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Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability (17480078)
For critical systems, such as satellites and aircraft, survivability can be extremely important as failures can result in irreversible economic loss and even casualties. A mission abort policy and the subsequent rescue procedure are effective tools for increasing the survivability of systems performing missions of fixed or variable duration. However, it comes at a price of decreasing the mission success probability. Therefore, a reasonable trade-off should be achieved. This problem has been studied in numerous publications, however, we are the first to discuss general multi-component coherent systems. Moreover, the new methodology based on signatures describing coherent systems is employed for description and defining a criterion of abort. Several optimization problems are formulated and discussed. The detailed numerical examples illustrate our findings and justify the developed innovative approach. © IMechE 2025.
Quality Technology and Quantitative Management (16843703) 21(5)pp. 656-673
This paper studies the reliability function of a weighted (Formula presented.) -out-of- (Formula presented.) system with multiple types of components. A weighted system with (Formula presented.) different types of components is considered and two real-life scenarios for the operation of the system are defined. In the first one, it is assumed that the system operates if the accumulated weight of all active components is more than a predetermined threshold (Formula presented.), otherwise the system fails. In the second scenario, the system is assumed to operate if the total weight of the operating components of type (Formula presented.) is more than or equal to the corresponding threshold (Formula presented.), for at least (Formula presented.) types of components, (Formula presented.). Our approaches in assessing the reliability function of the system lifetime rely on the notion of survival signature corresponding to multi-type weighted (Formula presented.) -out-of- (Formula presented.) system. The formulas for the proposed survival signature are presented and the corresponding computational algorithms are also given. To examine the theoretical results, the reliability function and other aging characteristics of a wind farm (system) consisting of three plants located in three different regions are assessed numerically and graphically. Finally, an allocation problem to determine the best choice for the distribution of each type in the weighted (Formula presented.) -out-of- (Formula presented.) systems is studied. © 2023 International Chinese Association of Quantitative Management.
Applied Stochastic Models in Business and Industry (15264025) 38(4)pp. 590-608
This paper investigates some maintenance strategies for repairable systems that are exposed to two distinct types of failure: internal failures due to aging over time and fatal external shocks arriving according to a nonhomogeneous Poisson process. When the system fails, it will be repaired, and it is assumed that the repair does not bring the system to an as-good-as-new state. Two maintenance models are developed to prevent the system from failure under the mentioned scenario. By imposing the related cost functions, we investigate the corresponding optimal policy for each model such that the expected cost rate is minimized. Some numerical examples and simulation studies are presented to demonstrate the proposed maintenance models. © 2022 John Wiley & Sons, Ltd.
Reliability Engineering and System Safety (18790836) 217
We investigate optimal maintenance models for warranted coherent systems consisting of n components (n≥1). The system is under a warranty policy with two consecutive phases under which the manufacturer's commitment goes in two different forms. In Phase I, upon the system failure, the failed components are replaced with new ones and a corrective maintenance is conducted on the whole system. If the system failure occurs during Phase II, only minimal repair is performed on the components. Following expiration of the warranty time, the customer is solely responsible for maintaining the system who, for a fixed length of the time period, replaces the failed components and preventively maintains the system at the end of such period. During the maintenance period, the same maintenance as that of in Phase I of the warranty period is conducted. Such a maintenance model can be considered as a generalization of the age-based maintenance model for a system under warranty model. We investigate, from the manufacturer's and customer's perspectives, the optimal length of each phase in the warranty period, and the optimal planned time of preventive maintenance based on some imposed cost functions, respectively. Numerical examples are provided to illustrate the proposed optimal maintenance models. © 2021
Computers and Industrial Engineering (03608352) 163
In this paper, we study some preventive maintenance policies for coherent systems with n,n⩾1, components. We consider a coherent system consisting of K,K⩾1, different types of independent components. The system may fail due to the aging of its components, or it may fail due to fatal shocks arriving from external sources. Under this mechanism of system failure, we propose optimal age-based and block preventive maintenance models by considering the costs of preventive maintenance, corrective maintenance, and minimal repairs. We provide some formulas for the average long-run cost rate of the proposed strategies. The existence of optimal values under which the imposed cost functions are minimized has been discussed. In addition, Monte Carlo simulations are carried out to evaluate the cost functions of the proposed maintenance models. Our derivations rely on the concept of survival signature. Real examples of coherent systems are also presented to examine and illustrate the theoretical results. © 2021 Elsevier Ltd
