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Operating Characteristic (OC) Curve

The BIS.Net Team BIS.Net Team

An OC curve is an important tool for the analyst to assess the protection a given sampling plan provides. It is not uncommon practice to set arbitrary sampling plans e.g. take a sample size of 5 and reject the batch if there are more than zero defectives. The OC Curve permits the analyst to evaluate the effectiveness of such plans.

Even when a sampling plan has been derived scientifically using BISNET Acceptance Sampling, the OC Curve provides additional insights over the complete range of possible defectives.

For example, when deriving a sampling plan only two levels of defectives are considered, the Acceptable Quality Level (AQL) and Lot Tolerance Percent Defective (LTPD).

Consider the example where we specify an AQL of 2%, LTPD of 5% with a Producer’s risk of 5% and Consumer’s Risk of 10%. We would obtain the following sampling plan with near matching producer’s and consumer’s risks at the specified AQL and LTPD

Shewhart chart demonstrating the issues with spc theory
Shewhart chart demonstrating the issues with spc theory

The OC Curve however allows the analyst to see what the risk of accepting a batch at different levels of defectives is. For example, at 4% defectives, slightly less than the specified LTPD of 5%, the risk of accepting such a batch is 30%, three times as high as the specified 10%. This may not be satisfactory. If not, then an alternative sampling plan can be trialed with the BIS.Net Acceptance Sampling App.

The OC Curve is also a useful tool to demonstrate the folly of believing sampling plans should have acceptance values of only zero. The zero-acceptance value myth is understandable from one perspective. If we accept batches with defectives in the sample, then we are accepting defective batches. By only accepting batches with zero defectives it is believed that we can be more certain that the batches are defect free. After all, if the sample has defectives in it then the batch must have defectives. The problem with the zero-acceptance values approach is that it fails to consider the AQL, i.e. the inherent process percent defectives which must be accepted until engineering efforts eliminate all defectives.

Consider the above sampling plan which would accept batches whenever there are less than 11 defectives (>0). The risk of rejecting a batch that has a percentage of defectives equal to the inherent, unavoidable AQL level of 2% is 5%. Now if we use a sampling plan of 306 samples, and an acceptance value of 0 the following OC Curve is obtained.

Shewhart chart demonstrating the issues with spc theory

The consumer’s risk is now zero, nearly eliminating the risk of accepting defective product at the chosen LTPD, which from one perspective, meets the objective of using zero acceptance values.

However, the Producers risk is almost 100%. This means that virtually every batch with a level of defectives equal to the process level will be rejected. Business will need to stop. The sampling plan is therefore unreasonable considering the reality that most process do have some defectives.

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