# Chapter 10Elements 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, R, and JMP for censored and uncensored 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 uncensored 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 uncensored data.

## 10.1 The Reliability Function

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

It follows from equation 10.1.1 ...

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