Guidance 062 – Statistical Rationale for Raw Material Sampling

Operating characteristic (OC) curves illustrate the probability of accepting a lot over varying percent defective rates (Figure 1). When evaluating sampling plans, two points on the curve are of primary interest: the defective rate when lots will be routinely passed and the defective rate when lots will be routinely failed. It is fairly common to use the 95% probability of accepting a lot as the routinely passing point and the defective rate is called the acceptable quality level or limit (AQL). Lots with a defective rate at or below the AQL would be expected to pass the sampling plan criteria 95% of the time. The 10% probability of accepting a lot is typically used as the failing point and the defective rate is commonly called the unacceptable quality level (UQL) or lot tolerance percent defective (LTPD). Lots with a defective rate at or above the UQL would be expected to pass the sampling plan criteria 10% of the time (fail 90% of the time). The

AQL and UQL of any sampling plan can be used to assess the risk in deciding whether a lot is acceptable.

Sampling plans with similar AQL and UQL levels or the entire OC curve offer similar protection against the risk of an incorrect lot acceptability decision. Figures 2-5 show the OC curves for √N+1 and the Military Standard for normal, general level-II inspection for the lot size categories N=16 to N=150 (codes C,D,E,F). The √N+1 plans are displayed for the minimum and maximum lot size in the category. The AQL levels for the Military Standard plans were chosen to completely bracket the √N+1 curves. For the most part the √N+1 curves are bracketed by Military Standard plans with

AQL levels between 1.0 and 1.5. The exception is shown in Figure 2 for the 16 to 25 lot size where the AQL of 2.5 must be used to bracket the √N+1 plans. The OC curves show that the protection for √N+1 plans are similar to the Military Standard for AQL levels between 1.0 and 1.5 (1.5 and 2.5 for code C, N=16 to 25). The √N+1 plans or Military Standard plans can be used interchangeably with similar risk to the lot acceptability decision. Table 1 displays the interchangeable plans for lot sizes 16-150.

The corresponding AQL, LTPD, and average outgoing quality level (AOQL) are shown in Tables 2-5. The AOQL is the maximum or worst possible defective rate for the average outgoing quality. Regardless of the incoming quality, the defective rate going to the customer should be no greater than the AOQL over an extended period of time. The LTPD levels may be higher than expected as Saranadasa  notes. The minimum LTPD of all the plans is 11.62 and the minimum AOQL is around 2.5. Long term outgoing defective rates would be in the 2-7% range if these plans were implemented. When the quality requirements of sampling plans are met by these AQL, LTPD, and AOQL levels, √N+1 plans, as well as the corresponding Military Standard plans, could be used. √N+1 sampling plans offer similar protection as Military Standard plans with specified AQL levels between 1.0 and 1.5 (2.5 for the 16 to 25 lot size) percent for small lot sizes up to 150 units. In these cases the two sampling plan approaches can be used interchangeably with similar risks to lot acceptability decisions and outgoing quality.