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A Bayesian Estimation Procedure of Reliability Function for Lifetime Distributions

Volume 13, Number 2, March 2017 - Paper 3 - pp. 129-134
DOI: 10.23940/ijpe.17.02.p3.129134

VASILIY KRIVTSOV and MICAHEL FRANKSTEIN

Department of Reliability Analytics, The Ford Motor Company, Dearborn, MI, USA

(Received on November 21, 2016 and Revised on February 28, 2017)

Abstract:

This paper is a sequel to [1], wherein we proposed a simple procedure to construct the joint prior and posterior distributions of Weibull parameters based on the underlying reliability function estimates in two time cross–sections. In this paper, we extend the procedure in three aspects: a) the prior data can now be taken in terms of a simple probability paper plot, b) the posterior now includes not only posterior estimates of distribution parameters, but also the posterior estimate of the underlying reliability function along with the respective credibility intervals, and c) we show that the proposed procedures can be applied to any parametric lifetime distribution, not necessarily limited to the location–scale family.

 

References: 5

[1] Kaminsky, M.P., and V.V. Krivtsov. A Simple Procedure for Bayesian Estimation of Weibull Distribution, IEEE Transactions on Reliability, 2005; 54(2): 612–616.
[2] Canavos, G.C., and C.P. Tsokos. (1973). Bayesian estimation of life parameters in the Weibull distribution, Operations Research, 1973; 21: 755–763.
[3] Meeker, W.Q., and L.A. Escobar, Statistical Methods for Reliability Data, John Wiley & Sons, New York, 1998.
[4] Google Scholar Citations, http://scholar.google.com/intl/en/scholar/citations.html, retrieved: 11/2/2016.
[5] SAS Institute Inc. New Features in JMP®11. Cary, NC, 2013.

 

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