Reliability Engineering and System Safety (18790836) 218
In reliability engineering, each component of the system, in addition to internal failures, is usually subject to lethal external shocks. Usually, the random shocks are produced by a random environment, and modeled by a stochastic process. In this paper, using the theory of signature and survival signature depending on whether the components of the system are of one type or several types, a general approach in assessing the system reliability is presented. We also propose some preventive maintenance strategies for a multi-component system whose components are subject to both internal failures and fatal shocks. In each policy, based on the maintenance costs of the system and its components, a cost function is computed as a criterion to be optimized. The signature-based representation of the system reliability is especially useful to maintain the system in optimal conditions by considering the component repair costs. To illustrate the theoretical results, extensive graphical and numerical examples are presented. © 2021 Elsevier Ltd
Reliability Engineering and System Safety (18790836) 205
Weighted k-out-of-n systems form an important class of redundant systems with a wide range of applications in reliability engineering. In this paper, we introduce novel optimal preventive maintenance models for the class of weighted k-out-of-n systems based on average cost and availability criteria. Depending on the average number of failed components, we set up a cost (availability) function corresponding to the time that the total weights of the working components become less than a predetermined threshold m, or the age of the system reaches TPM. The form of the cost (and availability) function relies on the mixture representation of the system reliability based on the notion of the signature of the system. Some examples of weighted k-out-of-n systems are presented to demonstrate the proposed models numerically and graphically. © 2020 Elsevier Ltd
Journal of Statistical Computation and Simulation (15635163) 90(17)pp. 3232-3249
We consider a coherent system consists of n components with independent and identically distributed lifetimes. We use the well-known signature-based representation of the system reliability to estimate the reliability of components of the system when the data is the system failure times collected according to a progressively censored scheme. Different estimators for the reliability of components are proposed and their properties are examined. A Monte Carlo simulation study have been carried out to compare the performance of the estimation methods. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
Mathematical Methods of Statistics (19348045) 29(3)pp. 149-158
Abstract: The concept of extended neighboring order statistics introduced in Asadi et al. (2001) is a general model containing models of ordered random variables that are included in the generalized order statistics. This model also includes several models of ordered random variables that are not included in the generalized order statistics and is a helpful tool in unifying characterization results from several models of ordered random variables. In this paper, some general classes of distributions with many applications in reliability analysis and engineering, such as negative exponential, inverse exponential, Pareto, negative Pareto, inverse Pareto, power function, negative power, beta of the first kind, rectangular, Cauchy, Raleigh, Lomax, etc., have been characterized by using the regression of extended neighboring order statistics and decreasingly ordered random variables. © 2020, Allerton Press, Inc.
Journal of Applied Probability (00219002) 57(3)pp. 899-910
In this paper the behaviour of the failure rate and reversed failure rate of an n-component coherent system is studied, where it is assumed that the lifetimes of the components are independent and have a common cumulative distribution function F. Sufficient conditions are provided under which the system failure rate is increasing and the corresponding reversed failure rate is decreasing. We also study the stochastic and ageing properties of doubly truncated random variables for coherent systems. © Applied Probability Trust 2020.
Statistics and Probability Letters (01677152) 145pp. 327-337
The paper describes and develops two concepts of conditional residual lifetime of the system, given that at a fixed time a certain number of components have failed but still there are some functioning components, and conditional inactivity time of the failed components in the system, given that at that time a certain number of components have failed but the system is still alive. We consider the [Formula presented]-out-of-[Formula presented] and the coherent systems consisting of [Formula presented] components whose lifetimes are assumed to have an exchangeable joint distribution function. Some stochastic ordering results on the conditional residual lifetime and the conditional inactivity time are provided. Several illustrative examples are also given. © 2018 Elsevier B.V.
IEEE Transactions on Reliability (15581721) 65(1)pp. 359-369
The purpose of this paper is to study the conditional inactivity time of failed components of a coherent system consisting of n identical components with statistically independent lifetimes. Different aging and stochastic properties of this conditional random variable are obtained. Some mixture representations for the conditional inactivity time of the components are also derived. We give sufficient conditions based on the signature and the common distribution of component lifetimes to obtain stochastic ordering results for coherent systems. Some stochastic orders on the dynamic signature of coherent systems are also provided. © 2015 IEEE.
