MANAGEMENT & QUALITY CONTROL
LAB 8
RELIABILITY
1.0
OBJECTIVE
1.0 Understand reliability and how to measure the system reliability.
2.0 To determine the failure rate and construct the life-history curve of a product.
2.0
INTRODUCTION AND THEORY
Reliability (R ) is defined as the probability that a product (device/ tool/ component/
system) functions the way it is supposed to in the time frame specified under a certain set
of conditions. •Reliability is also known as quality over the long term. It is the ability of a
product to perform its intended function over a period of time under prescribed
environmental conditions.
As products become more complex, the chance that they will not function increase. The
method of arranging the components effect the reliability of the entire system.
Components can be arranged in series, parallel or a combination.
When components are arrange in series, the reliability of the system is the product of
individual components. The system reliability, Rs;
RS = (RA) (RB) (RC)
= (0.955) (0.750) (0.999)
= 0.716
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When components are arranged in series and a component does not function, then the
entire system does not function. This is not the case when the components are arranged in
parallel. When a component does not function, the product continues to function using
another component until all parallel components do not function. The system reliability,
Rs;
RS = 1 – (1 – RI) (1 – RJ)
= 1 – (1 – 0.750) (1 – 0.840)
= 0.960
The most important aspect of reliability is the design. It should be as simple as possible.
As previously pointed out, the fewer the number of components, the greater the
reliability. If a system has 50 components in series and each component has a reliability
of 0.990, the system reliability is; RS = Rn = 0.99050 = 0.605. If the system has 20
components in series, the system reliability is; RS = Rn = 0.99020 =0.818.
Failure Rate
Failure rate is important in describing the life- history curve of a product. Failure rate can
be estimated from test data by use of the formula;
λest = number of test failures / sum of test time or cycles
est 
r
t
or
est 
r
 t  n  r T
where; λ =failure rate
r = number of test failures
t = test time for a failed item
n = number of item tested
T = termination time
When the failure rate is constant, the relationship between mean life and failure rate is as
follow:  = 1 / λ, where  = mean time between failure (MTBF)
Example:
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Life-history curve
Figure 1-1 shows a typical life-history curve of a complex product for an infinite number
of items. The curve, sometimes referred to as the ‘bathtub’ curve, is a comparison of
failure rate with time. It has three distinct phases: the debugging phase, chance failure
phase, and wear-out phase.
The debugging phase, which is also called the burn-in or infant-mortality phase, is
characterized by marginal and short-life parts that cause a rapid decrease in the failure
rate. The debugging phase may be part of the testing activity prior to shipping for some
products.
The chance failure phase is shown in the figure as a horizontal line, thereby making the
failure constant. Failure occur in a random manner due o the constant failure rate. The
assumption of a constant failure rate is valid for most product; however, some product
may have a failure rate that increase with time. In fact, a few products show a slight
decrease, which mean that the product is actually improving over time.
The wear-out phase, which is depicted by a sharp rise in the failure rate.
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Example:
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MANAGEMENT & QUALITY CONTROL
3.0
TUTORIAL
1. A system has 4 components, A, B, C, and D, with reliability values of 0.98, 0.89,
0.94, and 0.95 respectively. If the components are in series, what is the system
reliability?
2. Christmas tree light bulbs used to be manufactured in series. What would be the
reliability of this system if each bulb had a reliability of 0.999 and there are 20
bulbs in the system?
3. What is the reliability of the system below where the reliabilities of components
A, B, C, and D are 0.975, 0.985, 0.988, and 0.993 respectively?
4. What is the reliability of the system below?
5. Construct the life-history curve for the following test data.
6. Determine the failure rate for a 150-h test of 9 items where 3 items failed without
replacement at 5, 76, and 135 h. What is the mean life for a constant failure rate?
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LAB 8
RELIABILITY
Lab Result
GROUP NUMBER
:___________________________
DATE OF EXPERIMENT :___________________________
GROUP MEMBERS NAME
:
(Reminder: Do not accept your group member to sign if his/her contribution is not satisfy)
1)_______________________________signature:__________
2)_______________________________signature:___________
3)_______________________________signature:__________
4)_______________________________signature:___________
5)_______________________________signature:___________
Mark :
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