|
|
|
 |
Search published articles |
 |
|
Showing 13 results for Stochastic Order
Ghobad Barmalzan, Abedin Haidari, Khaled Masomifard,
Volume 9, Issue 2 (2-2016)
Abstract
In this paper, series and parallel systems, when the lifetimes of their components following the scale model are studied and different stochastic orderings between them are discussed. Moreover, we apply these results to the series and parallel systems consisting of exponentiated Weibull or generalized gamma components. The presented results in this paper complete and extend some known results in the literature.
Shahrokh Hashemi-Bosra, Ebrahim Salehi,
Volume 11, Issue 1 (9-2017)
Abstract
The (n-k+1)-out-of-n systems are important types of coherent systems and have many applications in various areas of engineering. In this paper, the general inactivity time of failed components of (n-k+1)-out-of-n system is studied when the system fails at time t>0. First we consider a parallel system including two exchangeable components and then using Farlie-Gumbel-Morgenstern copula, investigate the behavior of mean inactivity time of failed components of the system. In the next part, (n-k+1)-out-of-n systems with exchangeable components are considered and then, some stochastic ordering properties of the general inactivity time of the systems are presented based on one sample or two samples.
Rabeeollah Rahmani, Muhyiddin Izadi,
Volume 12, Issue 2 (3-2019)
Abstract
Consider a system consisting of n independent binary components. Suppose that each component has a random weight and the system works, at time t, if the sum of the weight of all working components at time t, is above a pre-specified value k. We call such a system as random-weighted-k-out-of-n system. In this paper, we investigate the effect of the component weights and reliabilities on the system performance and show that the larger weights and reliabilities, the larger lifetime (with respect to the usual stochastic order). We also show that the best random-weighted-k-out-of-n system is obtaind when the components with the more weights have simultaneously more reliability. The reliability function and mean time to failure of a random-weighted-k-out-of-n system are stated based on the reliability function of coherent systems. Furthermore, a simulation algorithm is presented to observe the mean time to failure of random-weighted-k-out-of-n system.
Ghobad Barmalzan,
Volume 12, Issue 2 (3-2019)
Abstract
The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, the usual stochastic order between aggregate claim amounts is discussed when the survival function of claims is a increasing and concave. The results established here complete some results of Li and Li (2016).
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.
Ghobad Barmalzan, Abedin Haidari,
Volume 13, Issue 2 (2-2020)
Abstract
This paper examines the problem of stochastic comparisons of series and parallel systems with independent and heterogeneous components generalized linear failure rate. First, we consider two series system with possibly different parameters and obtain the usual stochastic order between the series systems. Next, we drive the usual stochastic order between parallel systems. We also discuss the usual stochastic order between parallel systems by using the unordered majorization and the weighted majorization order between the parameters on the Ɗп.
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.
Masoud Amiri, muhyiddin Izadi, baha-Eldin Khaledi,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, the worst allocation of deductibles and limits in layer policies are discussed from the viewpoint of the insurer. It is shown that if n independent and identically distributed exponential risks are covered by the layer policies and the policy limits are equal, then the worst allocation of deductibles from the viewpoint of the insurer is (d, 0, ..., 0).
Mohadaseh Khayyat, Rasool Rozegar, Ghobad Barmalzan,
Volume 14, Issue 1 (8-2020)
Abstract
The modified proportional hazard rates model, as one of the flexible families of distributions in reliability and survival analysis, and stochastic comparisons of (n-k+1) -out-of- n systems comprising this model have been introduced by Balakrishnan et al. (2018). In this paper, we consider the modified proportional hazard rates model with a discrete baseline case and investigate ageing properties and preservation of the usual stochastic order, hazard rate order and likelihood ratio order in this family of distributions.
Ebrahim Amini Seresht, Ghobad Barmalzan,
Volume 14, Issue 2 (2-2021)
Abstract
This paper examines the problem of stochastic comparisons of k-out-of-n systems with independent multiple-outlier scale components. In this regard, we first consider a k-out-of-n system comprising multiple-outlier scale components and then, by using a permanent function, investigate the likelihood ratio order between these systems.
Ghobad Barmalzan, Ali Akbar Hosseinzadeh, Ebrahim Amini Seresht,
Volume 15, Issue 2 (3-2022)
Abstract
This paper discusses the hazard rate order of the fail-safe systems arising from two sets of independent multiple-outlier scale distributed components. Under certain conditions on scale parameters in the scale model and the submajorization order between the sample size vectors, the hazard rate ordering between the corresponding fail-safe systems from multiple-outlier scale random variables is established. Under certain conditions on the Archimedean copula and scale parameters, we also discuss the usual stochastic order of these systems with dependent components.
Abdol Saeed Toomaj,
Volume 18, Issue 1 (8-2024)
Abstract
In this paper, the entropy characteristics of the lifetime of coherent systems are investigated using the concept of system signature. The results are based on the assumption that the lifetime distribution of system components is independent and identically distributed. In particular, a formula for calculating the Tsallis entropy of a coherent system's lifetime is presented, which is used to compare systems with the same characteristics. Also, bounds for the lifetime Tsallis entropy of coherent systems are presented. These bounds are especially useful when the system has many components or a complex structure. Finally, a criterion for selecting the preferred system among coherent systems based on the relative Tsallis entropy is presented.
Aqeel Lazam Razzaq, Isaac Almasi, Ghobad Saadat Kia,
Volume 18, Issue 2 (2-2025)
Abstract
Adding parameters to a known distribution is a valuable way of constructing flexible families of distributions. In this paper, we introduce a new model, the modified additive hazard rate model, by replacing the additive hazard rate distribution in the general proportional add ratio model. Next, when two sets of random variables follow the modified additive hazard model, we establish stochastic comparisons between the series and parallel systems comprising these components.
|
|
