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Showing 2 results for stochastic Orders
Majid Chahkandi,
Volume 13, Issue 2 (2-2020)
Abstract
The performance of a system depends not only on its design and operation but also on the servicing and maintenance of the item during its operational lifetime. Thus, the repair and maintenance are important issues in the reliability. In this paper, a repairable k-out-of-n system is considered that starts operating at time 0. If the system fails, then it undergoes minimal repair and begins to operate again. The reliability function, hazard rate function, mean residual life function and some reliability properties of the system are obtained by using the connection between the concepts of minimal repair and record values. Some known stochastic orders are also used to compare the lifetimes and residual lifetimes of two repairable k-out-of-n systems. Finally, based on the given information about the lifetimes of k-out-of-n systems, some prediction intervals for the lifetime of the proposed repairable system are obtained.
Jafar Ahmadi, Fatemeh Hooti,
Volume 13, Issue 2 (2-2020)
Abstract
In survival studies, frailty models are used to explain the unobserved heterogeneity hazards. In most cases, they are usually considered as the product of the function of the frailty random variable and baseline hazard rate. Which is useful for right censored data. In this paper, the frailty model is explained as the product of the frailty random variable and baseline reversed hazard rate, which can be used for left censored data. The general reversed hazard rate frailty model is introduced and the distributional properties of the proposed model and lifetime random variables are studied. Some dependency properties between lifetime random variable and frailty random variable are investigated. It is shown that some stochastic orderings preserved from frailty random variables to lifetime variables. Some theorems are used to obtain numerical results. The application of the proposed model is discussed in the analysis of left censored data. The results are used to model lung cancer data.
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