Main Article Content
In this article, the reliability inference for a multicomponent stress-strength (MSS) model, when both stress and strength random variables follow inverse Topp-Leone distributions, was studied. The maximum likelihood and uniformly minimum variance unbiased estimates for the reliability of MSS model were obtained explicitly. The exact Bayes estimate of MSS reliability was derived the under squared error loss function. Also, the Bayes estimate was obtained using the Monte Carlo Markov Chain method for comparison with the aforementioned exact estimate. The asymptotic confidence interval was determined under the expected Fisher information matrix. Furthermore, the highest probability density credible interval was established through using Gibbs sampling method. Monte Carlo simulations were implemented to compare the different proposed methods. Finally, a real life example was presented in support of the suggested procedures.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following License
CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.
- Akgül F. G. (2019). Reliability estimation in multicomponent stressâ€“strength model for Topp-Leone distribution. Journal of Statistical Computation and Simulation, 89(15), 2914-2929.
- Akgül, F. G., & ÅženoÄŸlu, B. (2017). Estimation of P (X< Y) using ranked set sampling for the Weibull distribution. Quality Technology & Quantitative Management, 14(3), 296-309.
- Al-Mutairi, D. K., Ghitany, M. E., & Kundu, D. (2013). Inferences on stress-strength reliability from Lindley distributions. Communications in Statistics-Theory and Methods, 42(8), 1443-1463.
- Al-Zahrani, B., & Basloom, S. (2016). Estimation of the Stress-Strength Reliability for the Dagum Distribution. Journal of Advanced Statistics, 1(3), 156-170.
- Bai, X., Shi, Y., Liu, Y., & Liu, B. (2019). Reliability inference of stressâ€“strength model for the truncated proportional hazard rate distribution under progressively Type-II censored samples. Applied Mathematical Modelling, 65, 377-389.
- Basirat, M., Baratpour, S., & Ahmadi, J. (2016). On estimation of stressâ€“strength parameter using record values from proportional hazard rate models. Communications in Statistics-Theory and Methods, 45(19), 5787-5801.
- Bhattacharyya, G. K., & Johnson, R. A. (1974). Estimation of reliability in a multicomponent stress-strength model. Journal of the American Statistical Association, 69(348), 966-970.
- Birnbaum, Z. W. (1956). On a use of the Mann-Whitney statistic. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1, 13-17.
- Chen, M. H., & Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69-92.
- Dey, S., Mazucheli, J., & Anis, M. Z. (2017). Estimation of reliability of multicomponent stressâ€“strength for a Kumaraswamy distribution. Communications in Statistics-Theory and Methods, 46(4), 1560-1572.
- Genc, A. I. (2013). Estimation of P (X> Y) with Toppâ€“Leone distribution. Journal of Statistical Computation and Simulation, 83(2), 326-339.
- Ghitany, M. E., Al-Mutairi, D. K., & Aboukhamseen, S. M. (2015). Estimation of the reliability of a stress-strength system from power Lindley distributions. Communications in Statistics-Simulation and Computation, 44(1), 118-136.
- Hassan, A. S., Elgarhy, M., & Ragab, R. (2020). Statistical properties and estimation of inverted Topp-Leone distribution. Journal of Statistics Appllications and Probability, 9(2), 319-331.
- Jha, M. K., Dey, S., & Tripathi, Y. M. (2019). Reliability estimation in a multicomponent stressâ€“strength based on unit-Gompertz distribution. International Journal of Quality & Reliability Management, 37(3), 428-450.
- Kayal, T., Tripathi, Y. M., Dey, S., & Wu, S. J. (2020). On estimating the reliability in a multicomponent stress-strength model based on Chen distribution. Communications in Statistics-Theory and Methods, 49(10), 2429-2447.
- Kizilaslan, F. (2017). Classical and Bayesian estimation of reliability in a multicomponent stressâ€“strength model based on the proportional reversed hazard rate mode. Mathematics and Computers in Simulation, 38(2), 36-62.
- Kizilaslan, F., & Nadar, M. (2018). Estimation of reliability in a multicomponent stressâ€“strength model based on a bivariate Kumaraswamy distribution. Statistical Papers, 59(1), 307-340.
- Kohansal, A., & Shoaee, S. (2019). Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data. Statistical Papers, 60, 1-51.
- Mahto, A. K., Tripathi, Y. M., & Kizilaslan, F. (2020). Estimation of Reliability in a Multicomponent Stressâ€“Strength Model for a General Class of Inverted Exponentiated Distributions Under Progressive Censoring. Journal of Statistical Theory and Practice, 14(4), 1-35.
- Maurya, R. K., & Tripathi, Y. M. (2020). Reliability estimation in a multicomponent stress-strength model for Burr XII distribution under progressive censoring. Brazilian Journal of Probability and Statistics, 34(2), 345-369.
- Nelson, W. B. (2003). Applied life data analysis (Vol. 521). John Wiley & Sons.
- Pak, A., Khoolenjani, N. B., & Rastogi, M. K. (2019). Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values. Pakistan Journal of Statistics and Operation Research, 15 (2), 431-444.
- Rezaei, S., Noughabi, R. A., & Nadarajah, S. (2015). Estimation of stress-strength reliability for the generalized Pareto distribution based on progressively censored samples. Annals of Data Science, 2(1), 83-101.
- Topp, C. W., & Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269), 209-219.