The Use of Regression Techniques for Matching Reliability Models to the Real World

Abstract

Similar models are often used in various disciplines. For example, models for time to an event or for times between successive events are needed in biometry and sociology applications, as well as in reliability. The specific circumstances of a particular discipline may suggest a particular family of distribution functions, e.g., the Weibull distribution, when modeling time to an event. Alternatively, a specific point process, e.g. the power law process (a nonhomogeneous Poisson process of specific functional form, see Ascher and Feingold (1984)) may be appropriate in a particular reliability application dealing with times between successive failures of a repairable system. In a biometry application, in which times between successive nonfatal illnesses of a patient are studied, another point process might be suggested. In practice, however, instead of considering that models are suggested by circumstances, there is far too much reliance on a priori specification of models. For example, in hardware reliability applications it is usually assumed that the exponential distribution is the appropriate model to use, regardless of the application. If this model is generalized at all, the “generalization” usually is restricted to using a Weibull distribution. In fact, one or the other of these distributions is usually invoked even when no distribution whatsoever is the appropriate model! That is, when dealing with a repairable system—and most systems are designed to be repaired rather than replaced after failure—the correct model is a sequence of distribution functions, i.e., a point process. Distribution functions and point processes are not equivalent models, even in the most special cases. A homogeneous Poisson process (HPP) can be defined as a nonterminating sequence of independent and identically exponentially distributed times between events. Ascher and Feingold (1979, 1984) show that there are important distinctions between the exponential distribution and HPP models.