On minimum variance unbiased estimation of a reliability system

• Autorzy: El Sayed H.S. , Nassar M.M. , Shawky A.I.
• Języki publikacji: EN

Abstrakty

EN

This paper investigates the minimum variance unbiased estimation (MVUE) of the reliability function R = P(Y < X) under the assumption that, both, the strength X and the stress Y are independent Gamma random variables. An approximate one- and two-sided confidence intervals for R is obtained. Some numerical results are evaluated for particular sample sizes. Also the MVUE results of this paper are compared with the results obtained by Tong [7].

Słowa kluczowe

EN

minimum variance unbiased estimation; independent Gamma random variables; stress-strength model

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 1998
• Tom: Vol. 46, nr 3
• Strony: 375--381
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

El Sayed H.S.

autor

Nassar M.M.

autor

Shawky A.I.

• Ain Sams University, Faculty of Science, Cairo, Egypt.

Bibliografia

• [1] M. A. Beg, Estimation of Pr(Y < X) for exponential family, I Trans. Rel., 29 (1980) 158-159.
• [2] R. C. Davis, On Minimum variance in nonregular estimation, Ann. Math. Stat., 22 (1951) 43-57.
• [3] R. V. Hogg, A. T. Craig, Introduction to mathematical statistics, Macmillan, New York 1959.
• [4] A. G. Laurent, Conditional distribution of order statistics and distribution of the reduced ith order statistic of the erponential model, Ann. Math. Stat., 34 (1963) 652-657.
• [5] N. Singh, MVUE of P(X < Y) for multivariate normal populations: an application to stress-strength models, IEEE Trans. Rel., 30 (1981) 192-193.
• [6] H. Tong, A note on the estimation of P(Y < X) in the exponential case, Technometrics, 16 (1974) 625, Technometrics, 17 (1975) 395.
• [7] H. Tong, Letter to Editor, Technometrics, 17 (1975) 393.
• [8] W. A. Woodward, G. D. Kelley, Minimum variance unbiased estimation of P(Y < X) in the normal case, Technometrics, 19 (1977) 95-98.