Stress-strength reliability for general bivariate distributions

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• 作者：Alaa H. Abdel-Hamid<sup> ; sup><sup>hamid_alh@science.bsu.edu.eg" class="auth_mail" title="E-mail the corresponding authorsup>
• 关键词：General bivariate distribution ; Parametric estimation of parameters and stress-strength reliability ; Govindarajulu's non-par-ametric interval bounds of R
• 刊名：Journal of the Egyptian Mathematical Society
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：24
• 期：4
• 页码：617-621
• 全文大小：341 K

文摘

An expression for the stress-strength reliability mmlsi9" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1110256X16000213&_mathId=si9.gif&_user=111111111&_pii=S1110256X16000213&_rdoc=1&_issn=1110256X&md5=32f87e1ad8999599a8d0bb31b602cfde">mg class="imgLazyJSB inlineImage" height="16" width="131" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1110256X16000213-si9.gif">mathContainer hidden">mathCode"><math altimg="si9.gif" overflow="scroll"><mrow><mi>Rmi><mo>=mo><mi>Pmi><mo>(mo><mrow><msub><mi>Xmi><mn>1mn>msub><mo><mo><mspace width="0.16em">mspace><msub><mi>Xmi><mn>2mn>msub>mrow><mo>)mo>mrow>math> is obtained when the vector (m>Xm><sub>1sub>, m>Xm><sub>2sub>) follows a general bivariate distribution. Such distribution includes bivariate compound Weibull, bivariate compound Gompertz, bivariate compound Pareto, among others. In the parametric case, the maximum likelihood estimates of the parameters and reliability function m>Rm> are obtained. In the non-parametric case, point and interval estimates of m>Rm> are developed using Govindarajulu's asymptotic distribution-free method when m>Xm><sub>1sub> and m>Xm><sub>2sub> are dependent. An example is given when the population distribution is bivariate compound Weibull. Simulation is performed, based on different sample sizes to study the performance of estimates.