et al. [131] deal with consumer
245
reactions to product failures when the timing of
warranty expiration varies.
7.2. Sale price and sales for warranted products
The price for a product sold with warranty
needs to take into account the cost of servicing the
warranty. The sales for a product sold with
warranty needs to take into account the negative
impact of warranty on the sale price and the
positive impact as a promotional tool.
Blischke and Murthy (WCA, Chapter 10)
discuss one of the earliest models (due to
Glickman and Berger [132]) which uses a
Cobb–Douglas function with sales being a
function of price and warranty duration.
Menezes and Currim [133] model the total sales
by a more general formulation that is a function
of several variables that include price, warranty
period, quality, advertising and competitor’s
actions. They derive expressions for the
optimal price and warranty as functions of the
price and warranty elasticities. They illustrate it
with an application to historical data on automobiles.
Mesak [134] models sales through a continuous
time diffusion model. The demand rate is modelled
as a function of price and warranty length that can
vary with time. Mesak examines different structures for the diffusion model and characterises the
optimal price and warranty length.
Chun and Tang [135] deal with a model where
the buyer has the choice of buying a product with
or without warranty. They examine the optimal
warranty price taking into account the producer’s
and consumers’ risk aversion.
Marcellus and Pirojboot (PWH, Chapter 20)
discuss the design of warranty policies that takes
into account the risks and benefits of offering
warranty and examine the choice of warranty
price.
Loomba and Kumar (PWH, Chapter 19) deal
with warranty and alternate product distribution
channels. The decentralised distribution and decentralised service support channel structure involves retailer and an independent service provider
to service warranties. As a result, there are three
players making decisions. The model involves
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several decision variables with the sale price
decided by the retailer and the warranty duration
decided by the manufacturer. They derive the
optimal pricing and warranty period as a function
of several marketing parameters.
DeCroix [136] deals with the optimal warranties,
reliabilities and prices for durable goods in an
oligopoly. He uses a game-theoretic approach to
obtain the optimal solutions for each firm. Under
general assumptions, it is shown that each firm can
set its warranty and reliability independently of
price and competitor’s actions and a study of the
impact of different market factors on optimal
warranty and reliability is carried out.
7.3. Warranty and market outcome
The market outcome is determined by the
interaction between individual consumers and
manufacturers. Microeconomics deals with this
topic and examines the effect of the decisions made
by individual consumers and manufacturers and
other market related factors on the market outcome. The literature on warranties and market
outcome is extensive and is reviewed under
Warranty and economics in Section 9.
cannot meet the competition or can do so only
at substantially higher cost. Warranty in this
situation is an offensive marketing tool in that
the manufacturer is able to take a pro-active stance
in setting warranty terms. If, instead, the manufacturer is reacting to the competition, warranty
will be used as a defensive tool. The objective here
is (i) to meet competition to avoid losing sales; (ii)
correct possible consumer misperceptions concerning the quality of the item; and (iii) limit liability.
The FRW is sometimes thought of as an
offensive strategy, while the PRW is defensive
Menezes and Quelch [137]. In this context, a
combination FRW/PRW would be a reasonable
compromise between these two strategies. Menezes
and Quelch focus mainly on warranty as a
marketing strategy. There are many other issues
involved in the strategic management of warranty
and these are discussed in the next section.
Mitra and Patankar [40] examine market share
as a function of warranty and the option of
extending the warranty at the end of the base
warranty should the item not fail in the base
warranty period. They study the effect of warranty
decisions on the market share.
7.4. Warranty as a marketing strategy
8. Warranty and logistics
As a marketing tool, warranty plays many roles.
One of the most important of these is that it
provides the buyer with a degree of assurance
against uncertainty. Warranty decisions as a
marketing tool depend on whether the manufacturer is a leader or a follower with the product
being introduced and the warranty being offered,
i.e., whether an offensive or a defensive warranty
strategy, as defined by Menezes and Quelch [137],
is being pursued.
Warranty is viewed as an offensive tool when it
is used as a signal of reliability. Better warranty
terms imply higher product quality and the
manufacturer will stand behind the product. A
longer warranty requires higher reliability for cost
control and as such higher reliability gives a
competitive advantage (as long as the customer is
convinced that the product is, in fact, more
reliable). Producers of lower quality products
For products sold with warranty, the manufacturer is obligated to service all claims made under
warranty. The actions taken by the manufacturer
to accomplish this depend on the type and the
terms of the warranty. This implies that the
manufacturer incurs additional costs in the servicing of warranty. This cost can be minimised
through optimal servicing strategies and effective
warranty logistic management. Warranty servicing
deals with study of such actions and related
planning issues. In this section, we briefly discuss
some of these issues.
