Estimation of the lifetime distribution of mechatronic systems in the presence of a covariate: A comparison among parametric, semiparametric and nonparametric models

• We estimate the lifetime distribution in the presence of a covariate.
• Three types of regression models are considered and compared.
• A new nonparametric estimator based on our particular data structure is introduced.
• We propose a goodness of fit measure and show a new model selection procedure.
• A case study with real data and Monte Carlo simulations are performed.

In practice manufacturers may have lots of failure data of similar products using the same technology basis under different operating conditions. Thus, one can try to derive predictions for the distribution of the lifetime of newly developed components or new application environments through the existing data using regression models based on covariates.Three categories of such regression models are considered: a parametric, a semiparametric and a nonparametric approach. First, we assume that the lifetime is Weibull distributed, where its parameters are modelled as linear functions of the covariate. Second, the Cox proportional hazards model, well-known in Survival Analysis, is applied. Finally, a kernel estimator is used to interpolate between empirical distribution functions. In particular the last case is new in the context of reliability analysis.We propose a goodness of fit measure (GoF), which can be applied to all three types of regression models. Using this GoF measure we discuss a new model selection procedure.To illustrate this method of reliability prediction, the three classes of regression models are applied to real test data of motor experiments. Further the performance of the approaches is investigated by Monte Carlo simulations.