10

Elements of Reliability Theory

The focus of this chapter is a discussion of the basic concepts of reliability theory.

# Topics Covered:

- Reliability and hazard rate functions
- Derivation of an appropriate form for the life distribution using the hazard rate function
- Estimation and testing of hypotheses for parameters of different life distributions
- Probability plots and plots of the life distribution and hazard rate functions using MINITAB, EXCEL, and JMP for censored and noncensored data

# Learning Outcomes:

After studying this chapter, the reader will be able to

- Determine the reliability and hazard rate functions for different life probability models.
- Fit different models such as exponential, normal, lognormal, and Weibull to a censored or noncensored data set.
- Determine estimates of parameters of different life probability models.
- Perform testing of hypotheses concerning various parameters of life probability models.
- Use various statistical packages to construct survival plots using censored and noncensored data.

# 10.1 The Reliability Function

Let T represent the random variable which is the time to failure of an item and let f(t) be its probability density function, where . Then we define the reliability function R(t) at time t as

It follows from (10.1.1) that ...