Chapter 7 - Statistical Inference of an Imperfect Repair Model with Uniform Distributed Repair Degrees

Abstract

The main purpose of this work is to introduce the inference of Weibull intensity parameters, which are used in the general repair model. This intensity is often used to describe failure models that analyze the reliability of different types of repairable systems. We consider an imperfect repair model as one that is not perfect (“as good as new”) as in renewal process and not minimal (“as bad as old”) as in a nonhomogeneous Poisson process but lies between these border cases. When a failure occurs, our repairable system will be restored with a uniform distributed degree of repair including as special cases minimal, perfect, and imperfect repair models. To determine the estimation of the model parameters, the maximum likelihood estimator is considered. For the scale and shape parameter estimators of the Weibull intensity, simultaneous confidence regions based on the likelihood ratio statistics are developed.