A Bounded Intensity Process for the Reliability of Repairable Equipment

In the failure pattern of repairable equipment subjected to reliability deterioration with operating time, the repeated application of the repair actions sometimes produces a finite bound for the increasing failure intensity. In this paper, a non-homogeneous Poisson process for which the failure intensity is an increasing bounded function is proposed. The characteristics of the proposed model and the physical meaning of its parameters are discussed. It is shown that the proposed model evolves initially as the power law process with shape parameter equal to 2, and then converges asymptotically to the homogeneous Poisson process, the latter being a limiting form of the proposed bounded intensity model. Maximum likelihood estimates and approximate confidence intervals for the model parameters are given as well as a testing procedure for a time trend. Percentile points of the test statistic are computed by simulation for failure truncated samples, and the power of the proposed testing procedure is evaluated and compared to that of two commonly used tests. Finally, numerical examples are given to illustrate the proposed model and related inference and testing procedures.