Field data analyses with additional after-warranty failure data

This paper proposes methods of estimating the lifetime distribution for situations where additional field data can be gathered after the warranty expires in a parametric time to failure distribution. For satisfactory inference about parameters involved, it is desirable to incorporate these after-warranty data in the analysis. It is assumed that after-warranty data are reported with probability p1(<1), while within-warranty data are reported with probability 1. Methods of obtaining maximum likelihood estimators are outlined, their asymptotic properties are studied, and specific formulas for Weibull distribution are obtained. An estimation procedure using the expectation and maximization algorithm is also proposed when the reporting probability is unknown. Simulation studies are performed to investigate the properties of the estimates.