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 images be its probability density function (p.d.f.), where images. Then, we define the reliability function at time t as

It follows from equation 10.1.1 ...

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