References
- Abravesh, A., M. Ganji, and B. Mostafaiy. 2018. Classical and Bayesian estimation of stress-strength reliability in type-II censored Pareto distributions. Communications in Statistics - Simulation and Computation 48 (8):2333–58. doi:10.1080/03610918.2018.1457688.
- Alotaibi, R. M., Y. M. Tripathi, S. Dey, and H. R. Rezk. 2020. Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution. Journal of Taibah University for Science 14 (1):1164–81. doi:10.1080/16583655.2020.1806525.
- Angel, M, and K. R. Deepa. 2022. Stress-strength reliability: A quantile approach. Statistics 56 (1): 206–21. doi:10.1080/02331888.2022.2038167.
- Asmussen, S., O. Nerman, and M. Olsson. 1996. Fitting phase-type distributions via the EM algorithm. Scandinavian Journal of Statistics 23:419–41.
- Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring theory, methods, and applications. Boston, MA: Birkhauser.
- Balakrishnan, N., and E. Cramer. 2014. Art of progressive censoring: Applications to reliability and quality. New York, NY: Birkhauser.
- Birnbaum, Z. M. 1956. On a use of the Mann-Whitney statistic. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1, 13–7. Berkeley, CA: University of California Press.
- Bladt, M., L. J. R. Esparza, and B. F. Nielsen. 2011. Fisher information and statistical inference for phase-type distributions. Journal of Applied Probability 48 (A):277–93. doi:10.1239/jap/1318940471.
- Bladt, M., A. Gonzalez, and S. L. Lauritzen. 2003. The estimation of phase-type related functionals using Markov chain Monte Carlo methods. Scandinavian Actuarial Journal 2003 (4):280–300. doi:10.1080/03461230110106435.
- Çetinkaya, Ç. 2021. Reliability estimation of a stress-strength model with non-identical component strengths under generalized progressive hybrid censoring scheme. Statistics 55 (2):250–75. doi:10.1080/02331888.2021.1890739.
- Deb, P., and P. K. Trivedi. 1997. Demand for medical care by the elderly: A finite mixture approach. Journal of Applied Econometrics 12:13–336.
- Drisya, M., and J. K. Jose. 2020. Time-dependent stress-strength reliability models with phase-type cycle times. Stochastics and Quality Control 35 (2):97–112.
- Drisya, M., J. K. Jose, and K. Krishnendu. 2022. Time-dependent stress-strength reliability model with phase-type cycle time based on finite mixture models. American Journal of Mathematical and Management Sciences 41 (2):128–47. doi:10.1080/01966324.2021.1933661.
- Erlang, A. K. 1909. The theory of probabilities and telephone conversations. Nyt Tidsskrift Matematika 20:33–9.
- Eryilmaz, S. 2017. Phase-type stress-strength models with reliability applications. Communications in Statistics-Simulation and Computation 47 (4):954–63. doi:10.1080/03610918.2017.1300266.
- Jose, J. K., and M. Drisya. 2020. Time-dependent stress–strength reliability models based on phase type distribution. Computational Statistics 35 (3):1345–71. doi:10.1007/s00180-020-00991-3.
- Jose, J. K., and M. Drisya. 2021. Stress-strength reliability estimation of time-dependent models with fixed stress and phase type strength distribution. Revista Colombiana De Estadistica 44 (1):201–23. doi:10.15446/rce.v44n1.86519.
- Jose, Joby. K., M. Drisya, and M. Manoharan. 2022. Estimation of Stress-Strength Reliability using Discrete Phase Type Distribution. Communications in Statistics- Theory and Methods 51 (2):368–86. doi:10.1080/03610926.2020.1749663.
- Joukar, A., Ramezani, M., and Mirmostafaee, S. M. T. K. 2020. Estimation of P(X > Y) for the power Lindley distribution based on progressively type-II right censored samples. Journal of Statistical Computation and Simulation 90 (2):355–89. doi:10.1080/00949655.2019.1685994.
- Kotz, S.Y. Lumelskii, and M. Pensky. 2003. The stress-strength model and its generalizations: Theory and applications. Singapore: World Scientific Publishing Co. Pvt. Ltd.
- Latouche, G., and V. Ramaswami. 1999. Introduction to matrix analytic methods in stochastic modeling. Philadelphia: ASA-SIAM.
- Mahmoud, M. A. W., R. M. El-Sagheer, A. A. Soliman, and A. H. Abd Ellah. Bayesian estimation of P[Y < X] based on record values from the Lomax distribution and MCMC technique. Journal of Modern Applied Statistical Methods 2016. 15 (1):488–510. doi:10.22237/jmasm/1462076640.
- Neuts, M. F. 1975. Probability distributions of phase-type, 173–206. Belgium: Liber Amicorum Prof. Emeritus H. Florin, University of Louvain.
- Rezaei, S., R. Tahmasbi, and M. Mahmoodi. 2010. Estimation of for generalized Pareto distribution. Journal of Statistical Planning and Inference 140 (2):480–94. doi:10.1016/j.jspi.2009.07.024.
- Rezaei, S., R. A. Noughabi, and S. Nadarajah. 2015. Estimation of stress-strength reliability for the generalized pareto distribution based on progressively censored samples. Annals of Data Science 2 (1):83–101. doi:10.1007/s40745-015-0033-0.
- Roy, S., B. Pradhan, and E. V. Gijo. 2017. Estimation of P(X < Y) for generalized half logistic distribution based on Type-II censored data. International Journal of Quality & Reliability Management 34 (7):1111–22. doi:10.1108/IJQRM-05-2016-0070.
- Sauer, L., Y. Lio, and T.-R. Tsai. 2020. Reliability inference for the multicomponent system based on progressively type II censored samples from generalized Pareto distributions. Mathematics 8 (7):1176. doi:10.3390/math8071176.
- Singh, D. P., M. K. Jha, Y. Tripathi, and L. Wang. 2022. Reliability estimation in a multicomponent stress-strength model for unit Burr III distribution under progressive censoring. Quality Technology & Quantitative Management 19 (5):605–32. doi:10.1080/16843703.2022.2049508.
- Thummler, A., P. Buchholz, and M. Telek. 2006. A novel approach for phase-type fitting with the EM algorithm. IEEE Transactions on Dependable and Secure Computing 3 (3):245–58. doi:10.1109/TDSC.2006.27.
- Ventura, L., and W. Racugno. 2011. Recent advances on Bayesian inference for P(X < Y). Journal of the American Statistical Association 436:1566–74.
- Xavier, T., and J. K. Jose. 2021a. A study of stress-strength reliability using a generalization of power transformed half-logistic distribution. Communications in Statistics - Theory and Methods 50 (18):4335–51. doi:10.1080/03610926.2020.1716250.
- Xavier, T, and J. K. Jose. 2021b. Estimation of reliability in a multicomponent stress-strength model based on power transformed half-logistic distribution. International Journal of Reliability, Quality and Safety Engineering 28 (2):4.
- Xavier, T., J. K. Jose, and S. Nadarajah. 2022. An additive power-transformed half-logistic model and its applications in reliability. Quality and Reliability Engineering International 38:3179–3196. doi:10.1002/qre.3119.
- Xavier, T., J. K. Jose, and S. C. Bagui. 2023. Stress-strength reliability estimation of a series system with cold standby redundancy based on Kumaraswamy half-logistic distribution. American Journal of Mathematical and Management Sciences 42 (3):183–201. doi:10.1080/01966324.2023.2213835.