ABSTRACT
This chapter discusses the alternative approach of deriving the joint likelihoods for Type I data and for Type II censored data as functions of the parameters in the survival model. It aims to estimate these parameters by maximising the likelihoods and focuses on the exponential and Weibull survival models. The chapter discusses the form of the likelihood function for modelled lifetimes with survival function S and probability density function f under forms of censorship and truncation. Certainly in engineering applications, the exponential model is of prime importance, being one of the most widely applied models to continuous lifetimes. It also has the added utility: the likelihood is easily maximised. The chapter estimates reliabilities at specific times under the exponential model, and also under a gamma mixture distribution which has a decreasing hazard appropriate for the burn in time of the equipment.
