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ACCEPTANCE SAMPLING:CHOOSING A PLAN, CONSUMER’S AND PRODUCER’S RISK

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Production and Operations Management ­MGT613
VU
Lesson 28
ACCEPTANCE SAMPLING
Acceptance sampling is an important form of inspection applied to lots or batches of items before or
after a process, to judge conformance with predetermined standards. Similarly Sampling plans are the
plans that specify lot size, sample size, number of samples, and acceptance/rejection criteria
Single-sampling
Double-sampling
Multiple-sampling
Single Sampling Characteristics
One random is drawn from each lot.
Every item in the sample is examined
Each item after examination is classified good or defective.
If the sample contains more than a specified number of defectives say c, then that lot is
rejected.
Double Sampling Plan Characteristics
Takes care of limitation of Single Sampling Plan by taking another sample if results of the
initial sample are inconclusive.
If results from second sample also indicate poor quality than the lot is rejected or otherwise
decision reached on the basis of both samples.
A double sampling plan specifies the lot size, the size of the initial sample, accept/reject criteria
for the initial sample, the size of the second sample and a single acceptance number.
With double sampling plan, 2 values are specified for number of defective items, a lower level
c1 and an upper level c2. E.g. if we have c1 equal to 2 and c2 to 7, if number of defects is
smaller than c1 than sampling is terminated and lot is accepted.
If defects are greater than c2, than lot is rejected.
If its between c1 and c2 then second sample is selected and compared to a third value c3 which
can be 8 and if the cumulative defects from 1 and 2 does not exceeds c3, the lot is accepted.
CHOOSING A PLAN
Cost and time are prime determinants of choosing a plan.
Primary considerations are number of samples needed and total number of observations
required.
Single sample has only one sample but large sample size.
Where the cost to obtain a sample is high than cost of analyzing the sample, single sample plan
is followed.
Where inspection costs are higher than costs of obtaining the sample, multiple samples are
carried to ensure that a good or bad result can help terminate the sample testing thus ensuring
savings in inspection cost.
Multiple Sampling Plans
Similar to double sampling plan but allows more than two samples.
A sampling plan will specify each sample size and two limits for each sample.
The values increase with number of samples.
If the cumulative number of defects ( in current and previous samples) exceed the upper limit,
then sampling is terminated and the lot is rejected.
If defects les than permissible, lot is accepted.
130
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Production and Operations Management ­MGT613
VU
OPERATING CHARACTERISTIC CURVE
Important criteria of sampling plan are how it discriminates between lots of high and low quality.
The ability of a Sampling Plan to discriminate is described by its OC.
The degree to which a sampling plan discriminates between good and bad lots is a function of
steepness of the curve
The ideal plan would require 100 % inspection of each lot.
OC Curves
P  100%
R
OC Curves come in
O
various shapes
B
depending on the
A
75%
sample size and risk of
B
α and β errors
I
L
50%
I
This curve is more
T
discriminating
Y
O
25%
This curve is less
F
discriminating
A
C
C
E
.03
.06
.09
P
T
Lot Quality (Fraction Defective)
I
N
G
L
O
T
The Perfect OC Curve
The Perfect OC Curve
Pr 100%
o
ba
bil
ity  75%
This curve distinguishes
of
perfectly between good
A
and bad lots.
cc
ep  50%
ti
n
What would allow you
g
to achieve a curve like
L
25%
this?
ot
.03
.06
.09
Lot Quality (Fraction Defective)
OC Curve Terms
131
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Production and Operations Management ­MGT613
VU
Acceptable Quality Level (AQL): Percentage of defective items a customer is willing to accept from
you (a property of mfg. process)
Lot Tolerance Percent Defective (LTPD): Upper limit on the percentage of defects a customer is
willing to accept ( a property of the consumer)
Average Outgoing Quality (AOQ):Average of rejected lots and accepted lots
Average Outgoing Quality Limit (AOQL):Maximum AOQ for a range of fractions defective
OC
The curve shows the probability that use of the sampling plan will result in lots with various fractions
defective being accepted. The graph shows that the lot with 3 percent defects ( a fraction of 0.03) would
have a probability of about 0.9 being accepted , 90%. And 1-0.9 =0.1 ( 10% being rejected)
As the lot quality decreases, the probability of acceptance decreases, although the relationship is not
linear.
