Numerical Prediction for the Two-Parameter Weibull Distribution

Δελλαπόρτας, Πέτρος; Wright, David

doi:10.2307/2348725

Cited by 32 publications

(7 citation statements)

References 6 publications

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“…Many of the researchers have discussed the Bayes prediction of future sample based on informative sample, see Ren et al (2006), and Al-Jarallah and Al-Hussaini (2007), etc. A numerical approach to Bayesian prediction for two parameter of Weibull distribution has been discussed by Dellaportas and Wright (1991). Recently, Pradhan and Kundu (2011) have proposed the procedure of estimation of posterior predicting density of future observation, based on the current sample and observed that Gibbs sampling technique can be used quite effectively.…”

Section: Bayes Predictionmentioning

confidence: 99%

Estimation for the Parameter of Poisson-Exponential Distribution under Bayesian Paradigm

Singh¹,

Singh²,

Kumar³

2021

Journal of Data Science

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The present paper deals with the maximum likelihood and Bayes estimation procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample. Bayes estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo (MCMC) technique. Performances of the proposed Bayes estimators have been studied and compared with their maximum likelihood estimators on the basis of Monte Carlo study of simulated samples in terms of their risks. The methodology is also illustrated on a real data set.

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Section: Bayes Predictionmentioning

confidence: 99%

Estimation for the Parameter of Poisson-Exponential Distribution under Bayesian Paradigm

Singh¹,

Singh²,

Kumar³

2021

Journal of Data Science

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“…Note that in this work, we have focused on system‐level reliability modeling and evaluation with the assumption that these component‐level failure parameters are known input parameters. In practice, estimation approaches based on collected failure data (eg, statistical inference, Bayesian estimation) are often applied to estimate component failure time distribution functions and related parameters.…”

Section: An Illustrative Example Smart Home Systemmentioning

confidence: 99%

A hierarchical combinatorial reliability model for smart home systems

Zhao

Xing

Zhang

et al. 2017

Quality & Reliability Eng

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As an application of the Internet of Things, smart home systems have received significant attentions in recent years due to their precedent advantages, eg, in ensuring efficient electricity transmission and integration with renewable energy. This paper proposes a hierarchical and combinatorial methodology for modeling and evaluating reliability of a smart home system. Particularly, the proposed methodology encompasses a multi-valued decision diagram-based method for addressing phased-mission, standby sparing, and functional dependence behaviors in the physical layer; and a combinatorial procedure based on the total probability theorem for addressing probabilistic competing failure behavior with random propagation time in the communication layer. The methods are applicable to arbitrary types of time-to-failure and time-to-propagation distributions for system components. A detailed case study of an example smart home system is performed to demonstrate applications of the proposed method and effects of different component parameters on the system reliability. (IoT) is an internetworking of myriad of "smart" objects and devices augmented with sensors and actuators (such as cell phones, smart appliances, electrical devices, etc.). [1][2][3] In other words, an IoT smart system incorporates sensing, actuation, and control functions for monitoring and analyzing a situation, and Abbreviations: EMS, Energy management system; FCE, Failure competition event; FDEP, Functional dependence; HSP, Hot spare; IFP, Isolation factor pair; IoT, Internet of Things; LF, Local failure; LS, Local sensing failure; LT, Local transmitting failure; MDD, Multi-valued decision diagram; PDEP, Probabilistic function dependence; PDF, Probability density function; PFDC, Probabilistic function dependence case; PFGE, Propagated failure with global effect; PMS, Phased mission system; PT, Propagation time. Notations: h, Phase number; f iP (t), f iLS (t), f iLT (t), PDF of time-to-PFGE/LS/LT of component i; f iPT (t), PDF of time-to-propagation of component i; FCE j , Failure competition event j, j = 1,2,3; ψ i , The failure function of the i-th phase in the physical layer; ψ xi;h , Unreliability of component i at the end of h; I, Union of set of components causing PFGE and set of components being isolated under an FCE; P FCEj t ð Þ, Probability of no PFGE to components in I; q iLS (t), q iLT (t), Occurrence probability of LS, LT to component i; q iP (t), Occurrence probability of PFGE to component i; q iS (t), q iT (t), Occurrence probability of LS, LT given that no PFGE to i; Q FCEj t ð Þ, Failure probability given that no PFGE happens to components in I; T h , Duration of phase h; x i = 0, Component i functions in all the phases; x i = h, Component i fails during h given that i is operational at the beginning of h; X iP , X iLS , X iLT , Event that component i has a PFGE, LS, LT; X iPT , Event that the propagation time is less than the time difference between the relay LT and the component i PFGE; U comm (t), Unreliability of the communicat...

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“…For a Bayesian approach to inference for this distribution, and a bibliography, see Dellaportas and Wright (1991). The probability density, reliability, and mean of the Weibull distribution are given by…”

Section: Weibull Distribution Of Livesmentioning

confidence: 99%

Parameter Estimation and Censored Lives

Hawkes

Jalali

2006

Communications in Statistics - Theory and Methods

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The usual likelihood used to make inferences about parameters of lifetime distributions when lives may be censored consists of the product of probability densities for completed lives and reliabilities for the censored lives. This works well in many situations. We consider two special cases of a model which assumes a Poisson birth process for the items: in one case the usual method works well, but in the other case it does not, and better estimates are found.

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Numerical Prediction for the Two-Parameter Weibull Distribution

Cited by 32 publications

References 6 publications

Estimation for the Parameter of Poisson-Exponential Distribution under Bayesian Paradigm

Estimation for the Parameter of Poisson-Exponential Distribution under Bayesian Paradigm

A hierarchical combinatorial reliability model for smart home systems

Parameter Estimation and Censored Lives

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