Reliability modeling and evaluation for degradation data with heterogeneous initiation time

Abstract

In engineering practice, some products start deteriorating only after a period of usage. Moreover, the degradation-free periods of different products show a phenomenon of clustering, that is, there are several heterogeneous subpopulations. Both the degradation-free period and its subpopulation label are often unobservable, which poses great challenges to the reliability modeling and evaluation. In this paper, a randomly delayed degradation model considering the heterogeneous initiation time is developed, where the mixture lognormal distribution and the Wiener process are integrated to characterize the overall degradation process. The model parameters are estimated by the stochastic expectation maximization algorithm which also produces the estimator of the degradation-free period for each product simultaneously. In addition, inferences on the choice of parameters’ initial values, interval estimation, determination of the number of subpopulations and classification of products are also presented. Finally, simulation studies are carried out to validate the proposed formulas and methods, and a practical example is provided for illustration.