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Nonparametric predictive inference for system reliability with redundancy allocation

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  • P Coolen-Schrijner
  • F P A Coolen
  • I M MacPhee

Abstract

This paper presents lower and upper probabilities for the reliability of k -out-of- m systems, which include series and parallel systems, and of series systems with independent k i -out-of- m i subsystems, for which optimal redundancy allocation is also presented in case of zero-failure testing. First, attention is restricted to k -out-of- m systems with exchangeable components. The lower and upper probabilities for successful functioning of the system are based on the nonparametric predictive inferential (NPI) approach for Bernoulli data. In this approach, it is assumed that test data are available on the components, and that the future components to be used in the system are exchangeable with these. Thereafter, systems are considered that consist of a series of independent subsystems, with subsystem i a k i -out-of- m i system consisting of exchangeable components. For such systems, an algorithm for optimal redundancy allocation after zero-failure testing is presented. A particularly attractive feature of NPI in reliability, with lower and upper probabilities, is that data containing zero failures can be dealt with in an attractive manner.

Suggested Citation

  • P Coolen-Schrijner & F P A Coolen & I M MacPhee, 2008. "Nonparametric predictive inference for system reliability with redundancy allocation," Journal of Risk and Reliability, , vol. 222(4), pages 463-476, December.
    • Handle: RePEc:sae:risrel:v:222:y:2008:i:4:p:463-476
    DOI: 10.1243/1748006XJRR179
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    References listed on IDEAS

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    1. J. F. Lawless & Marc Fredette, 2005. "Frequentist prediction intervals and predictive distributions," Biometrika, Biometrika Trust, vol. 92(3), pages 529-542, September.
    2. P Coolen-Schrijner & F P A Coolen, 2004. "Adaptive age replacement strategies based on nonparametric predictive inference," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1281-1297, December.
    3. Coolen, F. P. A., 1998. "Low structure imprecise predictive inference for Bayes' problem," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 349-357, January.
    4. P Coolen-Schrijner & F P A Coolen & S C Shaw, 2006. "Nonparametric adaptive opportunity-based age replacement strategies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 63-81, January.
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    1. Aboalkhair, Ahmad M. & Coolen, Frank P.A. & MacPhee, Iain M., 2014. "Nonparametric predictive inference for reliability of a k-out-of-m:G system with multiple component types," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 298-304.

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