1. BPT2423 – STATISTICAL PROCESS CONTROL
ACCEPTANCE SAMPLING
BPT2423 – STATISTICAL PROCESS CONTROL

2. CHAPTER OUTLINE Fundamental Concepts Types of Sampling Plans
Single, Double, Multiple and Sequential
Statistical Aspects
Lot-By-Lot Acceptance Sampling Plans for Attributes
Acceptance Sampling Plans For :
Continuous Production
Variables

3. LESSON OUTCOMES Know the advantages and disadvantages of sampling
Understand the types of sampling plans and selection factors
Determine the Operation Characteristic (OC) curve for a single sampling plan and the properties

4. FUNDAMENTAL CONCEPT
Lot-by-lot acceptance sampling by attributes is the most common type of sampling
A predetermined number of units (sample) from each lot is inspected by attributes
If the number of nonconforming units is less than the prescribed minimum, the lot is accepted; if not, the lot is not accepted
Acceptance sampling can be used either for the number of nonconforming units or for nonconformities per unit
Example :
Lot size, N = 9000
Sample size, n = 300
Acceptance number, c = 2

5. FUNDAMENTAL CONCEPT
Acceptance sampling is most likely to be used in one of five situations:
When the test is destructive, sampling is necessary; otherwise, all of the units will be destroyed by testing
When the cost of 100% inspection is high in relation to the cost of passing a nonconforming unit
When there are many similar units to be inspected; with manual inspection, fatigue and boredom cause a higher percentage of nonconforming material to be passed than would occur on the average using a sampling plan
When information concerning producer’s quality, such as X-Bar and R, p or c charts and Cpk is not available
When automated inspection is not available

6. FUNDAMENTAL CONCEPT Advantages Disadvantages
More economical (fewer inspectors and less handling)
Upgrades the inspection job (piece-by-piece to lot- by-lot)
Applies to destructive testing
Stronger motivation for improvement (entire lots are not accepted rather than the return of a few nonconforming units)
Certain risks of not accepting conforming lots and accepting non- conforming lots
More time and effort is devoted to planning and documentation
Less information is provided about the product
There is no assurance that the entire lot conforms to specifications

7. FUNDAMENTAL CONCEPT
Lot Formation can influence the effectiveness of the sampling plan:
Lots should be homogeneous
Lots should be as large as possible
The sample units selected for inspection should be representative of the entire lot – random sampling
There are a number of courses of action that can be taken on the non-accepted lots:
Passed to the production facilities and the non- conforming units sorted by production personnel
Rectified at the consumer’s plant by personnel from either the producer’s or the consumer’s plant
Returned to the producer for rectification

8. TYPES OF SAMPLING PLANS
Single – one sample is taken from the lot and a decision to accept or not accept the lot is made based on the inspection results of that sample
Double – on the initial sample, a decision, based on the inspection results, is made whether:
To accept the lot
Not to accept the lot
To take another sample
If the quality is very good, the lot is accepted on the first sample and a second sample is not taken; if the quality is very poor, the lot is not accepted on the first sample and a second sample is not taken
Only when the quality level is neither very good nor very bad is a second sample taken

9. TYPES OF SAMPLING PLANS

10. TYPES OF SAMPLING PLANS
Multiple – is a continuation of double sampling in that three, four, five or as many samples as desired can be established. Sample sizes are much smaller
Sequential – items are sampled and inspected one after another. A cumulative record is maintained and a decision is made to accept or not accept the lot as soon as there is sufficient cumulative evidence
Remarks:
All four types of sampling plans can give the same results. Thus, the type of plan for a particular unit is based on factors other than effectiveness
These factor are simplicity, administrative costs, quality information, number of units inspected and psychological impact

11. STATISTICAL ASPECTS
Operation Characteristic (OC) Curve for Single Sampling Plans
In judging a particular sampling plan, it is desirable to know the probability that a lot submitted with a certain percent nonconforming, 100po , will be accepted – the OC curve will provide this information
When the percent nonconforming is low, the probability of the lot being accepted is large and decreases as the percent nonconforming increases
In graphing the curve with the variables 100Pa (percent of lots accepted) and 100po (percent nonconforming), one value, 100po , will be assumed and the other calculated

12. OC Curve for the Single Sampling Plan
STATISTICAL ASPECTS
Construction of an OC Curve
Assume po value
Calculate npo value
Attain Pa values from the Poisson table using the applicable c and npo values
Plot point (100po , 100Pa)
Repeat 1,2,3 and 4 until a smooth curve is obtained
OC Curve for the Single Sampling Plan

13. STATISTICAL ASPECTS
Calculation:

14. Sample size as a fixed percentage of lot size
STATISTICAL ASPECTS
OC Curve Properties
Acceptance sampling plans with similar properties can give different Operation Characteristic (OC) curve:
Sample size as a fixed percentage of lot size
Fixed sample size

15. STATISTICAL ASPECTS OC Curve Properties (cont.)
As sample size increase, the curve becomes steeper
As the acceptance number decrease, the curve becomes steeper

16. STATISTICAL ASPECTS Consumer-Producer Relationship
There is a conflicting interest between the consumer and the producer when using acceptance sampling
Ideal OC curve that is a vertical line can satisfy both – can be achieved only with 100% inspection
Sampling carries risks of not accepting lots that are acceptable and of accepting lots that are unacceptable
Acceptance Quality Limit (AQL)
“Is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. It is a reference point on the OC curve and is not meant to convey to the producer that any percent nonconforming is acceptable. It is a statistical term and is not meant to be used by the general public”

17. STATISTICAL ASPECTS Consumer-Producer Relationship (cont.)
Producer’s Risk
Represented by the symbol α, is the probability of non acceptance of a conforming lot
This risk is frequently given as 0.05, but it can range from to 0.10 or more
It cannot be located on an OC curve unless specified in terms of the probability of acceptance
This conversion is accomplished by subtracting from 1
Thus, Pa = 1 – α and for α = 0.05, Pa = 0.95

18. STATISTICAL ASPECTS Consumer-Producer Relationship (cont.)
Limiting Quality (LQ)
“Is the percent nonconforming in a lot or batch for which, for acceptance sampling purposes, the consumer wishes the probability of acceptance to be low”
Consumer’s Risk
Represented by the symbol β, is the probability of acceptance of a nonconforming lot
This risk is frequently given as 0.10

19. STATISTICAL ASPECTS Consumer-Producer Relationship (cont.) Example:
AQL = 0.7%
There are 0.7% nonconforming will have a non-acceptance probability of 5% or in other words; 1 out of 20 lots that are 0.7% nonconforming will not be accepted by the sampling plan
LQ = 2.6%
There are 2.6% nonconforming will have a 10% chance of being accepted or in other words; 1 out of 10 lots that are 2.6% nonconforming will be accepted by this sampling plan

20. ACCEPTANCE SAMPLING PLANS
Attributes
Was first devised in 1942 by a group of engineers at Bell Telephone Laboratories for use by the US government
It was designated JAN-STD-105 and adopted by the ISO and designated ISO/DIS-2859
Have been revised 5 times (MIL-STD-105E) and modified by American Society for Quality (ASQ) under the designation ANSI/ASQ Z1.4 – all tables and procedures remain unchanged

21. ACCEPTANCE SAMPLING PLANS
Attributes (cont.)

22. ACCEPTANCE SAMPLING PLANS
Continuous Production

23. ACCEPTANCE SAMPLING PLANS
Variables

24. Table - Poisson Distribution