Comparison Various Estimation Methods for R = P (Y1 < X < Y2) Utilizing Restricted Generalized Weibull Distribution
Keywords:
Restricted generalized Weibull distribution, Stress–strength reliability, Maximum likelihood method, Shrunken method, Least Squares method, Mean Squared ErrorAbstract
The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y1 < X < Y2) while the system contains a single component with strength X subject to two stresses, Y1 and Y2. With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y1 and Y2 and the strength X constitute independent, non-identical random variables in our S-S model.
References
Z. Birnbaum, On a use of the mann-whitney statistic, in: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, Vol. 3, University of California Press, 1956, pp. 13–18.
S. Kotz, Y. Lumelskii, M. Pensky, The stress–strength model and its generalizations: theory and applications, World Scientific, New York, 2003.
W. Waegeman, B. De Baets, L. Boullart, On the scalability of ordered multi-class roc analysis, Computational Statistics & Data Analysis 52 (7) (2008) 3371–3388.
P. Guangming, W. Xiping, Z. Wang, Nonparametric statistical inference for p (x< y< z), Sankhya A 75 (2013) 118–138.
A. S. Hassan, A. E. Elsayed, M. S. Rania, On the estimation of for weibull distribution in the presence of k outliers, International Journal of Engineering Research and Applications 3 (6) (2013) 1728–1734.
S. H. Raheem, B. A. Kalaf, A. N. Salman, Comparison of some of estimation methods of stress-strength model: R= p (y
M. Bebbington, C.-D. Lai, R. Zitikis, A flexible weibull extension, Reliability Engineering & System Safety 92 (6) (2007) 719–726.
C.-D. Lai, Generalized weibull distributions, Springer, Berlin, Heidelberg, 2014.
G. S. Mudholkar, D. K. Srivastava, Exponentiated weibull family for analyzing bathtub failure-rate data, IEEE transactions on reliability 42 (2) (1993) 299–302.
M. M. Nassar, F. H. Eissa, On the exponentiated weibull distribution, Communications in Statistics-Theory and Methods 32 (7) (2003) 1317–1336.
M. Pal, M. M. Ali, J. Woo, Exponentiated weibull distribution, Statistica 66 (2) (2006) 139–147.
J. R. Thompson, Some shrinkage techniques for estimating the mean, Journal of the American Statistical Association 63 (321) (1968) 113–122.
Z. A. Al-Hemyari, A. Khurshid, A. Al-Joberi, On thompson type estimators for the mean of normal distribution, Investigacion Operacional 30 (2) (2009) 109–116.
A. I. Abdul-Nabi, A. N. Salman, M. M. Ameen, Employ shrinkage technique during estimate normal distribution mean, Journal of Interdisciplinary Mathematics 24 (6) (2021) 1685–1692.
I. Kamel, T. Anwar, A. Najim, Estimation of (ss) reliability for inverted exponential distribution, AIP Conference Proceedings 2591 (1) (2023).
B. A. Kalaf, S. H. Raheem, A. N. Salman, Estimation of the reliability system in model of stress-strength according to distribution of inverse rayleigh, periodicals of Engineering and Natural Sciences 9 (2) (2021) 524–533.
E. A. Abdulateef, A. N. Salman, A. A. Hussein, Estimate the parallel system reliability in stress-strength model based on exponentiated inverted weibull distribution, Journal of Physics: Conference Series 1879 (2) (2021) 1–14.
