In Part 1 we concluded that to have a reasonable chance at passing 3 consecutive lots, the process % defective must be much lower than the reliability used.

Can we boost the odds in our favor? One option is to modify the acceptance criterion per lot from a=0 to a<=1 (accept on at most 1 failure).

The corresponding probabilities using a<=1 (assuming the sample size and acceptance criterion are applied to each LOT), are shown below.

Using a<=1 results in a 58% increase in the sample size. However, this is most often a tradeoff we're willing to make because, for VERY RELIABLE processes (i.e. very low % defectives), the chance of passing is greatly enhanced.

A comparison of the probabilities for a=0 and a<=1 is shown in the figure below.

Experience tells us the benefits of using the a<=1 criterion is often greater than the raw statistics would reveal. Since reproducibility (variability due to different inspectors) is often a fairly large portion of measurement variation, and human beings are prone to error (due to fatigue, etc.), using a<=1 may mean the difference between passing the study or not. This is especially true for those processes whose inspection methods are manually very delicate, complex, or with higher variation.

We can do better. More in a future post...

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