ABSTRACT
This chapter presents a range of techniques for dealing with data involving covariates. In view of the widespread use of the Weibull distribution is reliability and survival data analysis, there is particular interest in models based on this distribution. In many applications of reliability, however, our real interest is in determining the way in which strength or lifetime depends on other variables, some of which may be under the operator's control. One example of this is the way in which failure time depends on the load applied to a component. It is almost always the case that increasing the load reduces the time to failure, but it is of interest to have a specific model for this. In this context, load is a covariate or explanatory variable. Other examples of possible covariates include temperature and the size of the specimens under study. The examples illustrate the wide range of models that can be fitted by numerical maximum likelihood techniques.
