Template:Bayesian test design: Difference between revisions

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== Bayesian Non-Parameteric Test Design ==
#REDIRECT [[Reliability 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>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 <span class="texhtml" sab="459">α<sub sab="460">0</sub></span> and <span class="texhtml" sab="461">β<sub sab="462">0</sub></span> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <span class="texhtml" sab="463">α<sub sab="464">0</sub></span> and <span class="texhtml" sab="465">β<sub sab="466">0</sub></span> depending on the type of prior information available.
 
{{btd w info on reliability}}
 
{{btd w info from subsystem tests}}

Latest revision as of 08:04, 29 June 2012

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