Estimation of reliability under ordered restriction on the parameters |
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Authors: | Ramesh C Gupta Rameshwar D Gupta Olcay H-Akman |
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Institution: | 1. Department of Mathematics and Statistics , University of Maine , Orono, Maine, 04469-5752, U.S.A;2. Department of Math.. , stat. and Computer Science , University of New Brunswick , Saint John, N.B, E2L-4L5, Canada;3. Department of Mathematics , Cornell University , Ithaca, N.Y, 14853-7901 |
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Abstract: | This paper deals with the estimation of reliability for a strength-stress model under ordered restriction on the parameters. It is assumed that components have exponential distributions and are arranged in a parallel system and the failure of one component, results in increasing the failure rate of the remaining components. Results are derived when (i) the ordering of the means is taken into account and when (ii) the ordering of the means is ignored. Simulation studies are carried out to compare the results. It is noticed that, in almost all cases, in case (i) the estimates are closer to the true value with smaller mean squared error (MSE) and smaller’ standard deviation than in case (ii). Thus when the ordering of the means is present in the model, such information should be incorporated in the estimation of reliability. |
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Keywords: | maximum likelihood estimator minimum variance unbiased estimator stress strength model simulation parallel system |
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