Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 10

Elements of Reliability Theory

The focus of this chapter is a discussion of the basic concepts of reliability theory. The topics covered are:

• The reliability function and the hazard rate function
• Derivation of an appropriate form for the life distribution using the hazard rate function
• Estimation and testing of hypothesis for parameters of different life distributions
• Probability plots and plots of the life distribution function and hazard rate function using MINITAB, EXCEL, and JMP for censored and non-censored 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 non-censored 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 non-censored data.

10.1 The Reliability Function

Let T represent the random variable equal to the time to failure of an item and let f(t) be its probability density function, where T ≥ 0. Then we define the reliability function R(t) at time t as

It follows from (10.1.1) that and R(0) = R(∞) = 0. Note that the reliability function R(t) is a non-increasing ...