Imperfect Inspection Policy for Systems with Multiple Correlated Degradation Processes

This paper develops an imperfect inspection policy for systems subject to multiple correlated degradation processes. The degradation processes are characterized by a multivariate Wiener process, and the dependency among the processes is described by a covariance matrix. A failure occurs when any of the degradation level exceeds a specific threshold. As degradation-based failures are usually dormant, inspection is required to detect the failures and prevent potential losses. The inspection is imperfect, in such a way that a failure may not be discovered at an inspection. Optimal inspection interval is obtained by minimizing the long run cost rate. In addition, the properties of the optimal inspection interval are studied and the upper and lower bounds of the optimum value are achieved. An example of fatigue crack development is used to illustrate and evaluate the inspection policy. The results imply that inspection accuracy contributes significantly to reducing the operating cost and more efforts should be made to improve the inspection quality.