Part I

Introduction In this chapter acceptance sampling and procedures for product acceptance or rejection will be examined.

Acceptance sampling plans when inspection is by

Attributes

Variables

Acceptance sampling can be performed during

Inspection of incoming raw materials, components and assemblies, in various phases of in-process operations or during final product inspection.

Acceptance sampling does not control or improve the quality of a process. It is a method for determining the general tendency of the lot.

Because of the nature of sampling, acceptance sampling procedures will accept some lots and reject others, even though they are of the same quality..

Acceptance sampling should be viewed as an auditing tool.

Methods of process control and improvement are essential for maximizing quality.

Advantages of Acceptance Sampling

(Compared to 100% inspection)

1. 100% inspection is not feasible

2. Sampling is more economical (inspection cost can be high, inspection can take a long time, and resources can be limited… In this case sampling becomes preferable).

3. Sampling reduces inspection error (especially when inspection is repetitive)

4. In sampling, an entire lot or batch may be rejected, this provides a strong motivation to improve quality.

Disadvantages of sampling

1. There is a risk of rejecting “good” lots called producers’ risk and a risk of accepting “poor” lots called consumers’ risk.

2. There is less information about the product compared to 100% inspection.

3. The selection and adoption of a sampling plan require more time and effort in planning and documentation.

Producer’s Risk (In acceptance sampling units are randomly chosen from the batch, lot or process.)

Producers Risk: Is the risk of rejecting (not accepting) a lot of good quality.

Acceptable Quality Level (AQL): this is the numerical definition of “good” lot associated with producer’s risk.

ANSI/ASQC standard A2 (1987) describes AQL as “the maximum percentage or proportion of nonconforming items or number of nonconformities in a lot or batch that can be considered satisfactory as a process average”

If producers risk is 5% for an AQL of 0.02, the batches that are 2% non conforming are considered good and the producer prefers to reject such batches no more than 5 % of the time.

Consumer’s Risk Consumers risk is the risk of accepting poor lot.

Limiting Quality Level (LQL): This is the numerical definition of poor lot associated with a consumers risk.

The ANSI/ASQC A2 (1987) describes LQL as “the percentage of proportion of nonconforming items or number of nonconformities in a batch or a lot for which the consumer wishes the probability of acceptance to be a low value”.

LQL is also called

RQL: rejectable quality level

UQL: Unacceptable quality level

LQ: Limiting quality

Example: explain the meaning of the following.

Consumers risk is 10% for a limiting quality level (LQL) of 0.08.

Means: the batches that are 8% nonconforming are poor and we prefer to accept these batches no more than 10% of a time.

Acceptable Sampling plans for Attributes Types of sampling plans

There are three types of sampling plans:

1. Single sampling plans (SSP)

2. Double sampling plans (DSP)

3. Multiple sampling plans

Single Sampling Plan (SSP)

Lot size: N (N is usually more than 10 n)

Sample size: n

Acceptance number: c

How the plan works:

random samples of size n is selected from the lot

The number of nonconformities in the sample (x) is found and compared to the acceptance number c

If the observed number of nonconformities is less than or equal to the acceptance number, the lot is accepted

If the number of nonconformities in the sample is greater than c the lot is rejected.

Example: Explain how the following single sampling plan works.

N=4000, n=100, c=2

Random sample of size 100 is selected from the lot of size 4000, if two or less nonconformities (or nonconforming items) are found the lot is accepted, otherwise it is rejected.

Operating Characteristic Curve (OC)’s are used to compare sampling plans.

Probability of accepting a lot vs proportion non conforming

To plot an operating characteristic curve:

First list the probability of accepting the lot at different values of proportions nonconforming p.

Construct the OC curve for the single sampling plan:

N=2000

n=50

c=2

And lets say p=0.02 (lot is 2% nonconforming)

Probability of acceptance is equal to

Pa=P(x≤2/p=0.02)=P(x≤2/λ=50*0.02)=P(x≤2/λ=1)=.920

λ=n.p=50(0.02)=1.0 From appendix table A2 (poisson distrbn)

At λ=1 and x=2 Pa=.920

Pa for different values of proportions non-conforming are Tabulated in Table 10.1

As the lot quality becomes poorer the probability of lot acceptance decreases (and it should) Note: Follow the lecture notes for the rest of the topics