From runs to patterns

Abstract

Previous work related to runs is extended to include various patterns. The familiar CSCF, CSTF and TSCSTFCF procedures for reliability demonstration tests are generalized for patterns. The waiting time distributions and the value of the expected number of required tests are presented. Like for runs, some auxiliary functions are defined, a set of equations is set up and a numerical solution is presented. In some cases, closed-form expressions are provided. The analysis is generalized for the case of testing a number of units in parallel. Following the case of runs, a constrained optimization procedure is shown for evaluating the optimal values of the parameters involved within the procedure. It is observed that in some cases it is preferable to deal with patterns instead of runs. In addition, the following problem is solved: given ‘i’ successes within ‘n’ tests, what is the probability of not having a certain number of k_cs consecutive successes within a given pattern.

Keywords:

• Patterns
• Startup demonstration tests
• Acceptance testing
• Expected number of tests
• Probability of acceptance