Bayesian Test for Lifetime Performance Index of Exponential Distribution under Symmetric Entropy Loss Function
Mathematics Letters
Volume 4, Issue 1, March 2018, Pages: 20-24
Received: Mar. 1, 2018; Accepted: Mar. 27, 2018; Published: May 4, 2018
Views 708      Downloads 45
Guobing Fan, School of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha, China
Article Tools
Follow on us
The task of this paper is to estimate the lifetime performance index of Exponential distribution. A Bayesian test procedure is established under symmetric entropy loss function. Firstly, Bayesian estimation of life performance index is obtained, then a Bayesian test procedure for lifetime performance index is proposed. Finally, an applied example is used to illustrate the effectiveness of the proposed test method.
Lifetime Performance Index, Bayesian Test, Exponential Distribution, Symmetric Entropy Loss Function
To cite this article
Guobing Fan, Bayesian Test for Lifetime Performance Index of Exponential Distribution under Symmetric Entropy Loss Function, Mathematics Letters. Vol. 4, No. 1, 2018, pp. 20-24. doi: 10.11648/
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Shu M H, Wu H C. Manufacturing process performance evaluation for fuzzy data based on loss-based capability index [J]. Soft Computing, 2012, 16 (1):89-99.
Chen C C, Lai C M, Nien H Y. Measuring process capability index Cpm with fuzzy data [J]. Quality & Quantity, 2010, 44 (3):529-535.
Juran J M, Gryna F M, Bingham R S J. Quality Control Handbook. New York: McGraw-Hill., 1974.
Eslamipoor R, Hosseini-Nasab H. A modified process capability index using loss function concept [J]. Quality & Reliability Engineering International, 2016, 32 (2):435-442.
Chen K S, Huang C F, Chang T C. A mathematical programming model for constructing the confidence interval of process capability index Cpm in evaluating process performance: an example of five-way pipe [J]. Journal of the Chinese Institute of Engineers, 2017, 40 (2):126-133.
Gu X, Ma Y, Liu J, et al. Robust parameter design for multivariate quality characteristics based on process capability index with individual observations [J]. Systems Engineering & Electronics, 2017, 39 (2):362-368.
Abdolshah M, Yusuff R M, Hong T S, et al. Measuring process capability index Cpmk, with fuzzy data and compare it with other fuzzy process capability indices [J]. Expert Systems with Applications, 2011, 38 (6):6452-6457.
Kurniati N, Yeh R H, Wu C W. A sampling scheme for resubmitted lots based on one-sided capability indices [J]. Quality Technology & Quantitative Management, 2015, 12 (4):501-515.
Seifi S, Nezhad M S F. Variable sampling plan for resubmitted lots based on process capability index and Bayesian approach [J]. The International Journal of Advanced Manufacturing Technology, 2017, 88 (9-12): 2547-2555.
Montgomery D C. Introduction to Statistical Quality Control, New York: John Wiley & Sons, 1985.
Lee W C, Hong C W, Wu J W. Computational procedure of performance assessment of lifetime index of normal products with fuzzy data under the type II right censored sampling plan [J]. Journal of Intelligent & Fuzzy Systems, 2015, 28 (4):1755-1773.
Liu M. F., Ren H. P. Bayesian test procedure of lifetime performance index for exponential distribution under progressive type-II censoring. International Journal of Applied Mathematics & Statistics, 2013, 32 (2):27-38.
Wu C W, Shu M H, Chang Y N. Variable-sampling plans based on lifetime-performance index under exponential distribution with censoring and its extensions [J]. Applied Mathematical Modelling, 2018, 55:81-93.
Soliman A E. Assessing the lifetime performance index using exponentiated frechet distribution with the progressive first-failure-censoring scheme [J]. American Journal of Theoretical and Applied Statistics, 2014, 3 (6):167-176.
Li L. Bayesian test for lifetime performance index of Ailamujia distribution under squared error loss function [J]. Pure and Applied Mathematics Journal, 2016, 5 (6):181-185.
Zhao S, Song Y, Song L, et al. Estimation of ordered means of two sample exponential distributions under symmetric entropy loss [J]. Journal of Jilin University, 2007, 45 (1):44-48.
Li L. Bayes estimation of Topp-Leone distribution under symmetric entropy loss function based on lower record values [J]. 2016, 4 (6):284.
Lawless J F. Statistical Model and Methods for Lifetime Data. John Wiley & Sons, New York, 1982.
Balakrishnan N, Lin C T, and Chan P S. A comparison of two simple prediction intervals for exponential distribution. IEEE Transactions on Reliability, 2005, 54: 27-33.
Gail M H and Gastwirth J L. A scale-free goodness of fit test for the exponential distribution based on the Gini statistics, Journal of the Royal Statistical Society, B, 1978, 40: 350-357.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186