Distribution Failure

Chapter 4

TIME TO FAILURE

DISTRIBUTIONS

4.1

Introduction

This chapter considers probability distributions which are most often used in

reliability as time to failure distributions. These distributions include the distributions which have well-known probability density functions for describing

time-to-failure (TTF) in many situations. The chapter also considers other

less used distributions of TTF, and presents characteristics and properties of

the distributions considered.

The probability distribution of TTF indicates beliefs about the likelihood

of failure times. These beliefs can be based on the frequency of data values

and have a frequency interpretation or they can be based on judgment and

have a frequency or a subjective interpretation. Basically, the probability distribution is a model for knowledge about the time to failure or the reliability

of a device.

In the first sections of this chapter, probability distributions of TTF are

considered from the point of view of their corresponding hazard functions.

These sections also subscribe to the relatively simple point of view that a

single hazard function is sufficient for describing the behavior of the TTF over

the entire range of the failure times. In the last section of this chapter, more

complex models are introduced where the use of several hazard functions or

several distributions is necessary to model the situation.

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4.2

CHAPTER 4. TIME TO FAILURE DISTRIBUTIONS

Monotone hazard functions

The hazard function of a distribution was defined earlier but it is important

to consider such functions here since they describe the relationship between

the instantaneous probability of failure and time. Sometimes there is physical or data information about the hazard function and not the probability

distribution itself and then the hazard is useful in determining the distribution of TTF. There may also be more general information about the hazard

function, such as the fact...