Reliability: Modeling, Prediction, and Optimization

CHAPTER 5

Basic Statistical Methods for Data Analysis

5.1 INTRODUCTION

Chapter 2 dealt with applications of reliability and included many examples of data sets of various types that might be obtained in reliability studies. In Chapter 3, we looked more closely at the structure of these many types of data sets and discussed methods of description and summarization of data. Chapter 4 dealt with probability models for representing failure data as well as other types of data that may be relevant in reliability studies.

The topics covered in this chapter are all in the general category of statistical inference, which in a very real sense relates all of the concepts of the previous three chapters. In probability, we model uncertainty (randomness), for example, through the distribution function, and can use this model to make statements about the nature of the data that may result if the model is correct. The principal objective of statistical inference is to use data to make statements about the probability model, either in terms of the probability distribution itself or in terms of its parameters or some other characteristics. Thus probability and statistical inference may be thought of as inverses of one another:

Probability: Model → Data

Statistics: Data → Model

The statistical inference procedures we will look at here will be appropriate for part or item data, i.e., data at a single level. Multi-level data will be considered in later chapters. We will assume that the data have ...