Optimal test termination time in reliability growth management for systems with multiple failure modes

Reliability growth management is the positive improvement in a reliability metric due to implementation of corrective actions upon system design, operation or maintenance process through a dedicated test-analyze-and-fix (TAAF) procedure. Taking the reliability of a complex system is in fact a multidimensional outcome which is a function of various failure modes into account, the mixed-AMSAA model is constructed in this current research based on the mixed Weibull distribution. The parameters in the mixed-AMSAA model are estimated based on the Weibull probability plot (WPP) in the presence of limited failure data and the goodness-of-fit is tested with the Kolmogorov–Smirnov (K-S) statistic. To determine the optimal termination time of the reliability growth test plan for systems with multiple failure modes, a joint optimization framework under the planing objective of minimizing the total cost by considering the release time in terminating the reliability growth test and the quantity of spare parts inventory for corrective actions is proposed. Numerical solutions to the joint optimization model are theoretically analyzed and two cases from real engineering systems are validated to verify the proposed model. Illustrative results show that the mixed-AMSAA model is capable to capture the growth characteristic of systems with multiple failure modes and is effective in determining the optimal termination time of a reliability growth test program.