SMU EMIS 7364

1. SMU EMIS 7364 NTU TO-570-N Statistical Quality Control Dr. Jerrell T. Stracener, SAE Fellow Sequential Sampling Plans Updated: 4.15.04

2. Lot-by-Lot Acceptance Sampling by Attributes – Sequential Sampling Plans

3. Sequential Sampling Sequential Sampling is an extension of the double-sampling and multiple-sampling concept. In sequential sampling, we take a sequence of samples from the lot and allow the number of samples to be determined entirely by the results of the sampling process. In practice, sequential-sampling plans are usually truncated after the number inspected is equal to three times the number that would have been inspected using a corresponding single-sampling plan. If the sample size selected at each stage is greater than one, the process is usually called group sequential sampling. If the sample size inspected at each stage is one, the procedure is usually called item-by-item sequential sampling.

4. Item-by-Item Sequential Sampling • Item-by-item sequential sampling is based on the sequential probability ratio test (SPRT). • The cumulative observed number of defectives is plotted on the chart. • For each point, the abscissa is the total number of items selected up to that time, and the ordinate is the total number of observed defectives. • If the plotted points stay within the boundaries of the acceptance and rejection lines, another sample must be drawn. • As soon as the point falls on or above the upper line, the lot is rejected. • When a cumulative plot falls on or below the lower line, the lot is accepted.

5. Item-by-Item Sequential Sampling Plan Rejection line Number of defectives Reject Continue Sampling Acceptance line Accept n

6. Item-by-Item Sequential Sampling The equations for the two limit lines for specified values of p1, 1 – a, p2, and b are where (acceptance line) (rejection line)

7. Item-by-Item Sequential Sampling Suppose that we wish to find a sequential-sampling plan for which p1 = 0.01, a = 0.05, p2 = 0.06, and b = 0.10.

8. Item-by-Item Sequential Sampling Therefore the limit lines are

9. Military Standard 105E (ANSI/ASQC Z1.4, ISO 2859)

10. Description of MIL STD 105E Standard Sampling procedures for inspection by attributes were developed during World War II. MIL STD 105E is the most widely used acceptance sampling system for attributes in the world today. The original version of the standard, MIL STD 105A, was issued in 1950. Since then, there have been four revisions; the latest version was issued in 1989. MIL STD 105E is a collection of sampling schemes; therefore, it is an acceptance sampling system.

11. Description of MIL STD 105E The standard provides for three types of sampling, single sampling, double sampling, and multiple sampling. For each type of sampling plan, a provision is made for either normal inspection, tightened inspection, or reduced inspection. Normal inspection is used at the stat of the inspection activity. Tightened inspection is instituted when the vendor’s recent quality history has deteriorated. Acceptance requirements for lots under tightened inspection are more stringent than under normal inspection. Reduced inspection is instituted when the vendor’s recent quality history has been exceptionally good. The sample size used under reduced inspection is less than that under normal inspection.

12. Levels of MIL STD 105E The sample size used in MIL STD 105E is determined by the lot size and by the choice of inspection level. Three general levels of inspection are provided. Level II is designated as normal. Level I requires about one-half the amount of inspection as Level II and may be used when less discrimination is needed. Level III requires about twice as much inspection as Level II and should be used when more discrimination is needed. There are also four special inspection levels, S-1, S-2, S-3 and S-4. The special inspection levels use very small samples, and should only be employed when the small sample sizes are necessary and when large sampling risks can or must be tolerated.

13. Switching Procedures Switching procedures between normal, tightened, and reduced inspection: • Normal to tightened. When normal inspection is in effect, tightened inspection is instituted when two out of five consecutive lots have been rejected on original submission. • Tightened to normal. When tightened is in effect, reduced inspection is instituted when five consecutive lots or batches are accepted on original inspection. • Normal to reduced. When normal inspection is in effect, reduced inspection is instituted provided all four of the following conditions are satisfied.

14. Switching Procedures • Normal to reduced. When normal inspection is in effect, reduced inspection is instituted provided all four of the following conditions are satisfied. • The preceding 10 lots have been on normal inspection, and none of the lots have been rejected on original inspection. • The total number of defectives in the samples from the preceding 10 lots is less than or equal to the applicable limit number specified in the standard. • Production is at a steady state; that is, no difficulty such as machine breakdowns, material shortages, or other problems have recently occurred. • Reduced inspection is considered by the authority responsible for sampling.

15. Switching Procedures • Reduced to normal. When reduced inspection is in effect, normal inspection is instituted provided any of the following four conditions has been met. • A lot or batch is rejected. • When the sampling procedure terminates with neither acceptance nor rejection criteria having been met, the lot or batch is accepted, but normal inspection is reinstituted starting with the next lot. • Production is irregular or delayed. • Other conditions warrant that normal inspection be instituted.

16. Start “and” conditions • production steady • 10 consecutive lots accepted • Approved by responsible authority 2 out of 5 consecutive lots rejected Reduced Normal Tightened 5 consecutive lots accepted “or” conditions • Lot rejected • Irregular production • A lot meets neither the accept nor the reject criteria • Other conditions warrant return to normal inspection 10 consecutive lots remain on tightened inspection Discontinue inspection Switching Rules for normal, tightened and reduced inspection

17. Procedure • A step-by-step procedure for using MIL STD 105E is as follows: • Specify • AQL • Inspection Level • Lot Size • Select MIL STD 105E Normal Sampling Plan • To be used as long as supplier is producing the product at AQL quality or better • MIL STD 105E provides procedure for switching to tightened or reduced inspection if there is an indication that the supplier’s quality has changed.

18. Sample Size Code Letters (MIL STD 105E, Table 1) Other charts and tables are available on the courses website under resources.