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| ==Bayeisan Nonparameteric Test Design==
| | #REDIRECT [[Reliability Test Design]] |
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| 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.
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| ===Assumption on System Reliability===
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| 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.
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| ::<math>1-CL=\text{Beta}\left(R,\alpha,\beta\right)=\text{Beta}\left(R,n-r+\alpha_{0},r+\beta_{0}\right)</math>
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| where Beta is the incomplete Beta function. If <math>\alpha_{0}</math> and <math>\beta\,\!_{0}</math> are known, then any quantity of interest can be calculated using the remaining three. The next two examples demonstrate how to calculate <math>\alpha\,\!_{0}</math> and <math>\beta\,\!_{0}</math> depending on the type of prior information available.
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| {{btd w info on reliability}}
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| {{btd w info from subsystem tests}}
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