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Improved Operational Testing and Evaluation and Methods of Combining Test Information for the Stryker Family of Vehicles and Related Army Systems Phase II Report (2004) / Chapter Skim
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Appendix B: Technical Details on Combining Information in Estimation: A Treatment of Separate Failure Modes
Pages 85-89

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From page 85...
... PRIOR INFORMATION Prior to the start of operational testing, we assume that previous engineerins, experience. analysis of developmental test data, and redesign ac__= -- -r -- -- -- -- , ~_~' tions support the assessment of an a priori prior probability density function (p.~.f.)
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From page 86...
... In addition, the same tests and judgments support the assignment of a priori probabilities for four possible scenarios: = probability Ino failure modes remainT = probability Tonly mode 1 remainsT · P2 = probability T only mo de 2 remains T · pa = 1 - To -P1-P2 = Probability Iboth mode 1 and mode 2 remainT i, For the purpose of this exposition, we assume that ~1 and ~2 are ndependent, and their priors can each be well represented by a Gamma p d f: fA1 (l )
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From page 87...
... ofthe sum of two gamma distributed random variables, a reasonable approximation can be obtained. In particular, if fx1 (x)
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From page 88...
... X, an estimate of the system's total failure rate, A, and its uncertainty (expressed by itS standard deviation, MA = N Var(A)
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From page 89...
... TECHNICAL DETAILS ON COMBINING INFORMATIONINESTIMATION 89 COMBINING PRIOR INFORMATION WITH DATA FROM OPERATIONAL TESTING . After t test miles in operational testing, if the data show n1 mode 1 failures and n2 mode 2 failures, then the performance measures can be calculated as above, but with the parameters "updated" so that ai and bi are replaced by a'i and <, respectively, where: a'=ai+f~i; ~=[i+t, i= 1,2 and the posterior probabilities for the failure mode scenarios are: Po =< P1 =< p, = P3 ='1 A(O, O)
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Key Terms

  • operational testing
  • prior information
  • exponentially distributed
  • developmental testing
  • technical details

  • random variables
  • judgments support
  • modes remain
  • previous engineerins
  • priori probabilities

  • information prior
  • failure rate
  • modes remaint
  • total failure
  • probability iboth

  • expected value
  • iboth mode
  • distributed random
  • priori prior
  • test data

  • probability tonly
  • tonly mode
  • prior probability
  • probability density
  • mean miles

  • tions support
  • modes remains
  • failure mode
  • density function
  • probability ino


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