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On the estimation of reliability of k-out-of-n systems

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Abstract

This paper presents a uniformly minimum variance unbiased estimator and the maximum likelihood estimates of reliability of k-out-of-n systems which are composed of n independent and identically distributed components with exponential lifetimes. The system is operational if and only if at least k of out the n components are operational. The reliability estimation results for the failure of uncensored cases (where there are m units put on test which is terminated when all the units have failed) and censored cases (when test termination is done upon the failure of r pre-assigned units) will be discussed. An application to illustrate the reliability estimation prediction for the power usages of computer system with quad-core, 8 GB of Ram, and a GeForce 9800GX-2 graphics card to perform various complex applications is discussed.

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Abbreviations

R(t):

component reliability

f(t):

component failure probability density function

Rs(t):

reliability of k-out-of-n system

fs(t):

system failure time density function

\( \hat R_s \left( t \right) \) :

MLE of R s(t)

\( \tilde R_s \left( t \right) \) :

UMVUE of R s(t)

i.i.d.:

independent and identically distributed

∧:

implies a maximum likelihood estimate (MLE)

∼:

implies a uniformly minimum variance unbiased estimate (UMVUE)

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers University, Rutgers, USA

    Hoang Pham

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  1. Hoang Pham
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Correspondence to Hoang Pham.

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Pham, H. On the estimation of reliability of k-out-of-n systems. Int J Syst Assur Eng Manag 1, 32–35 (2010). https://doi.org/10.1007/s13198-010-0010-0

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