Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples

Year 2017, Volume: 46 Issue: 2, 239 - 253, 01.04.2017

Neriman Akdam İsmail Kınacı , Bugra Saracoglu

Abstract

Suppose that X represents the stress which is applied to a component and Y is strength of this component. Let X and Y have Exponential Power (EP) distribution with $(\alpha_1,\beta_1)$ and $(\alpha_2,\beta_2)$ parameters, respectively. In this case, stress-strength reliability (SSR) is shown by $P=P(X<Y)$. In this study, the SSR for EP distribution are obtained with numerical methods. Also maximum likelihood estimate (MLE) and approximate bayes estimates by using Lindley approximation method under squared-error loss function for SSR under progressive type-II censoring are obtained. Moreover, performances of these estimators are compared in terms of MSEs by using Monte Carlo simulation. Furthermore coverage probabilities of parametric bootstrap estimates are computed. Finally, real data analysis is presented.

Keywords

Maximum likelihood estimation, Bayes estimation, Exponential Power distribution, Lindley’s approximation, Monte Carlo simulation, Bootstrap estimation

References

• Balakrishnan, N. and Sandhu, R.A.A Simple Simulation Algorithm for Generating Progressively Type-II Censored Sample, American Statistician 49 , 229-230, 1995.
• Balakrishnan, N., Aggarwala, R.Progressive Censoring:Theory, Methods and Applications. Birkhauser, Boston, 2000.
• Balakrishnan, N.Progressive censoring methodology: an appraisal, TEST 16 (2), 211-296, 2007.
• Bader, M. G., Priest, A. M. Statistical aspects of fibre and bundle strength in hyprid composites, Hayashi, T., Kawada, K., and Umekawa, S. eds, Progress in Science and Engineering of composites,ICCM-IV, Oct. 25-28,Tokyo, Japan. 1, 1129-1136, 1982.
• Basirat, M., Baratpour, S., Ahmadi, J. Statistical inferences for stress strength in the proportional hazard models based on progressive Type-II censored samples. Journal of Statistical Computation and Simulation, 85(3), 431-449, 2015.
• Chen, Z.Statistical inference about the shape parameter of the exponential power distribution, Statistical Papers 40, 459-468,1999.
• Efron, B. The jackknife, the bootstrap and other resampling plans. Philadelphia: Society for industrial and applied mathematics, 1982.
• Ghitany, M. E. , Al-Mutairi, D. K., Aboukhamseen, S. M., Estimation of the Reliability of a Stress-Strength System from Power Lindley distributions, Communications in Statistics- Simulation and Computation 44 (1) 118-136,2014.
• Leemis, L.M. Lifetime distribution identities, IEEE:Transactions on Realibility,35 170- 174,1986.
• Lin, C.T. and Ke, S.J. Estimation of $P(Y<X)$ for Location-Scale Distributionsunder Joint Progressively Type-II Right Censoring, Quality Technology and Quantitative Management 10 (3) 339-352,2013.
• Lindley, D.V.Approximate Bayesian methods, Trabajos de Estadistica 31 223-237, 1980. [12] Lio, Y. L. and Tsai, T.R. Estimation of  $\delta=P(X<Y)$ for Burr XII distribution based on the progressively first failure-censored samples, Journal of Applied Statistics, 39 (2) 309- 322,2012.
• Rajarshi M. B. and Rajarshi.S. Bathtub distributions, A review, Communications in Statistics A: Theory and Methods, 17 2597-2621,1988.
• Rezaei, S., Noughabi, R. A., Nadarajah, S. Estimation of Stress-Strength Reliability for the Generalized Pareto Distribution Based on Progressively Censored Samples. Annals of Data Science, 2(1), 83-101,2015.
• Saraçoglu, B., Kınacı, I., Kundu, D. On Estimation of $R=P(Y<X)$ For Exponential Distribution Under Progressive Type-II Censoring, Journal Of Statistical Computation and Simulation 82 (2) 729-744,2012.
• Smith R.M. and Bain L.J. An exponential power life-testing distribution, Communication in Statistics 4 469-481,1975.
• Valiollahi R. , Asgharzadeh A., Mohammad Z. Raqab. Estimation of $P(Y<X)$ for Weibull Distribution Under Progressive Type-II Censoring, Communications in Statistics - Theory and Methods 42 (24) 4476-4498,2013.