8.1. Warranty servicing [single item]
8.1.1. Replace versus repair
When a repairable item is returned to the
manufacturer for repair under free replacement
warranty, the manufacturer has the option of
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
either repairing it or replacing it by a new one. The
optimal strategy is one that minimises the expected
cost of servicing the warranty over the warranty
period. Blischke and Murthy (WCA, Chapter 9)
and Murthy (PWH, Chapter 24) discuss the two
sub-optimal strategies for one-dimensional warranties and Iskandar and Murthy [138] look at the
two-dimensional case. Jack and van der Duyn
Schouten [139] deal with the optimal repair–
replace strategies. Here the decision to repair or
replace is based on the age of the item at failure.
Jack and Murthy [140] examine at a sub-optimal
policy which is very close to the optimal strategy
and involves at most one replacement over the
warranty period. Iskandar et al. [141] deal with a
similar strategy in the context of two-dimensional
warranties.
8.1.2. Cost repair limit strategy
In general, the cost to repair a failed item is a
random variable which can be characterised by a
distribution function HðzÞ: Analogous to the
notion of a failure rate, one can define a repair
cost rate given by fhðzÞ=½1 HðzÞg; where hðzÞ is
the derivative of HðzÞ: Depending on the form of
HðzÞ; the repair cost rate can increase, decrease or
remain constant with z: A decreasing repair cost
rate is usually an appropriate characterisation for
the repair cost distribution Mahon and Bailey
[142]. Optimal repair limit strategy is discussed in
Blischke and Murthy (WCA, Chapter 9), Chung
[143], Murthy (PWH, Chapter 24) and Zuo et al.
[144].
8.2. Warranty servicing (dynamic sales)
Under a non-renewing PRW policy the manufacturer is required to refund a fraction of the sale
price on failure of an item in the warranty period.
In order to carry this out, the manufacturer must
set aside a fraction of the sale price. This is called
warranty reserving. For non-repairable items sold
with an FRW policy the manufacturer is required
to supply a replacement item for failures under
warranty. In this case, the number of spares
needed is of interest and this is of importance in
the context of production and inventory control.
For repairable products sold with an FRW policy
247
planning of repair facilities requires evaluation of
the demand for repairs over the warranty period.
This depends on the type of repair action and on
anticipated sales over the product life cycle.
8.2.1. Product sales over the life cycle
Let L denote the product life cycle and sðtÞ;
0ptpL; denote the sales rate (i.e., sales per unit
time) over the life cycle. This includes both first
and repeat purchases for the total consuming
population. It is assumed that the life cycle L
exceeds W ; the warranty period, and that items are
put into use immediately after they are purchased.
Since the manufacturer must provide a refund or
replacements for items that fail before reaching
age W ; and since the last sale occurs at or before
time L; the manufacturer has an obligation
to service warranty claims over the interval
½0; L þ W :
8.2.2. Warranty reserves
When items are sold with pro-rata warranties,
the manufacturer has to refund a fraction of the
sale price should an item fail within the warranty
period. This implies that the manufacturer needs
to set aside a fraction of the sale price to cover for
subsequent refunds. Murthy (PWH, Chapter 24)
deals with this problem taking into account the
option of investing the reserve to generate additional income.
8.2.3. Demand for spares and repairs
Most products are multi-component systems
where the product failure is due to the failure of
one or more components. If the component is nonrepairable, then failed items need to be replaced by
new ones. Murthy (PWH, Chapter 24) deals with
this problem to compute the expected number of
spares needed to service warranty over the product
life cycle.
When the failed item is repairable, then the
demand for repairs is needed for effective planning
of repair facilities. Murthy (PWH, Chapter 24)
deals with this problem and derives expressions for
the expected number of repairs under warranty
over the product life cycle.
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8.2.4. Service contracts
The servicing of service contract has received
very little attention. Asgharizadeh and Murthy
[145] deal with the problem where the service agent
has to decide on the optimal number of customers
that a service agent should have and Murthy and
Asgharizadeh [146] extend this model and look at
the optimal number of repair facilities to service
the customers.
8.3. Logistics related issues
The logistics of post-sale service has received
some attention in the literature (see for example,
Agnihothri and Karmarkar [147] and Cohen et al.
[148]) and some of it is relevant in the context of
servicing. However, the literature dealing specifically with warranty servicing is limited. In this
section we discuss various logistic related issues in
the context of warranty servicing.
