Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function

Lanping Li

doi:doi:10.11648/j.pamj.20160506.12

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Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function

Lanping Li

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 6)

Received: 5 October 2016 Accepted: 14 October 2016 Published: 7 November 2016

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Abstract

The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 6)
DOI	10.11648/j.pamj.20160506.12
Page(s)	181-185
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Bayes Estimation, Lifetime Performance Index, Bayes Test, Ailamujia Distribution, Squared Error Loss Function

References

[1]	Juran J. M., Gryna F. M., Bingham R. S. J., 1974. Quality Control Handbook. New York: McGraw-Hill.
[2]	Kane V. E., 1986. Process capability indices. Journal of Quality Technology, 18(1): 41-52.
[3]	Chan L. K., Cheng S. W., Spiring F. A., 1988. A new measure of process capability: Cpm. Journal of Quality Technology, 20(3): 162-75.
[4]	Pearn W. L., Kotz S., Johnson N. L., 1992. Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24(4): 216-33.
[5]	Shiau J. H., Chiang C. T., Hung H. N., 1999. A Bayesian procedure for process capability assessment. Quality & Reliability Engineering, 15(15): 369-378.
[6]	Pearn W. L., Wu C. W., 2005. Process capability assessment for index Cpk, based on Bayesian approach. Metrika, 61(2): 221-234.
[7]	Chen S. M., Hsu Y. S., 2016. Uniformly most powerful test for process capability index. Quality Technology & Quantitative Management, 1(2): 257-269.
[8]	Baral A. K., Anis M. Z., 2015. Assessment of Cpm in the presence of measurement errors. Journal of Statistical Theory & Applications, 14(1): 13-27.
[9]	Macintyre A., 2015. On process capability and system availability analysis of the inverse Rayleigh distribution. Pakistan Journal of Statistics & Operation Research, 11(1): 489-497.
[10]	Montgomery, D. C., 1985. Introduction to Statistical Quality Control, New York: John Wiley & Sons,.
[11]	Wu C. C., Chen L. C., Chen Y. J., 2013. Decision procedure of lifetime performance assessment of Rayleigh products under progressively Type II right censored samples. International Journal of Information & Management Sciences, 24(3): 225-237.
[12]	Lee W. C., Hong C. W., Wu J. W., 2015. Computational procedure of performance assessment of lifetime index of normal products with fuzzy data under the type II right censored sampling plan. Journal of Intelligent & Fuzzy Systems, 28(4): 1755-1773.
[13]	Lee W. C., Wu J. W., Hong M. L., et al., 2011. Assessing the lifetime performance index of Rayleigh products based on the Bayesian estimation under progressive type II right censored samples. Journal of Computational & Applied Mathematics, 235(6): 1676-1688.
[14]	Liu M. F., Ren H. P., 2013. Bayesian test procedure of lifetime performance index for exponential distribution under progressive type-II censoring. International Journal of Applied Mathematics & Statistics, 32(2): 27-38.
[15]	Shafay A. R., 2016. Exact inference for a simple step-stress model with generalized Type-I hybrid censored data from the exponential distribution. Communication in Statistics- Simulation and Computation, 45(1): 181-206.
[16]	Biradar B. S., Santosha C. D., 2014. Estimation of the mean of the exponential distribution using maximum ranked set sampling with unequal samples. Open Journal of Statistics, 4(4): 641-649.
[17]	Alomari A. I., 2014. Bayesian estimation of the mean of exponential distribution using moving extremes ranked set sampling. Statistical Papers, 44(3): 367-382.
[18]	Peng X., Yan Z., 2014. Estimation and application for a new extended Weibull distribution. Reliability Engineering & System Safety, 2014, 121(1): 34-42.
[19]	Horrace W. C., 2015. Moments of the truncated normal distribution. Journal of Productivity Analysis, 43(2):133-138.
[20]	Gunnar K., Kerstin V., 2012. Estimation of the location and scale parameters of a Pareto distribution by linear functions of order statistics. Journal of the American Statistical Association, 68(68): 218-227.
[21]	Lv H. Q., Gao L. H., Chen C. L., 2002. Эрланга distribution and its application in supportability data analysis. Journal of Academy of Armored Force Engineering, 16(3): 48-52.
[22]	Pan G. T., Wang B. H., Chen C. L., Huang Y. B., Dang M. T., 2009. The research of interval estimation and hypothetical test of small sample of Эрланга distribution. Application of Statistics and Management, 28(3): 468-472.
[23]	Long B., 2015. Bayesian estimation of parameter on Эрлангa distribution under different prior distribution. Mathematics in Practice & Theory, (4): 186-192.
[24]	Li L. P., 2016. Minimax estimation of the parameter of ЭРланга distribution under different loss functions, Science Journal of Applied Mathematics and Statistics. 4(5): 229-235.
[25]	Tong, L. I., Chen, K. T. and Chen, H. T., 2002. Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution, International Journal of Quality & Reliability Management, 19(7): 812-824.

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APA Style

Lanping Li. (2016). Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function. Pure and Applied Mathematics Journal, 5(6), 181-185. https://doi.org/10.11648/j.pamj.20160506.12

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ACS Style

Lanping Li. Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function. Pure Appl. Math. J. 2016, 5(6), 181-185. doi: 10.11648/j.pamj.20160506.12

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AMA Style

Lanping Li. Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function. Pure Appl Math J. 2016;5(6):181-185. doi: 10.11648/j.pamj.20160506.12

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@article{10.11648/j.pamj.20160506.12,
  author = {Lanping Li},
  title = {Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {6},
  pages = {181-185},
  doi = {10.11648/j.pamj.20160506.12},
  url = {https://doi.org/10.11648/j.pamj.20160506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160506.12},
  abstract = {The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.},
 year = {2016}
}

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TY  - JOUR
T1  - Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function
AU  - Lanping Li
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160506.12
DO  - 10.11648/j.pamj.20160506.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 181
EP  - 185
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.12
AB  - The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.
VL  - 5
IS  - 6
ER  -

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Author Information

Lanping Li

Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China

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Plain Text BibTeX RIS

APA Style

Lanping Li. (2016). Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function. Pure and Applied Mathematics Journal, 5(6), 181-185. https://doi.org/10.11648/j.pamj.20160506.12

Copy | Download

ACS Style

Lanping Li. Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function. Pure Appl. Math. J. 2016, 5(6), 181-185. doi: 10.11648/j.pamj.20160506.12

Copy | Download

AMA Style

Lanping Li. Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function. Pure Appl Math J. 2016;5(6):181-185. doi: 10.11648/j.pamj.20160506.12

Copy | Download

@article{10.11648/j.pamj.20160506.12,
  author = {Lanping Li},
  title = {Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {6},
  pages = {181-185},
  doi = {10.11648/j.pamj.20160506.12},
  url = {https://doi.org/10.11648/j.pamj.20160506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160506.12},
  abstract = {The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function
AU  - Lanping Li
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160506.12
DO  - 10.11648/j.pamj.20160506.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 181
EP  - 185
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.12
AB  - The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.
VL  - 5
IS  - 6
ER  -

Copy | Download