Adaptive testing policy for multi-state systems with application to the degrading final elements in safety-instrumented systems

The performance of many engineering systems in their lifetimes can be modeled as multiple states to facilitate operational decision-making. Based on the information that the system is at a certain state, maintenance is conducted to keep the system performing satisfactorily and prevent failures. Periodical tests are mainly used for the systems whose conditions cannot be automatically detected by condition monitoring, but the timing and necessity of such tests that are based on earlier standards and procedures may not be optimal. This paper thus presents an adaptive testing policy for multi-state systems by scheduling the upcoming tests based on the observed state in the current test. Analytical formulas based on the multi-phase Markov process are developed to evaluate the health of the time-dependent system. Algorithms are derived for estimating the average system performance and the expected number of tests in a certain service period. Then, the policy is implemented on the degrading final elements in safety-instrumented systems where structural redundancies are used. Case studies with verification by Monte Carlo simulation illustrate the benefits of the proposed testing policy in reducing the number of tests without sacrificing system performance.