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Nonparametric bayes estimation of the reliability function of a coherent system

AKM Fazlur Rahman, Edsel A. Pena
2021 Journal of Statistical Research  
The resulting estimator of the system life distribution, which is a function of the nonparametric Bayes estimators of the components lifetime distributions, is compared in terms of bias and variance with  ...  A coherent system is composed of components, which could be modules or sub-systems, that interact with each other according to some structure function.  ...  Polpo and Pereira (2009) considered Bayesian estimation of reliability in parallel systems and Polpo et al. (2013) considered Bayesian estimation of reliabilities in a class of coherent systems.  ... 
doi:10.47302/jsr.2020540206 fatcat:ypm7xpgn3ngvtohj6njd2orday

Bayesian Estimation of Component Reliability in Coherent Systems

Agatha S. Rodrigues, Felipe Bhering, Carlos A. De B. Pereira, Adriano Polpo
2018 IEEE Access  
The first step in statistical reliability studies of coherent systems is the estimation of the reliability of each system component.  ...  For the cases of parallel and series systems the literature is abundant. It seems that the present paper is the first that presents the general case of component inferences in coherent systems.  ...  for a class of coherent system.  ... 
doi:10.1109/access.2018.2821102 fatcat:cne3ybxobjckveoxbhjdqkrpza

Page 2385 of Mathematical Reviews Vol. , Issue 84f [page]

1984 Mathematical Reviews  
Author’s summary: “Given a coherent reliability system, let Z be the age of the machine at breakdown, / the set of parts dead by time Z.  ...  An asymptotic representation of the reliability function of an arbitrary coherent system is given assuming that the element failure rates are low.  ... 

Page 7182 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
Jewell, Bayesian exten- sions to a basic model of software reliability (pp. 394-404); W. S. Jewell, Bayesian estimation of undetected errors (pp. 405-425); W. S.  ...  Singpurwalla, Estimation of the failure rate—non-Bayesian, nonparametric methods (pp. 184-199); T. Mazzuchi and N. D.  ... 

Page 3568 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
951:62140 observation and the system equations, are shown to hold for a larger class of distributions.  ...  In this paper earlier work on the hazard rate ordering is reviewed, and new results related to coherent systems are derived.  ... 

Page 3694 of Mathematical Reviews Vol. 58, Issue 5 [page]

1979 Mathematical Reviews  
Mastran, David V.; Singpurwalla, Nozer D. 58 #24813 A Bayesian estimation of the reliability of coherent structures.  ...  On the calculation of the reliability of branching structures. (Russian) Methods of operations research and of reliability theory in systems analysis (Russian), pp. 3-8. Akad. Nauk. Ukrain. SSR Inst.  ... 

Overview of the 37th MaxEnt

Teresa Dias, Marcio Diniz, Carlos Pereira, Adriano Polpo
2018 Entropy  
The 37th edition of MaxEnt was held in Brazil, hosting several distinguished researchers and students.  ...  The event held a celebration to Julio Stern's 60th anniversary and awarded two prizes to young researchers.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e20090694 pmid:33265783 fatcat:4s53iiock5ht3i2qpm4tb47eka

Reliability Estimation in Coherent Systems [article]

Agatha Rodrigues and Carlos Alberto Pereira and Adriano Polpo
2018 arXiv   pre-print
We will treat the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series.  ...  Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is presented.  ...  Considering this celebrated property, Polpo et al. (2013) introduced Bayesian nonparametric statistics for a class of coherent system in order to estimate components reliabilities.  ... 
arXiv:1805.10540v1 fatcat:omhjlbkhf5gexbbaixdmj2ejze

Page 3212 of Mathematical Reviews Vol. , Issue 87f [page]

1987 Mathematical Reviews  
Rennie, Confidence bounds for reliability of coherent systems based on binomially distributed component data (pp. 265-280); P. K. Sen [Pranab Kumar Sen] and M. C.  ...  Bhattacharjee, Nonparametric estimators of availability un- der provisions of spare and repair.  ... 

Page 8025 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
The use- fulness of this property of coherent systems in obtaining sharper upper bounds on the reliability of the concerned system has been illustrated below for a bridge structure with components having  ...  We also study some preservation properties for certain nonparametric classes of life distributions and the monotonic- ity properties for several parameters.  ... 

Page 4634 of Mathematical Reviews Vol. , Issue 85j [page]

1985 Mathematical Reviews  
The au- thors |“Estimation of the failure rate—a survey of nonparametric methods. I. Non-Bayesian methods”, J. Amer. Statist.  ...  Further, they show that A is closed under convolutions and formation of coherent systems if G is a Weibull distribution. The authors also point out some applications of their results. A. H.  ... 

A Bayesian Parametric Test for Multichannel Adaptive Signal Detection in Nonhomogeneous Environments

Pu Wang, Hongbin Li, Braham Himed
2010 IEEE Signal Processing Letters  
The resulting detector is referred to as the Bayesian parametric adaptive matched filter (B-PAMF) which, compared with nonparametric Bayesian detectors, entails a lower training requirement and alleviates  ...  A Bayesian detector is proposed by incorporating some a priori knowledge of the disturbance covariance matrices, and exploring their inherent block-Toeplitz structure.  ...  More recently, a new class of Bayesian nonhomogeneous models for adaptive signal detection are introduced.  ... 
doi:10.1109/lsp.2009.2039380 fatcat:sltsza5f3ngsrbexzljwqjp22e

Page 5754 of Mathematical Reviews Vol. , Issue 86m [page]

1986 Mathematical Reviews  
Dimitrov, Boyan (BG-AOS) 86m:62178 Isotonic estimates of distributions in reliability.  ...  The uncensored case is treated in great detail and the modifications necessary for the censored case are indicated. The use of covariates and nonparametric methods of estimation is discussed.  ... 

A Conversation with Myles Hollander

Francisco J. Samaniego
2008 Statistical Science  
Hollander has published over 100 papers on nonparametric statistics, survival analysis, reliability theory, biostatistics, probability theory, decision theory, Bayesian statistics and multivariate analysis  ...  Myles Hollander was born in Brooklyn, New York, on March 21, 1941. He graduated from Carnegie Mellon University in 1961 with a B.S. in mathematics.  ...  I believe the paper stimulated more research in testing and estimation for the various nonparametric classes arising naturally in reliability, including more research avenues for us.  ... 
doi:10.1214/07-sts248 fatcat:t4jhwgsd35bjxo4ekbwvt73ety

The imprecise Dirichlet model

Jean-Marc Bernard
2009 International Journal of Approximate Reasoning  
As in the Bayesian framework, there is, in this IP theory, an equivalence between the two major problems of inference, namely the parametric and the predictive problems.  ...  In the (precise) Bayesian approach, the most common model is the precise Dirichlet model (PDM) where prior and posterior uncertainty about h are described by means of a single Dirichlet distribution, the  ...  Acknowledgement Many people helped in some way to make this issue possible.  ... 
doi:10.1016/j.ijar.2008.03.007 fatcat:rzq6pxbic5eytkhpusnwexvham
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