8.3.1. Inventory management
The expected demand for spares varies over the
product life cycle. Carrying excess inventory
results in higher servicing cost. With a small
inventory, servicing under warranty can be delayed and this affects customer satisfaction. Thus
the inventory level must be managed in an effective
manner. This requires building models and a
critical variable in doing so is product reliability.
Many models have been developed for inventory
management, but very few of these deal with
inventory management in the context of product
warranty.
8.3.2. Use of loaners
A critical issue in warranty servicing is the time
to service a warranty claim. Quality warranty
service requires that this should not exceed some
specified value. In some warranty contracts there is
a penalty should this happen. One way for the
manufacturer (or agent) to reduce the probability
of this happening is to have a stock of loaners
which are issued to the owners of failed items when
they are undergoing repair. This implies additional
servicing costs and the manufacturer must optimally decide on the number of loaners to be held
in stock. Again, because of the complexity of the
model needed to study this problem, the optimal
number can only be determined by simulation
studies. For models dealing with this, see Karmakar and Kubat [149].
8.3.3. Product recall
Occasionally, a manufacturer finds it necessary
to recall either a fraction or all of the items sold,
for some rectification action as a way of reducing
the overall warranty servicing costs. The recall of
only a fraction of the total production arises when
items are produced in batches and some of the
batches are defective due to inferior component(s)
having been used and this is not detected under
quality control. A total recall situation usually
arises because of poor design specifications that
can lead to malfunction under certain conditions
and is discovered only after the items have been
produced and sold. In such cases, the manufacturer can be held responsible for damages caused
under the terms of warranty for fitness and the
recall is to replace one or more old components by
newly designed ones.
8.3.4. Principal–agent problem
Most products are sold by agents (for example,
dealers in the case of automobiles) rather than
directly by the manufacturer. Often warranty
servicing is carried out by these agents. The
manufacturer is unable to monitor directly the
quality of service provided which has an impact on
product sales. This leads to the ‘‘principal–agent’’
problem. The behaviour of the agent is influenced
by the contract between the manufacturer and
agent.
Where service is to be provided by a dealer or a
third party, mechanisms must be put in place to
guard against the following undesirable actions on
the part of agents or dealers:
*
*
Providing poor quality of service.
Over charging (either the manufacturer or, in
case of less than full warranty coverage, the
customer).
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
249
strategic offensive weapon to increase sales and
profits in the context of consumer products.
9. Warranty management
Many manufacturers have failed to recognise
the importance of warranties, to say nothing of
warranty strategy, and have, in fact, reduced
factory warranties and attempted to maximise
profits by selling extended warranties instead
Murthy and Blischke [150]. In a discussion of this
phenomenon, Cope and Pellitier [151] state that
‘‘American business, in other words, has divorced
the warranty from the product, making it just
another saleable item. Sadly, this only reinforces
the impression that US companies have no
confidence in their products.’’ In the long run,
this strategy will not work. The authors provide
some guidelines for formulating ‘‘warranties that
work’’.
The management of warranty has received very
little attention, at least as far as consumer products
are concerned. Brennan [152] deals almost exclusively with the administration of warranties in the
context of government acquisition. Menezes and
Quelch [137] discuss the use of warranty as a
9.1. Strategic warranty management
Murthy and Blischke [150] deal with the broader
and strategic management aspects of warranty.
Strategic warranty management deals with
decision making with regard to all aspects of
warranty from an overall business viewpoint and
over the product life cycle, which encompasses the
period from initial conception to manufacture and
marketing to product obsolescence. It involves
formulating a warranty strategy that is coherent
and well integrated with other strategies of the
organisation. Warranty strategy formulation must
take into account the impact of warranty on the
activities of the various sections of the organisation and vice-versa.
An appropriate warranty strategy depends on
the type of product, the type of customer, and the
overall business strategy. It also depends on a
BUSINESS STRATEGY
NEW PRODUCT STRATEGY
R&D
STRATEGY
MANUFACTURING
STRATEGY
MARKETING
STRATEGY
POST-SALE SERVICE
STRATEGY
TESTING
STRATEGY
PROCESS
STRATEGY
ADVERTISING
STRATEGY
WARRANTY
STRATEGY
DEVELOPMENT
STRATEGY
QUALITY CONTROL
STRATEGY
PRICING
STRATEGY
EXTENDED WARRANTY
STRATEGY
TECHNOLOGY
ISSUES
COMMERCIAL
ISSUES
Fig. 2. Warranty strategy as part of overall business strategy.
