Practical Applications of Bayesian Reliability

4Reliability Distributions (Bayesian Perspective)

This chapter introduces common discrete and continuous probability distributions used in reliability applications from a Bayesian perspective. Examples and R codes are provided to show the estimation of posterior distributions of the parameters of these distributions.

4.1 Introduction

There are two major types of data: attribute data and variable data. Attribute data, or categorical data, are qualitative data (e.g. color, pass/fail, yes/no, etc.). Variable data are quantitative data (e.g. dimension, force, weight, etc.). Attribute data can be converted to count (or discrete) data for analysis, for example the number of units in a sample of 50 passing a certain quality requirement. Compared to discrete data, continuous data usually contain more information and should be a preferred choice during data collection and analysis if possible.

Pass/fail data is one type of commonly used attribute data, especially in acceptance testing or assurance testing, such as design verification testing and qualification testing. In these tests, reliability is defined as the percentage of products conforming to the requirement of interest. Results are recorded as either pass or fail. A predetermined quantity of products (e.g. 22, 59, or 299 parts), based on a desired level of confidence and reliability, is tested against a requirement to ensure that all are conforming so that the desired level of confidence and reliability can be achieved. A binomial ...