Communications in Statistics - Theory and Methods (1532415X) 45(2)pp. 226-235
In this paper, we consider a k-out-of-n system consisting of n identical components with independent lifetimes. We show that when the underlying distribution function F(t) is absolutely continuous, then it can be univocally determined by some particular mean residual lives or mean inactivity times of the system. It is then shown that these results may be extended to coherent (or mixed) systems. © 2016 Taylor & Francis Group, LLC.
IEEE Transactions on Reliability (15581721) 64(4)pp. 1276-1286
We consider a coherent system consisting of n components where the component lifetimes are assumed to be random variables following a probabilistically exchangeable joint distribution function, where the probability distribution does not change with any permutation of the components. We study stochastic properties of the residual lifetime of live components of the system, under different conditions. The number of failed components of the system are explored, under the assumption that the system is operating at time t. We also study the probability that the ith component failure in the system causes the system failure, given that the system is operating at time t. The results of the paper extend some of the existing results in the literature. © 1963-2012 IEEE.
Reliability Engineering and System Safety (18790836) 144pp. 225-233
In designing structures of technical systems, the reliability engineers often deal with the reliability analysis of coherent systems. Coherent system has monotone structure function and all components of the system are relevant. This paper considers some particular models of coherent systems having identical components with independent lifetimes. The main purpose of the paper is to study conditional residual lifetime of coherent system, given that at a fixed time certain number of components have failed but still there are some functioning components. Different aging and stochastic properties of variables connected with the conditional residual lifetimes of the coherent systems are obtained. An expression for the parent distribution in terms of conditional mean residual lifetime is provided. The similar result is obtained for the conditional mean inactivity time of the failed components of coherent system. The conditional mean inactivity time of failed components presents an interest in many engineering applications where the reliability of system structure is important for designing and constructing of systems. Some illustrative examples with given particular distributions are also presented. © 2015 Elsevier Ltd
Journal Of The Iranian Statistical Society (17264057) 14(1)pp. 63-87
We consider a (n - κ + 1)-out-of-n system with exchangeable lifetimes of the components. The paper investigates the stochastic ordering properties of the residual lifetime of the system under condition that, at time t, at least (n - r + 1) components are alive. Some results are then extended to the case where the system has a coherent structure with exchangeable components.
Sankhya B (09768394) 77(1)pp. 141-164
Most of the research, on the study of the reliability properties of technical systems, assume that the components of the systems operate independently. However, in real life situation, it is more reasonable to assume that there is dependency among the components of the system. In this paper, we consider a (n−k+1)-out-of-n structure in which the component lifetimes are dependent random variables. We investigate stochastic properties of the inactivity time of the failed components of the system, extending some existing results in the literature where the components of the system are assumed to be independent and identically distributed. The results are then extended to the case where the system has an arbitrary coherent structure with exchangeable components. © 2014, Indian Statistical Institute.
Australian and New Zealand Journal of Statistics (1467842X) 56(4)pp. 385-394
Summary: In this paper, we consider some results on distribution theory of multivariate progressively Type-II censored order statistics. We also establish some characterizations of Freund's bivariate exponential distribution based on the lack of memory property. © 2014 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Naval Research Logistics (15206750) 61(7)pp. 549-556
Most of the research, on the study of the reliability properties of technical systems, assume that the components of the system operate independently. However, in real life situation, it is more reasonable to assume that there is dependency among the components of the system. In this article, we give sufficient conditions based on the signature and the joint distribution of component lifetimes to obtain stochastic ordering results for coherent and mixed systems with exchangeable components. Some stochastic orders on dynamic (or conditional) signature of coherent systems are also provided. © 2014 Wiley Periodicals, Inc.
Statistical Papers (09325026) 54(2)pp. 381-390
It is well-known, in the literature, that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. In the present paper, we consider the functional F(x) = F(xy) + F(xQ(y)), x, xQ(y) ε[0, θ), y ε [0,1], where F and Q satisfy certain conditions, to give some new characterization results on the generalized Pareto distributions based on progressively Type-II right censored order statistics. We prove the main results without restricting to distributions that are absolutely continuous with respect to Lebesgue measure. © 2012 Springer-Verlag.
Applied And Computational Mathematics (16833511) 11(3)pp. 368-377
Suppose that n independent and identically distributed items have been placed in a life-test with Progressive Type-II censoring scheme (R1, R2, ⋯, Rm)- In this paper, we investigate some characterizations and ordering results based on the residual lifetimes of the remaining items following the kth failure in the test.
