A Study on Estimation of Lifetime Distribution with Covariates Under Misspecification for Baseline Distribution

In these days, the online monitoring information which includes usage history, system conditions, and environmental conditions is reported. On statistical modeling, these variables from the online monitoring are primary candidates for covariates which affect the failure mechanism. There is some literature on modeling by the cumulative exposure model for a products lifetime distribution with covariate effects. Some existing literatures require an already known parametric baseline distribution of the cumulative exposure. However such knowledge may be difficult to acquire in advance in some cases. When an incorrect baseline distribution is assumed, it is called misspecification. A previous study proposed the strategy which use a likelihood function under a log-normal distribution to estimate parameters which represent covariate effects when the truly underlying baseline distribution is either a Weibull distribution or a log-normal distribution. In this time, this paper widens the range of application of the strategy using the likelihood function under a log-normal distribution to estimate parameters of covariate effects. On that account, the simulation study and the discussion for the bias of estimation are shown under a normal condition.