Reliability analysis of repairable systems with recurrent misuse-induced failures and normal-operation failures

Highlights: • Recurrent misuse-induced failures and normal-operation failures are studied. • A novel stochastic model is proposed based on a NHPP and a trend-renewal process. • Bayesian parameter estimation and hypothesis testing are developed for the model. • A simulation study and a real case are used to demonstrated the proposed method. Failure of a repairable system may be attributed to operators' misuse or system deterioration. The misuse may further deteriorate the system under normal operating conditions. Motivated by a real-world data set that records the recurrence times of misuse-induced failures and the normal-operation failures, this study proposes a stochastic process model for recurrence data analysis, where one type of failures is affected by the other. A non-homogeneous Poisson process and a trend-renewal process are separately used as the baseline event process models for the misuse-induced failures and the normal-operation failures, respectively. These two models are then combined by treating the event count of misuse-induced failures as covariate of the event process of normal-operation failures. A Bayesian framework is developed for parameter estimation and dependence tests of the two failure modes. A simulation study and the recurrence data from a manufacturing system are used to demonstrate the proposed method.