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Date Submitted: 01/18/2013 04:09 AM
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...