7.1 Introduction

To predict various reliability and Six Sigma measures of a product, it is essential that we have sufficient information on the time to failure characteristics of that item. In most cases these characteristics are expressed using theoretical probability distributions. The selection of the appropriate probability distribution function to describe the empirical data plays a critical role in reliability analysis. Once the distribution is identified, then one can extract information about other reliability characteristics such as mean time between failures, hazard function and failure rate etc.

To begin with we look at ways of fitting probability distributions to in-service data, that is, the data relating to the age of the components at the time they failed while they were in operation. In the literature there are three popular tools available to find the best distribution that describes the in-service data: 1. Probability papers, 2. linear regression, and 3. Maximum likelihood estimator. In this book, we discuss linear regression and maximum likelihood estimator techniques. Very often we do not have a complete set of failure data; a section on censored data describes how such data can be used to predict reliability characteristics.

Components may fail due to a number of failure modes. Each of these modes may be more or less related to the age. One would not expect corrosion to be the cause of failure during the early stages of the component's life, unless it was subjected to...