A classical and Bayesian estimation of a -components load-sharing parallel system

Singh, Bhupal; Sharma, K.K.; Kumar, Anuj

doi:10.1016/j.csda.2008.05.026

Cited by 38 publications

(34 citation statements)

References 17 publications

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“…Now, on using Equations (11) and (12) in Equation (10), we have Equation (13) can be solved forp by using some suitable iterative procedure and finally on substitutingp in Equations (11) and (12), we getθ andˆ = (λ 1 ,λ 2 , . .…”

Section: Mles and Confidence Intervalsmentioning

confidence: 99%

Inferential statistics on the dynamic system model with time-dependent failure-rate

Singh

Rathi

Kumar

2013

Journal of Statistical Computation and Simulation

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Section: Mles and Confidence Intervalsmentioning

confidence: 99%

Inferential statistics on the dynamic system model with time-dependent failure-rate

Singh

Rathi

Kumar

2013

Journal of Statistical Computation and Simulation

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“…This is an interesting fi nding since many critical systems, in reality are likely to be in this category. Thus, it is worth the future research by analyzing the reliability estimation of other complex systems such as those with load-sharing dependent redundancy [4,15] and weighted voting systems [5] as well as other distributions including Weibull, gamma and logistics [10].…”

Section: Failure-censored Analysismentioning

confidence: 99%

“…Singh et al [15] recently obtained the maximum likelihood and Bayes estimates of the parameters of a k-component, load-sharing parallel system, where components follow exponential distribution. Scheuer (1988) obtained the reliability of m-out-of-n systems under the assumption that failure of a component changes the failure rates of the surviving components.…”

Section: Introductionmentioning

confidence: 99%

“…There are numerous studies on the estimation of reliability functions for one-unit component system [1,2] or for systems that are connected in series [11,17] and parallel [11,4,15]. The uniformly minimum variance unbiased estimate (UMVUE) of reliability of an item with exponential failure density function has been studied by several authors.…”

Section: Introductionmentioning

confidence: 99%

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

Pham

2010

Int J Syst Assur Eng Manag

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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. Keywords k-out-of-n system . Exponential distribution . Reliability estimation . Minimum variance unbiased . UMVUE . Maximum likelihood estimate Notation R(t): component reliability f(t): component failure probability density function R s (t): reliability of k-out-of-n system f s (t): system failure time density function R s (t): MLE of R s (t) R s (t): 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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“…For other load-sharing rules, the reader is referred to Durham et al (1997), who considered equal load-sharing, tapered loadsharing, local load-sharing, nearest-neighbor load-sharing, and a hybrid load-sharing rule. Other early works on loadsharing systems are referenced by Daniels (1945), Coleman (1957aColeman ( , 1957b, Birnbaum and Saunders (1958), Rosen (1964), Harlow andPhoenix (1978, 1982), Phoenix (1978), and Phoenix and Tierney (1983), while more recent results are considered by Lee et al (1995), Harlow (1997), Wang et al (1998), Durham and Lynch (2000), Wang et al (2000), Kim and Kvam (2004), Kvam and Peña (2005), Yang and Younis (2005), and Singh et al (2008).…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for the reliability of load-sharing systems

Park

2010

IIE Transactions

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Consider a multi-component system connected in parallel. In this system, as components fail one by one, the total load or traffic applied to the system is redistributed among the remaining surviving components, which is commonly referred to as load-sharing. This develops parameter estimation methods for these type of systems. A closed-form Maximum Likelihood Estimator (MLE) and Best Unbiased Estimator (BUE) are provided under a general load-sharing rule when the underlying lifetime distribution of the components in the system is exponential. As an extension, it is assumed that the underlying lifetime distribution of the components is Weibull and it is shown that, after the shape parameter is estimated by solving the one-dimensional log-likelihood estimating equation, the closed-form MLE and conditional BUE of the rate parameter are easily obtained. The asymptotic distribution of the proposed MLE is also provided. Illustrative examples and Monte Carlo simulation results are also presented and these substantiate the proposed methods.

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A classical and Bayesian estimation of a -components load-sharing parallel system

Cited by 38 publications

References 17 publications

Inferential statistics on the dynamic system model with time-dependent failure-rate

Inferential statistics on the dynamic system model with time-dependent failure-rate

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

Parameter estimation for the reliability of load-sharing systems

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