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This paper considers a shared parallel system consisting of n-units supported by single service facility to carry out both installation and repair of a unit. Initially, all the n units share the total load equally and when one or more units fail, they go for repair while the other surviving units share the entire load equally till the failed units are ready for operation after installation. The installation time (switchover time) of a repaired unit is assumed to be non-negligible and random. The system will be down when all the units are non-operative , Assuming that the failure rates are different when the units function under varying loads, the system characteristics, namely, (1) the expected up-time of the system during (0, t], (2) the expected repair time of the units which failed due to varying failure rates during (0, t] and (3) the expected time spent by the units in the installation state during the period (0, t], are obtained by identifying the system at suitable regeneration epochs. The repair time and the switchover time of the units are arbitrarily distributed. The failure rate of unit is assumed to be constant. It depends on the number of surviving units at any instant. The cost-benefit analysis is also carried out using these system characteristics 相似文献
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Let be a random vector, and denote by X1:n,X2:n,…,Xn:n the corresponding order statistics. When X1,X2,…,Xn represent the lifetimes of n components in a system, the order statistic Xn−k+1:n represents the lifetime of a k-out-of-n system (i.e., a system which works when at least k components work). In this paper, we obtain some expressions for the Pearson’s correlation coefficient between Xi:n and Xj:n. We pay special attention to the case n=2, that is, to measure the dependence between the first and second failure in a two-component parallel system. We also obtain the Spearman’s rho and Kendall’s tau coefficients when the variables X1,X2,…,Xn are independent and identically distributed or when they jointly have an exchangeable distribution. 相似文献
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Ismihan Bairamov Safar Parsi 《Journal of Computational and Applied Mathematics》2011,235(16):4629-4638
Two different exchangeable samples are considered and these two samples are assumed to be independent of each other. From these two samples a new sample is combined and treated as a single set of observations. The distribution of a single order statistic and the joint distribution of two order statistics for a new mixed sample are derived and expressed in terms of joint distribution functions. As a special case the distribution of a single order statistic and the joint distribution of two nonadjacent order statistics from exchangeable random variables are obtained. The results presented in this paper allows widespread applications in modelling of various lifetime data, biomedical sciences, reliability and survival analysis, actuarial sciences etc., where the assumption of independence of data cannot be accepted and the exchangeability is a more realistic assumption. 相似文献
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Lorenzo Albertazzi Mike Heilemann 《Angewandte Chemie (International ed. in English)》2023,62(35):e202303390
The exploitation of low-affinity molecular interactions in protein labeling is an emerging topic in optical microscopy. Such non-covalent and low-affinity interactions can be realized with various concepts from chemistry and for different molecule classes, and lead to a constant renewal of fluorescence signals at target sites. Further benefits are a versatile use across microscopy methods, in 3D, live and many-target applications. In recent years, several classes of low-affinity labels were developed and a variety of powerful applications demonstrated. Still, this research field is underdeveloped, while the potential is huge. 相似文献