1. Double and Multiple Sampling Plan
Outline
Double Sampling Plan
Multiple Sampling Plan

2. Double Sampling Plan
A double sampling plan is more difficult to construct and more difficult to implement than a single sampling plan. However, it has the following advantages:
A double sampling plan may give similar levels of the consumer’s and the producer’s risk but require less sampling in the long run than a single sampling plan

3. Double Sampling Plan Example
A double sampling plan is associated with four numbers:
The interpretation of the numbers is shown by an example:
1. Inspect a sample of size 20
2. If the sample contains 3 or less defectives, accept the lot
3. If the sample contains more than 5 defectives, reject the lot.

4. Double Sampling Plan Example
4. If the sample contains more than 3 and less than or equal to 5 defectives (i.e., 4 or 5 defectives), then inspect a second sample of size 10
5. If the cumulative number of defectives in the combined sample of 30 is not more than 5, then accept the lot.
6. Reject the lot if there are more than 5 defectives in the combined lot of 30

5. Double Sampling Plan Finding Probability of Acceptance
Example: Assume that a lot contains 2% defectives. If the double sampling plan with
is used, what is the probability that the lot will be accepted? Assume that the lot size is large enough for Table G to be applicable.
Solution: The solution to the above problem takes a tree structure that is shown next. Computing probabilities at all the branches and nodes, the probability of acceptance is:

7. Multiple Sampling Plan Finding Probability of Acceptance
Double sampling plans may be extended to triple sampling plans, which may also be extended to higher order plans. The logical conclusion of this process is the multiple or sequential sampling plan.
Multiple sampling and sequential sampling are very similar. Usually, in a multiple sampling plan the decisions (regarding accept/reject/continue) are made after each lot is sampled. On the other hand, in a sequential sampling plan, the decisions are made after each item is sampled. In a multiple sampling, a finite number of samples (at least 3) are taken. A sequential sampling may not have any limit on the number of items inspected.

8. Example: A multiple sampling plan is as follows:
Sample Individual Combined Acceptance Rejection
Number Sample Size Sample Size Number Number
Compute the probability of acceptance of a 10% defective lot.

10. Reading and Exercises Chapter 11
Reading: (Handout) E.L Grant and R.S. Leavenworth, Statistical Quality Control 7th Edition, pp ,
Problems: 11.6, 11.7, p. 458