A Note on Estimation of Stress-Strength Reliability under Generalized Uniform Distribution when Strength Stochastically Dominates Stress
Keywords:Stress-strength reliability, Generalized uniform distribution, Stochastic dominance, Estimation
In this note we find the UMVUE and a consistent estimator of the stress strength reliability of a system, whose strength stochastically dominates the stress. Strength of the system and the stress on it are assumed to be independently distributed, each having a generalized uniformdistribution. Simulation study has been carried out, and an application to real life data has also been cited.
M. M. ALI, M. PAL, J. WOO (2005). Inference on P(Y < X) in generalized uniform distributions. Calcutta Statistical Association Bulletin, 57, no. 1-2, pp. 35–48.
A. M. ALMARASHI, A. ALGARNI, M. NASSAR (2020). On estimation procedures of stress-strength reliability for Weibull distribution with application. Plos one, 15, no. 8, p. e0237997.
N. BASHIR, R. BASHIR, J. R, S. MIR (2019). Estimation of stress strength reliability in single component models for different distributions. Current Journal of Applied Science and Technology, 34, no. 6, pp. 1–10.
A. IRANMANESH, K. FATHI VAJARGAH, M.HASANZADEH (2018). On the estimation of stress strength reliability parameter of inverted gamma distribution. Mathematical Sciences, 12, no. 1, pp. 71–77.
A. A. JAFARI, S. BAFEKRI (2021). Inference on stress-strength reliability for the twoparameter exponential distribution based on generalized order statistics. Mathematical Population Studies, 28, no. 4, pp. 201–227.
N. JANA, S. KUMAR, K. CHATTERJEE (2019). Inference on stress–strength reliability for exponential distributions with a common scale parameter. Journal of Applied Statistics, 46, no. 16, pp. 3008–3031.
X. JIA, S. NADARAJAH, B. GUO (2017). Bayes estimation of P(Y < X) for the Weibull distribution with arbitrary parameters. Applied Mathematical Modelling, 47, pp. 249–259.
P. KUNDU, N. JANA, S. KUMAR, K. CHATTERJEE (2020). Stress-strength reliability estimation for exponentially distributed system with common minimum guarantee time. Communications in Statistics-Theory and Methods, 49, no. 14, pp. 3375–3396.
J. I. MCCOOL (1991). Inference on P(Y < X) in the Weibull case. Communications in Statistics-Simulation and Computation, 20, no. 1, pp. 129–148.
H. NADEB, H. TORABI, Y. ZHAO (2019). Stress-strength reliability of exponentiated Fréchet distributions based on Type-II censored data. Journal of Statistical Computation and Simulation, 89, no. 10, pp. 1863–1876.
M. PAL, M. MASOOM ALI, J. WOO (2005). Estimation and testing of P(Y > X) in two-parameter exponential distributions. Statistics, 39, no. 5, pp. 415–428.
S. REZAEI, R. A. NOUGHABI, S. NADARAJAH (2015). Estimation of stress-strength reliability for the generalized Pareto distribution based on progressively censored samples. Annals of Data Science, 2, no. 1, pp. 83–101.
B. SARAÇO˘GLU, I. KINACI, D. KUNDU (2012). On estimation of R = P(Y < X) for exponential distribution under progressive Type-II censoring. Journal of Statistical Computation and Simulation, 82, no. 5, pp. 729–744.
B. SARAÇOGLU, K. MF, A.-E. AM (2009). Comparison of estimators for stress-strength reliability in the Gompertz case. Hacettepe Journal of Mathematics and Statistics, 38, no. 3, pp. 339–349.
R. C. TIWARI, Y. YANG, J.N. ZALKIKAR (1996). Bayes estimation for the Pareto failure model using Gibbs sampling. IEEE transactions on reliability, 45, no. 3, pp. 471–476.
H. TONG, et al. (1974). A note on the estimation of P(Y < X) in the exponential case. Technometrics, 16, no. 4, p. 625.
R. VALIOLLAHI, A. ASGHARZADEH, M. Z. RAQAB (2013). Estimation of P(Y < X) for Weibull distribution under progressive Type-II censoring. Communications in Statistics-Theory and Methods, 42, no. 24, pp. 4476–4498.
Z. XIA, J. YU, L. CHENG, L. LIU, W. WANG (2009). Study on the breaking strength of jute fibres using modified Weibull distribution. Composites Part A: Applied Science and Manufacturing, 40, no. 1, pp. 54–59.
How to Cite
Copyright (c) 2022 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.