Practical Applications of Bayesian Reliability

6Capability and Design for Reliability

This chapter introduces Bayesian methods for design capability analysis and design for reliability analysis. Design capability analysis and design for reliability analysis have been widely practiced in industry, using methods including Monte Carlo simulations. Typically, traditional methods using Monte Carlo simulations provide a point estimate of reliability. However, these methods can be extended to incorporate the uncertainty associated with the parameter point estimates and to obtain approximate distribution of reliability. In this approach, often we have to rely on the large sample approximations of the distributions of the parameter estimates. In a Bayesian framework, uncertainty of the parameters can also be taken into account and be propagated to the final outcome of reliability estimation. With Bayesian analysis, posterior distributions of the parameter estimates can be easily used to obtain the distribution of any quantity of interest that depends on the parameters. The method we use for estimating the distribution of reliability is called two‐level nested Monte Carlo simulations.

6.1 Introduction

Predictive methods are often used to ensure that products meet design requirements during the development phase to avoid or minimize late findings and “firefighting.” Design capability analysis and design for reliability analysis are common predictive methods to ensure first‐pass success during design verification tests. These methods ...