Template:Bayesian test design

Bayeisan Nonparameteric Test Design
The regular nonparametric analysis performed based on either the Binomial or the Chi-Square 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 reliablity follows a Beta distribuiton, the values of system reliability R, confidence level CL, number of units tested n, and number of failures r are related by the 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 $$\alpha_{0}$$ and $$\beta\,\!_{0}$$ are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate $$\alpha\,\!_{0}$$ and $$\beta\,\!_{0}$$ depending on the type of prior information available.