Regularization techniques for recurrent failure prediction under Kijima models

Abstract

The problem of recurrent failure prediction arises in forecasting warranty repairs/cost, maintenance optimization and evaluation of repair quality. The most comprehensive prediction model is the g-renewal process proposed by Kijima [1], which allows for modelling of both perfect and imperfect repairs through the use of the so-called restoration factor. Krivtsov and Yevkin [2] showed that statistical estimation of the g-renewal process parameters is an ill-posed inverse problem (the solution is not unique and/or is sensitive to statistical errors). They proposed a regularization approach specifically suited to the g-renewal process: separating the estimation of the underlying life distribution parameters from the restoration factor in two consecutive steps. Using numerical studies, they showed that the estimation/prediction accuracy of the proposed method was considerably higher than that of the existing methods. This paper elaborates on more advanced regularization techniques, which allow to even further increase the estimation/prediction accuracy in the framework of both Least Squares and Maximum Likelihood estimation. Proposed regularization becomes especially useful for limited sample sizes. The accuracy and efficiency of the proposed approach is validated through extensive numerical studies under various underlying lifetime distributions including Weibull, Gaussian and log-normal.