OC Definitions on the Curve
Pr 100%
α = 0.10
o
90%
ba
bil
ity  75%
of
A
cc
ep  50%
ti
n
g
L
25%
LTPD
ot
AQL
β = 0.10
Indifferent
Good
Bad
.03
.06
.09
Lot Quality (Fraction Defective)
OPERATING CHARACTERISTIC CURVE
132
img
Production and Operations Management ­MGT613
VU
1
Pr  0.9
ob  0.8
ab  0.7
ilit  0.6
y
0.5
of   0.4
ac  0.3
ce   0.2
3
0.1
pti
0
ng
0
.05
.10
.15
.20
.25
Lot quality (fraction
DECISION CRITERIA
1.00
P
Idea
R
O
B
A
B
I
L
I
Not very
T
Discriminatin
Y
OF
A
C
C
"Good
"Bad
E
P
T
I
0
N
G
LOT
Lot quality (fraction
Sampling Terms
Acceptance quality level (AQL): the percentage of defects at which consumers are willing to accept
lots as "good"
Lot tolerance percent defective (LTPD): the upper limit on the percentage of defects that a
consumer is willing to accept
Consumer's risk: the probability that a lot contained defectives exceeding the LTPD will be
accepted
Producer's risk: the probability that a lot containing the acceptable quality level will be rejected
CONSUMER'S AND PRODUCER'S RISK
133
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Production and Operations Management ­MGT613
VU
1
α=
Proba
0.9
bility
of
0.8
accepti
ng lot
0.7
0.6
0.5
LTP
0.4
0.3
Indifferen
"Bad
"Good
0.2
0.1
β=
0
.05
.10
.15
.20
.25
0
Lot quality (fraction defective)
AQ
1
.913
0.
Pr
0.
.736
ob
0.
ab
0.
.544
ilit
0.
y
0.
.375
of
0.
.244
ac
0.
.149
ce
.086
0.
pt
0
an
.1
.3
.4
.5
.20
0
Fraction defective in lot
Average Quality is the Average outgoing quality (AOQ): Average of inspected lots (100%) and un
inspected lots
134
Table of Contents:
  1. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT
  2. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Decision Making
  3. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Strategy
  4. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Service Delivery System
  5. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Productivity
  6. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:The Decision Process
  7. INTRODUCTION TO PRODUCTION AND OPERATIONS MANAGEMENT:Demand Management
  8. Roadmap to the Lecture:Fundamental Types of Forecasts, Finer Classification of Forecasts
  9. Time Series Forecasts:Techniques for Averaging, Simple Moving Average Solution
  10. The formula for the moving average is:Exponential Smoothing Model, Common Nonlinear Trends
  11. The formula for the moving average is:Major factors in design strategy
  12. The formula for the moving average is:Standardization, Mass Customization
  13. The formula for the moving average is:DESIGN STRATEGIES
  14. The formula for the moving average is:Measuring Reliability, AVAILABILITY
  15. The formula for the moving average is:Learning Objectives, Capacity Planning
  16. The formula for the moving average is:Efficiency and Utilization, Evaluating Alternatives
  17. The formula for the moving average is:Evaluating Alternatives, Financial Analysis
  18. PROCESS SELECTION:Types of Operation, Intermittent Processing
  19. PROCESS SELECTION:Basic Layout Types, Advantages of Product Layout
  20. PROCESS SELECTION:Cellular Layouts, Facilities Layouts, Importance of Layout Decisions
  21. DESIGN OF WORK SYSTEMS:Job Design, Specialization, Methods Analysis
  22. LOCATION PLANNING AND ANALYSIS:MANAGING GLOBAL OPERATIONS, Regional Factors
  23. MANAGEMENT OF QUALITY:Dimensions of Quality, Examples of Service Quality
  24. SERVICE QUALITY:Moments of Truth, Perceived Service Quality, Service Gap Analysis
  25. TOTAL QUALITY MANAGEMENT:Determinants of Quality, Responsibility for Quality
  26. TQM QUALITY:Six Sigma Team, PROCESS IMPROVEMENT
  27. QUALITY CONTROL & QUALITY ASSURANCE:INSPECTION, Control Chart
  28. ACCEPTANCE SAMPLING:CHOOSING A PLAN, CONSUMER’S AND PRODUCER’S RISK
  29. AGGREGATE PLANNING:Demand and Capacity Options
  30. AGGREGATE PLANNING:Aggregate Planning Relationships, Master Scheduling
  31. INVENTORY MANAGEMENT:Objective of Inventory Control, Inventory Counting Systems
  32. INVENTORY MANAGEMENT:ABC Classification System, Cycle Counting
  33. INVENTORY MANAGEMENT:Economic Production Quantity Assumptions
  34. INVENTORY MANAGEMENT:Independent and Dependent Demand
  35. INVENTORY MANAGEMENT:Capacity Planning, Manufacturing Resource Planning
  36. JUST IN TIME PRODUCTION SYSTEMS:Organizational and Operational Strategies
  37. JUST IN TIME PRODUCTION SYSTEMS:Operational Benefits, Kanban Formula
  38. JUST IN TIME PRODUCTION SYSTEMS:Secondary Goals, Tiered Supplier Network
  39. SUPPLY CHAIN MANAGEMENT:Logistics, Distribution Requirements Planning
  40. SUPPLY CHAIN MANAGEMENT:Supply Chain Benefits and Drawbacks
  41. SCHEDULING:High-Volume Systems, Load Chart, Hungarian Method
  42. SEQUENCING:Assumptions to Priority Rules, Scheduling Service Operations
  43. PROJECT MANAGEMENT:Project Life Cycle, Work Breakdown Structure
  44. PROJECT MANAGEMENT:Computing Algorithm, Project Crashing, Risk Management
  45. Waiting Lines:Queuing Analysis, System Characteristics, Priority Model