A new NHPP model for modeling failure process with S-shaped mean cumulative function

Abstract

The mean cumulative function (MCF) characterizes the failure behavior of a repairable system. Typical model for modeling failure process is the power-law model. It is only applicable for the situations where the empirical MCF is concave or convex. In practical applications, the empirical MCF can be S-shaped. The intensity function associated with an S-shaped MCF is unimodal. The unimodal failure intensity results from interaction between aging and maintenance improvement. In the literature, few models are available for representing the failure process with unimodal failure intensity. In this paper, we present such a model. The model has three parameters and its expression is relatively simple. A regression method is developed to help determine whether the model is appropriate for modeling a given set of data and obtain the initial estimates of the model parameters. The maximum likelihood method is used to obtain the final parameter estimates. Two real-world examples are included to illustrate the appropriateness and usefulness of the proposed model and the parameter estimation method.