The planning of environmental or reliability testing becomes a question of sample size at some point. It’s probably the most common question I hear as a reliability engineer: How many samples do we need?

Also, when evaluating supplier-run test results, we need to understand the implications of the results, again based on the number of samples in the test. If the supplier runs 22 samples without failure over a test that replicates the shipping set of stresses, then we need a way to interpret those results.

We often use success testing (no expected or actual failures during the testing) to minimize the number of samples required for a test and still show some level of confidence for a specified reliability level. The basis for success testing is the binomial distribution. The result of the applied stress results in the product either working or not. Binary results.

Recently I received a request to explain where the success-testing sample size formula comes from, or it’s derivation. First here’s the formula:

Where, C is confidence and R is the lower limit of the reliability.

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