Statistics for Maintenance Modelling: Regression Modelling

# Introduction¤

In earlier sessions we have been concerned with modelling the time to failure, with no other variables involved. However, it is often the case that the lifetime depends on other variables, some of which it may be possible to control. One example of this is the way failure time is dependent on the load applied to the component - it is likely that increasing the load will cause the component to fail sooner. In statistics, the terminology used for this situation is as follows:

the failure time is a dependent variable, and the load is the independent variable, or covariate.

## Regression Models for Modelling a Dependent Variable

Throughout statistics the use of regression models provide a powerful tool for modelling a dependent variable as a function of one or more independent variables or covariates. From the simplest regression model, the normal linear regression model, to the more complex generalised linear models and non-linear models, regression is an invaluable methodology for any researcher. For an introduction to regression and the basic principles there are many good books, for example see Neter et. al. (1996).

In this session we present the regression models used in reliability and maintenance modelling, namely 'accelerated life models', 'the proportional hazards model' and 'the Weibull model'. It is worth remembering that we are just introducing the theories and concepts behind these models here. Computer software packages such as Minitab, Stata and SPSS can be used to fit these models. You need to understand the background of each model, as introduced here, in order to help with correct implementation.