SYSTEM RELIABILITY ESTIMATION IN MULTICOMPONENT EXPONENTIAL-LINDLEY STRESS- STRENGTH MODELS
Keywords:
Exponential Distribution, Lindley Distribution, Maximum Likelihood Estimators, Bayes Estimator, Stress-Strength Model, Multicomponent System, System Reliability.Abstract
A stress-strength model is formulated for a multi-component system consisting of k identical components. The k components of the system with random strengths ( X1, X 2 , ..., Xk ) are subjected to one of the r random stresses(Y1 ,Y2 ,..., Yr ). The estimation of system reliability based on maximum likelihood estimates (MLEs) and Bayes estimators in k component system are obtained when the system is either parallel or series with the assumption that strengths and stresses follow Lindley distribution and Exponential distribution respectively. A simulation study is conducted to compare MLE and Bayes estimator through the mean squared errors of the estimators.
Downloads
References
Epstein B. (1958). The exponential distribution and its role in life testing,
Industrial Quality Control, 15, p. 4-9.
Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008). Lindley Distribution and
its application, Mathematics and Computers in Simulation, 78, p. 493-506.
Gogoi, J. and Borah, M. (2012). Estimation of system reliability for
multicomponent systems using Exponential, Gamma and Lindley Stress-
Strength Distributions, Journal of Reliability and Statistical Studies, 5(1), p.
-41.
Kotz, S., Lumelskii, Y. and Pensky, M. (2003). The Stress-Strength Model and
its Generalizations: Theory and Applications, Singapore: World Scientific
Press.
Lindley, D. V. (1958). Fudicial Distributions and Bayes’ Theorem, Journal of
the Royal Statistical Society, Series B (Methodological), Vol. 20, No 1, p. 102-
Pandit, P.V. and Kantu, K. J. (2013). System reliability estimation in multi-
component exponential stress-strength models, International journal of
reliability and applications, Vol.14, No.2, p. 97-105.
Rao, C.R. (1984). Linear Statistical Inference and Its Applications, John
Wiley and Sons, New York.
Sandhya, K. and Umamaheswari, T. S. (2013). Reliability of a
multicomponent stress strength model with standby system using mixture of
two Exponential distributions, Journal of Reliability and Statistical Studies,
(2), p. 105-113.
Sinha S. K. and Kale, B. K. (1986). Life Testing and Reliability Estimation,
Wiley Eastern Limited, New Delhi.
Sriwastav, G. L. and Kakati, M. C. (1981). A Stress- Strength Model with
Redundancy, IAPQR Trans., 6, No. 1, p. 21-27.
