Chapter 4 Supplement
Acceptance Sampling
Operations Management - 5th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2006 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga
Lecture Outline
 Single-Sample Attribute Plan
 Operating Characteristic Curve
 Developing a Sampling Plan with Excel
 Average Outgoing Quality
 Double - and Multiple-Sampling Plans
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-2
Acceptance Sampling
 Accepting or rejecting a production
lot based on the number of defects
in a sample
 Not consistent with TQM or Zero
Defects philosophy



producer and customer agree on the
number of acceptable defects
a means of identifying not preventing
poor quality
percent of defective parts versus PPM
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-3
Single–Sample
Attribute Plan
Single sampling plan
N = lot size
n = sample size (random)
c = acceptance number
d = number of defective items in sample
If d ≤ c, accept lot; else reject
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-4
Producer’s and
Consumer’s Risk
 AQL or acceptable quality level

proportion defect the customer will accept a
given lot
 LTPD or lot tolerance percent defective

limit on the number of defectives the
customer will accept
  or producer’s risk

probability of rejecting a good lot
 β or consumer’s risk

probability of accepting a bad lot
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-5
Producer’s and
Consumer’s Risk (cont.)
Good Lot
Reject
No Error
Type I Error
Producer’ Risk
Bad Lot
Accept
Type II Error
Consumer’s Risk
No Error
Sampling Errors
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-6
Operating Characteristic
(OC) Curve
 shows probability of accepting lots of
different quality levels for a specific
sampling plan
 assists management to discriminate
between good and bad lots
 exact shape and location of the curve is
defined by the sample size (n) and
acceptance level (c) for the sampling
plan
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-7
OC Curve (cont.)
1.00 –
 = 0.05
Probability of acceptance, Pa
0.80 –
0.60 –
OC curve for n and c
0.40 –
0.20 –
 = 0.10
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0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
AQL
Copyright 2006 John Wiley & Sons, Inc.
Proportion defective
LTPD
Supplement 4-8
Developing a Sampling Plan
with Excel
ABC Company produces mugs in
lots of 10,000. Performance
measures for quality of mugs sent
to stores call for a producer’s risk
of 0.05 with an AQL of 1%
defective and a consumer’s risk of
0.10 with a LTPD of 5% defective.
What size sample and what
acceptance number should ABC
use to achieve performance
measures called for in the sampling
plan?
Copyright 2006 John Wiley & Sons, Inc.
N = 10,000
α = 0.05
β = 0.10
AQL = 1%
LTPD = 5%
n=?
c=?
Supplement 4-9
Sampling Plan and OC Curve
Input
Use Poisson
distribution function
to calculate PAs
Use chart wizard to
graph OC
Use Solver to find
values for n and c
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-10
Average Outgoing
Quality (AOQ)
 Expected number of defective
items that will pass on to
customer with a sampling plan
 Average outgoing quality limit
(AOQL)


maximum point on the curve
worst level of outgoing quality
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-11
AOQ Curve
AOQL 1.39%
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-12
Double Sampling Plans
 Take small initial sample
 If # defective < lower limit, accept
 If # defective > upper limit, reject
 If # defective between limits, take second
sample
 Accept or reject based on 2 samples
 Less costly than single-sampling plans
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-13
Multiple Sampling Plans
 Uses smaller sample sizes
 Take initial sample
 If # defective < lower limit, accept
 If # defective > upper limit, reject
 If # defective between limits, resample
 Continue sampling until accept or reject
lot based on all sample data
Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-14
Copyright 2006 John Wiley & Sons, Inc.
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Copyright 2006 John Wiley & Sons, Inc.
Supplement 4-15