On a New Stochastic Usage Model (Non-Time-Homogeneous Poisson) for Testing a Multi-Stage System to Promote Reliability Growth

Abstract A new model for reliability growth for a multi-stage system is introduced; the system may be either hardware or software, or a combination thereof. The usage of each stage of the system during a mission is modeled as a non-time-homogenous Poisson process (NHPP). During system design, manufacture, installation, usage and development, failure-causing design defects (DDs) may inadvertently be introduced into each stage of the system. The system undergoes a sequence of test missions before it is fielded. During each test mission DDs may, with probability less than one, cause failure and thus reveal themselves. These DDs are then identified and removed (by redesign or re-programming) at the end of the test mission, but with probability less than one. Expressions and an approximation are given for the probability no DDs are activated during a field mission after a specified number of test-fix-test missions.

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