An AQL System For LotByLot Acceptance Sampling By

An AQL System For Lot-By-Lot Acceptance Sampling By Attributes Outline • • • Acceptance Criteria Acceptable Quality Level (AQL) Appendix 3 Tables Determining Sample Size Code Letter A Single Sampling Plan Example 1

Acceptance Criteria 1. In order to establish acceptance criteria, it is necessary to prescribe a maximum percent defective that, for acceptance sampling purposes only, is considered acceptable as a process average. This percent defective is Acceptable Quality Level, AQL 2. The acceptance criteria should be selected with the objective of protecting the producer. Hence, at AQL the producer’s risk, should be small, say 0. 05, or between 0. 01 and 0. 10, etc. 2

Acceptance Criteria 3. More severe acceptance criteria designed to protect the customer must be used whenever the quality history is unsatisfactory. This gives the concept of tightened inspection as an alternative to normal inspection 4. Relatively low AQL values should be used for those types of defects that would have serious consequences and relatively high AQL values for those defects that are of little importance 3

Acceptance Criteria 5. Economies for the consumer can be realized by permitting reduced inspection when the quality is good 6. The relationship between lot size and sample size is based more on empirical grounds than on considerations arising from the mathematics of probability. Three general inspection levels (I, II, and III) are used. 4

Acceptable Quality Level (AQL) • Alternative definitions of AQL: – (ABC, ANSI/ASQC) The AQL is the maximum percent defective (or the maximum number of defects per hundred units) that, for purposes of sampling inspection, can be considered satisfactory as a process average. The phrase “can be considered satisfactory” is interpreted as a producer’s risk, , equal to 0. 05; actually, varies from 0. 01 to 0. 10 5

Acceptable Quality Level (AQL) • Alternative definitions of AQL: – (JAN-STD-105) Percentage of defective items in an inspection lot such that the sampling plan will result in the acceptance of 95% of submitted inspection lots containing that percentage of defective items – (MIL-STD-105 A) The AQL is a nominal value expressed in terms of percent defective or defects per hundred units, whichever is applicable, specified for a given group of defects of a product 6

Appendix 3 Tables • Table K gives the sample size code letter • Tables L to T give sample sizes and acceptance and rejection numbers for various cases of single/double/ multiple sampling plan and normal/tightened/reduced inspection. To enter any one of these tables, it is necessary to know the AQL and sample size code letter • Notice that some AQL values are very high such as above 10 and even 100 or above. The AQL values may be interpreted as percent defective or as percent defects per hundred units. AQL values above 10 are interpreted as applying to defects per hundred units 7

Determining Sample Size Code Letter • Table K in Appendix 3 gives the sample size code that is used in Tables L to T. • General inspection levels as opposed to special inspection levels are used in most cases • Unless otherwise specified, Inspection Level II is used. Inspection Level I may be used when less discrimination is needed, or Inspection Level III may be specified for greater discrimination • Inspection Level II is the norm, with Level I providing about one-half the amount of inspection and Level III providing about twice the amount of inspection 8

Determining Sample Size Code Letter • Thus, Level III gives a steeper OC curve and consequently more discrimination and increased inspection costs • The decision on the inspection level is also a function of the type of product. For inexpensive items, for destructive testing, or for harmful testing, inspection level II should be considered. When subsequent production costs are high or when the items are complex and expensive, Inspection Level III may be applicable. 9

A Single Sampling Plan Example: For a lot size of 2000, and AQL of 0. 65%, and an Inspection Level of III, determine the single sampling plans for normal, tightened, and reduced inspection Sample Size Code Letter: See Table K in Appendix 3. For a lot size of 2000 and an inspection Level of III, the sample size code letter is L This sample size code letter is used for each of the normal, tightened, and reduced inspection. Change all font colors to black to see the missing part 10

A Single Sampling Plan Example: For a lot size of 2000, and AQL of 0. 65%, and an Inspection Level of III, determine the single sampling plans for normal, tightened, and reduced inspection Normal: See Table L in Appendix 3. For AQL = 0. 65 and sample size code letter L, we get n = sample size = 200 Ac = 3, Re = 4 – If 3 or fewer are defective, the lot is accepted Change all font colors to black to see the missing part 11

A Single Sampling Plan Example: For a lot size of 2000, and AQL of 0. 65%, and an Inspection Level of III, determine the single sampling plans for normal, tightened, and reduced inspection Tightened: See Table M in Appendix 3. For AQL = 0. 65 and sample size code letter L, we get n = sample size = 200 Ac = 2, Re = 3 – If 2 or fewer are defective, the lot is accepted Change all font colors to black to see the missing part 12

A Single Sampling Plan Example: For a lot size of 2000, and AQL of 0. 65%, and an Inspection Level of III, determine the single sampling plans for normal, tightened, and reduced inspection Reduced: See Table N in Appendix 3. For AQL = 0. 65 and sample size code letter L, we get n = sample size = 80, Ac = 1, Re = 4 – If 3 or less are defective, the lot is accepted – If 2 or 3 are defective, a change to normal sampling is required Change all font colors to black to see the missing part 13

Normal, Tightened, and Reduced Inspection • Inspection starts with normal inspection condition • Normal to tightened: 2 out of 5 consecutive lots or batches have not been accepted on original inspection (i. e. , ignoring resubmitted lots) • Tightened to normal: 5 consecutive lots or batches are accepted on original inspection. After tightened inspection has been in effect for 10 consecutive lots, the sampling inspection under the ABC standard is terminated. Hence, a return to normal inspection must occur within 10 consecutive lots. 14

Normal, Tightened, and Reduced Inspection • Normal to reduced: – 10 consecutive lots or batches have been on normal inspection and all of the lots have been accepted on original inspection – Production is at a steady state. In other words, there are no difficulties such as machine breakdowns, material shortages, or labor problems – Reduced inspection is considered desirable by the responsible authority (consumer) – Another criteria is omitted from here 15

Normal, Tightened, and Reduced Inspection • Reduced to normal: – A lot or batch is not accepted – When the sampling procedure terminates with neither acceptance nor rejection criteria have been met, the lot is accepted, but normal inspectio is reinstated. For example AC = 1, Re = 4 and there are 2 or 3 defectives in the sample – Production is irregular or delayed – Other conditions, such as customer desire, etc. 16

Reading and Exercises • Chapter 12 – Reading: pp. 463 -474 – Problems: 12. 1 - 12. 6 17