250
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
Target Values:
Technical
Technical
Considerations
Research and
Development
Pre-Launch Stage:
Target Values for
Warranty Terms
Launch Window:
Finalisation of
Warranty Terms
Target Values:
Commercial
Commercial
Considerations
Marketing
Post-Launch Stage:
Possible Changes to
Warranty Terms
Manufacturing
Post-Sale Service
Fig. 3. Warranty management at different stages.
number of external factors, especially competition
and competitors’ strategies. Most importantly, it
must link both technical and commercial issues
over the product life cycle since technical issues
(e.g., design) affect warranty cost and this in turn
affects commercial issues (e.g., pricing) and,
finally, overall business performance. This is shown
schematically in Fig. 2 where warranty strategy is
an element of the post-sale service strategy.
A key aspect of the strategic warranty management is that decisions with regard to warranty
must begin at a very early stage in the product life
cycle and not as an after thought just prior to the
launch stage. The decisions need to be regularly
updated over the product life cycle. Of interest to
this paper are only those activities that are closely
linked to warranty at the three different stages
– Pre-launch, Launch and Post-launch – of the
product life cycle. Decisions about these activities
must take into account warranty decisions and
vice-versa. This process is shown schematically in
Fig. 3 from Blischke and Murthy [97] where
further details can be found.
Tang and Leong [153] deal with warranty
strategy for hybrid products. These are products
designed in one country (usually a developed
country) and manufactured in another country (a
developing country). In this case, the consumer
perception of quality is affected by the information
that the product is a hybrid product. This has
serious implications for international marketing.
See also, Lee et al. [154].
9.2. Warranty management system
The purpose of a warranty management system
is to evaluate trade-offs between competing
objectives or variables by using models, and to
provide information to management for the
development of functional and operational strategies. Data that is relevant to warranty is extracted
from the business operations, organised, analysed
and used to assist managers in decision making.
Examples of these objectives or variables include
reliability, sale price, warranty type and duration,
warranty costs or manufacturing (unit) cost.
The warranty management involves models to
evaluate the objective in terms of the decision
variables to assist the decision-maker in the
decision making process. This may be in the form
of expected outcomes of proposed actions (for
example, increasing reliability will reduce expected
warranty costs by a certain amount), or optimal
values for decision variables (for example, to
reduce expected warranty costs or to increase
reliability by some specified amount). Lyons and
Murthy [155] suggest the grouping of the various
models into four modules – Design & Engineering
(D&E), Manufacturing, Marketing, and Post Sale
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
251
Warranty Management System
Design &
Engineering
Module
Manufacturing
Module
Problem /
Objective
Decision
Support
Post Sale
Servicing
Module
Marketing
Module
Fig. 4. Warranty management system.
Servicing – that interact with each other as shown
in Fig. 4.
While warranty involves many decision aspects,
the most important to the financial success of a
product is the total warranty cost; the total
amount expended on warranty claims throughout
the product line’s entire life. It is dependent on
information and decisions from each of the four
modules as indicated in Fig. 5 (from Lyons and
Murthy [155]). Estimating this cost accurately
depends on the quality, quantity and timeliness
of data gathered from operational processes.
Lyons and Murthy [155] discuss the four
modules in more detail and the different types of
data needed and exchange of information between
the modules for effective warranty management.
Proper data collection is critical.
Another source of information is warranty
cards. Spiegler and Herniter [156] discuss this
and Decision Support System. Oh and Bai [157]
discusses warranty data in the context of product
reliability.
9.3. Optimal warranty management
As can be seen from the discussion so far,
product warranty is influenced by various technical decisions made during the design and manufacturing of the product and warranty in turn
influences various commercial factors such as
price, sales etc. Optimal warranty management
deals with decisions making to optimise some
stated objective while at the same time taking into
account the various interactions between the
variables involved.
In Section 7 we looked at optimal engineering
decisions for products sold with warranty so as to
achieve a trade-off between expected warranty cost
and the cost of the engineering actions involved. In
Section 8 some of the market related models
looked at optimal price and warranty terms to
maximise total profits.
In real life, there is often more than one
objective function. Mitra and Patankar ([158]
and PWH, Chapter 32) look at multi-criteria
model for determining the warranty parameters.
The objective function includes several goals such
as
*
*
Market share: To achieve a certain market
share.
Expected warranty reserve costs: The total
warranty cost does not exceed a given proportion of total sales.