Pakistan Journal Of Statistics (10129367) 28(3)pp. 303-313
For practical applications in reliability analysis, the assumption of dependence among lifetimes of components of the system is more realistic than the assumption of independence. This paper investigates the residual lifetimes of coherent systems in situation where there exists a stochastic dependence among the components of the system. A stochastic comparison among residual lives of k-out-of-n systems with exchangeable components is conducted. The mean residual life function of a k-out-of-n system with exchangeable components is investigated. Special examples in the case of a system consisting of two dependent components with a joint Gumbel's bivariate exponential distribution and for a system having n components with Marshall and Olkin's multivariate exponential distribution, illustrating the behavior of the mean residual life function are provided. The extension to general coherent systems with exchangeable components using properties of Samaniego's signature are given. © 2012 Pakistan Journal of Statistics.
Metrika (1435926X) 75(7)pp. 997-1007
In the present study we extend and unify some existing results in the literature on characterization of the generalized Pareto distributions based on generalized order statistics. © 2011 Springer-Verlag.
Probability in the Engineering and Informational Sciences (02699648) 25(2)pp. 187-204
The generalized order statistics (GOS) model is a unified model that contains the well-known ordered random data such as order statistics and record values. In the present article, we investigate some stochastic ordering results and aging properties of the conditional GOS. The results of the article subsume some of the existing results, which recently are obtained in the literature, on conditional GOS. In particular, our results hold for the model of progressively type II right censored order statistics without any restriction on the censoring scheme. © 2011 Cambridge University Press.
Journal Of The Iranian Statistical Society (17264057) 10(1)pp. 13-27
The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any restriction on the parameters of the model of dual GOS.
Statistics (02331888) 45(3)pp. 237-255
In this paper, we propose a measure for obtaining the expectation of time between two lower k-records under the condition that the greater one is given. Several properties of the proposed measure are derived. Some characterization results and stochastic comparisons based on the new measure are also provided. © 2011 Taylor & Francis.
Metrika (1435926X) 72(1)pp. 59-73
In the present paper, we consider a (n - k + 1)-out-of-n system with identical components where it is assumed that the lifetimes of the components are independent and have a common distribution function F. We assume that the system fails at time t or sometime before t, t > 0. Under these conditions, we are interested in the study of the mean time elapsed since the failure of the components. We call this as the mean past lifetime (MPL) of the components at the system level. Several properties of the MPL are studied. It is proved that the relation between the proposed MPL and the underlying distribution is one-to-one. We have shown that when the components of the system have decreasing reversed hazard then the MPL of the system is increasing with respect to time. Some examples are also provided. © Springer-Verlag 2009.
Bulletin Of The Iranian Mathematical Society (1017060X) 36(1)pp. 257-272
It is well-known that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. Here, we consider the functional equation F(x) = F(xy) + F(xQ(y)), x, xQ(y) ∈ [0, θ), y ∈ [0, 1], where F and Q satisfy certain conditions, to give some new characterization results on exponential, power and Pareto distributions using the concepts of conditional random variables and order statistics. © 2010 Iranian Mathematical Society.
Statistics and Probability Letters (01677152) 80(9-10)pp. 848-859
In the present paper we propose a new concept of the residual lifetime of progressively Type-II right censored order statistics (PCOS) and study some of its properties. Some new stochastic comparisons are made on the residual lifetimes of PCOS. The case when the behavior of the data generator F, in terms of different aging concepts, is given the behavior of the residual lifetimes of PCOS is investigated. We also concentrate on the mean of the residual lifetime of the PCOS. Some characterizations of the generalized Pareto distribution based on the mean of the residual lifetime of PCOS are also presented. © 2010 Elsevier B.V. All rights reserved.
Communications in Statistics - Theory and Methods (1532415X) 37(9)pp. 1347-1352
In recent years, several attempts have been made to characterize the generalized Pareto distribution (GPD) based on the properties of order statistics and record values. In the present article, we give a characterization result on GPD based on the spacing of generalized order statistics.
Communications in Statistics - Theory and Methods (1532415X) 36(7)pp. 1333-1341
In recent years, several attempts have been made to characterize the generalized Pareto distributions (GPD) based on the properties of order statistics and record values. In the present article, we give some characterization results on GPD based on order statistics and generalized order statistics. Some characterizations of uniform distribution based on expectation of some functions of order statistics are also given.
