Template:Bayesian test design: Difference between revisions
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== Bayesian Non-Parametric Test Design == | == Bayesian Non-Parametric Test Design == | ||
The regular | 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 === | === Assumption on System Reliability === | ||
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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: | 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: | ||
<center><math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math></center> | |||
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. | 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. | ||
Revision as of 23:47, 29 March 2012
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:
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.