They propose a method that involves the
decision-maker to prioritise the selected goals.
See also, Patankar and Mitra [39].
Murthy and Kumar [159] deals with a model
which integrates the design, manufacturing quality
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
252
D&E
Module
Manufacturing
Module
Designed
Reliability
Manufacturing
Quality
Post Sale Servicing
Module
Usage
Patterns
Repair
Quality
Claim Execution
Patterns
Marketing
Module
Demand
Product
Performance
Characteristics
No of Failures
per item
No of Claims
per item
Warranty
Mix
Cost
per Claim
Warranty Cost
per item
Total
Warranty Cost
Fig. 5. An integrated model for total warranty costs.
control and warranty servicing in the context of a
new product. Lin et al. [160] deal with a model
which links design with preventive maintenance
and warranty.
9.4. Other topics
Offering warranty involves risk of high warranty
servicing cost. Hadel and Lakey [161] discuss a
structured approach to warranty preparation and
risk management. See also, Issacson et al. [162].
Offering warranty implies an obligation on the
part of the manufacturing firm to service the all
claims over the warranty period. If the firm goes
bankrupt it has implications for customers.
Applebaum [163] deals with this interesting aspect.
10. Other warranty related topics
10.1. Warranty and the law
There is a vast literature in various law journals.
USA seems to be leading other nations in warranty
legislation.
Kelley (PWH, Chapter 4) deals with warranty
legislation in the USA in a historical context and
also discusses international warranty and warranties in government procurement. The implications
for businesses and consumers are discussed along
with future trends in the legislation.
Kowal (PWH, Chapter 5) deals with warranty
and the courts and highlights issues of concern to
manufacturers.
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
Blischke and Murthy (WCA, Chapter 14)
discuss briefly the alternate dispute resolution
mechanisms and where additional references can
be found.
As buyers in other countries become more
aware of their rights, warranty legislation will
assume greater importance.
10.2. Warranty and accounting
253
25), the literature deals with the following two
issues.
1. Consumer demand warranties in the sense that
they are willing to pay more for a product
covered by some form of warranty.
2. Given the demand for warranties, the optimal
warranty decisions by manufacturing firms to
maximise their profits.
Warranty costs are incurred subsequent
to the sale of the product. These occur
randomly over the warranty period since item
failures are uncertain and the costs themselves are random variables. This has implications
for accounting purposes. Maschmeyer and
Balachandran (PWH, Chapter 26) discuss this in
the context of manufacturing businesses in
the USA and the reporting requirements as
specified by the Financial Accounting Standards
Board (FASB) and the Internal Revenue Service
(IRS).
Two issues of importance are (i) warranties as a
contingent liability and the disclosure of warranty
loss contingencies and (ii) accounting for warranty
litigation.
Maschmeyer and Balachandran (PWH, Chapter
29) deal with cost management planning and
control for product quality and warranties and
the reporting of warranty costs as components of
quality cost for control. They then discuss strategic
management of warranty costs.
Finally, Yost and Rasch [164] deals with
warranty management for accounting information
systems.
Various factors affect the decisions of both
parties. These include
10.3. Warranty and economics
Most products require maintenance on the part
of buyers. When the manufacturer is unable to
monitor the maintenance actions of buyers, there
is a possibility that some of the buyers might not
expend enough maintenance effort and as a result
claims under warranty can increase significantly.
This leads to a ‘‘moral hazard’’ problem. Similarly,
when buyers cannot evaluate the reliability of a
product, there is a possibility that the manufacturer might sell inferior products. This leads to
Microeconomics deals with the decisions of
individual manufacturing firms and consumers
and how they interact within a product market.
The under lying assumption is that the decisions
are made rationally by both parties with consumers maximising their satisfaction captured
through utility functions and firms maximising
their profits. According to Lutz (PWH, Chapter
(a) Information available to consumers at the
time of the purchase of the product.
For consumer durables, when the manufacturer offers a range of warranty policies
designed for different usage or buyer needs,
the choice of the buyer is influenced by the
information (about product performance,
reliability etc) available to the buyer. Often
the information is incomplete and this can
lead to adverse selection and hence negating
the reason for the manufacturer offering the
choice. An understanding of this problem is
important for the manufacturer in making
optimal decisions with regards warranty options.
(b) Risk attitude of consumers.
When warranty is viewed as an insurance
against unsatisfactory product performance, a
risk-averse consumer is willing to pay more
for warranty compared to a risk-neutral
consumer.
(c) Maintenance efforts of consumers and its
impact on the degradation when the product
fails to perform satisfactorily.
