# CHAPTER 8

# Advanced Statistical Methods for Data Analysis

## 8.1 INTRODUCTION

Chapter 3 introduced the notion of statistical data, discussed various data sources and data structures of importance in reliability applications, and provided some statistical tools for preliminary analysis and description of data. In Chapter 5, basic statistical methods for data analysis were discussed. These included estimation of parameters of the probability functions given in Chapter 4, confidence intervals and tests of hypotheses about these parameters, estimation and tests for functions of parameters, and tolerance intervals.

In this chapter, we extend these results in a number of ways, and show how statistical methods may be applied to provide data-based information concerning the models discussed in Chapters 6 and 7. Included in the discussion are methods for analysis of censored data (see Chapter 3), use of various types of information in statistical analysis, including judgmental or subjective information, and estimation of system reliability using various models, data sources, and methods.

In Section 8.2, we look at analysis of grouped data, that is, data for which we know only frequencies in specified intervals, rather than the individual *X* values. As discussed in Chapter 3, there are a number of situations in which this occurs, and the calculations must be modified to take the grouping into account. We look at estimation of the mean and variance, and comment on MLE procedures.

Censored data ...