Template:Bayesian test design

Bayesian Non-Parametric Test Design
The regular non-parametric analyses performed based on either the binomial or the chi-squared equation were performed with only the direct system test data. However, if prior information regarding system performance is available, it can be incorporated into a Bayesian non-parametric 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:

$$1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)$$

where $$Beta$$ is the incomplete beta function. If α 0 and β 0  are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate α 0 and β 0  depending on the type of prior information available.