Template:Bayesian test design

Bayesian Non-Parameteric Test Design

The regular nonparametric analysis performed based on either the binomial or the chi-squared equation was performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian nonparametric analysis. This subsection will demonstrate how to incorporate prior information about system reliability and also how to incorporate prior information from subsystem tests into system test design.

Assumption on System Reliability

If we assume the system reliability follows a Beta distribution, the values of system reliability, R, confidence level, CL, number of units tested, n, and number of failures, r, are related by the following equation:

[math]\displaystyle{ 1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right) }[/math]

where Beta is the incomplete Beta function. If α₀ and β₀ are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate α₀ and β₀ depending on the type of prior information available.