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D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
another moral hazard problem. The moral hazard
problem in the context of warranty has received
some attention.
Most of the models studied are stylistic. They
are predominantly static in nature (dealing with
one time period corresponding to the warranty
period).
The choice between base warranty and extended
warranty has received considerable attention.
Chen and Ross [165] discuss the reason for
extended warranties being expensive in a competitive market. Padmanabhan [166] shows that
consumer moral hazard and heterogeneity in
product usage create variations in the evaluation
of the product warranties by the different segments
in the market. This implies that manufacturing
firms can meet this demand by offering a selfselecting menu of base and extended warranties.
Lutz and Padmanabhan [167] discuss the reason
for the base warranty being minimal even though
all consumers are risk-averse. It is based on
consumer moral hazard and competition in the
insurance after-market for the product where third
parties provide optional extended warranties.
Finally, Lutz and Padmanabhan [168] consider
the extended warranties are also offered by third
parties (such as insurance companies, retailers)
and study their impact on the manufacturer’s
menu choices. When third parties offer warranty,
Flechtner [169] deals with the remedies available to
a buyer who has suffered a breach of warranty.
Mann and Wissink [170,171] investigate warranties in a market setting with adverse selection
and buyer and seller moral hazard. Competitive
equilibrium contact involves a positive correlation
between price and warranty coverage.
Dybvig and Lutz [172] look at the two-sided
moral hazard in the context of warranties,
durability and maintenance effort. They show that
the optimal warranty is a block warranty – a high
level of insurance for an initial block of time and
no insurance against later breakdown. In other
words, it a pro-rata policy with full refund for a
length of time which is a fraction of the useful life
of the product.
Bigelow et al. [173] consider the situation where
the manufacturer firm offering warranty can exit
the market before the warranty obligations cease.
This can be because of the form going bankrupt or
the firm choosing this option to avoid its warranty
obligations. They look at alternate market structures and the influence of government role.
Al-Najjar [174] deals with warranty reputation
and product quality. Here the manufacturing firm
has the choice between implicit and explicit
contracts as alternate methods of assuring product
quality. The explicit warranty contracts are
enforced through formal third-party sanctions
and implicit contracts are informally enforced
through the reputation of the contracting parties.
Shieh [175] deals with full money back guarantees (pro-rata warranty with full refund) and
studies the informational role and optimality in a
signalling model with quality uncertainty and riskneutral consumers. He shows that the money back
guarantee and price together reveal a monopolist
manufacturer’s private information about product
quality.
Boom [176] looks at three different warranty
rules in a monopoly setting with risk-averse
consumers. These include: (i) no warranty, (ii) full
refund (or money back guarantee), and (iii)
renewing free replacement.
10.4. Warranty and societal aspects
Warranties from a public policy perspective are
discussed in Mosier and Wiener (PWH, Chapter
27). Burton (PWH, Chapter 28) deals with
warranty protection from a consumerist perspective and suggests improvements in the warranty
legislation to enhance buyer protection.
10.5. Applications
For most companies, warranty costs are a
closely guarded secret, as evidenced by the fact
that very little warranty data is available in the
public domain. These costs are, of course, related
to product quality. If warranty costs are high, then
product quality is more likely to be low, in an
inverse proportionate sense. As a result papers on
the applications of warranty in the open literature
are very small in number.
Blischke and Murthy (WCA, Chapter 13 and
2000) deal with warranties for Boeing 747 wind-
D.N.P. Murthy, I. Djamaludin / Int. J. Production Economics 79 (2002) 231–260
shields and carries out a cost analysis using failure
data provided by the manufacturer.
Lyons and Murthy [177] deal with warranty
data where items to consumers are sold in batches
(of varying sizes) and failed items under warranty
are also returned in batches. A detailed study of
this can be found in Blischke and Murthy [97].
Majeske and Herrin [178] deal with automobile
warranty data and model it by a mixture model.
Lu [179] deals with automotive reliability prediction based on early field failure warranty data. Gill
and Roberts [180] deal with warranty repair for
new cars. They develop a microeconomics model
and test it using empirical data. Douglas et al.
[181] deal with warranty, quality and price in the
US automobile market based on a model proposed
by Cooper and Ross [182]. Finally, some of the
papers by Lawless and Kalbfleisch cited earlier in
Section 5.1.4 deal with modelling real warranty
data.
Acknowledgements
The authors thank the two referees for their
constructive comments and suggestions on an
earlier version of the paper.
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