# 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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