Importance measures in reliability and mathematical programming

The importance measures have been a sensitivity analysis for a probabilistic system and are applied in diverse fields along with other design tools. This paper provides a comprehensive view on modeling the importance measures to solve the reliability problems such as component assignment problems, redundancy allocation, system upgrading, and fault diagnosis and maintenance. It also investigates importance measures in broad applications such as networks, mathematical programming, sensitivity and uncertainty analysis, and probabilistic risk analysis and probabilistic safety assessment. The importance-measure based methods are among the most practical decision tools.     

An effective immune based two-phase approach for the optimal reliability-redundancy allocation problem

Highly reliable systems can reduce loss of money and time in practice. System reliability can be enhanced by: (i) increasing component reliabilities and/or (ii) providing redundancy at the component level. A trade-off between these two options is necessary for nonlinear-constrained reliability optimization. The problem of maximizing system reliability through component reliability choices and component redundancy is called as reliability-redundancy allocation problem, and it is a difficult but realistic nonlinear mixed-integer optimization problem. In this paper, under nonlinear constraints of weight, cost, and volume, we propose a new immune based two-phase approach to solve the reliability-redundancy allocation problem. In the first phase, an immune based algorithm (IA) is developed to solve the allocation problem, and in the second phase we present a new procedure to improve the solutions by IA. Numerical results of four benchmark problems are reported and compared. As shown, the solutions by the new proposed approach are all superior to those best solutions by typical approaches in the literature.     

Modelling redundancy allocation for a fuzzy random parallel-series system

Due to subjective judgment, imprecise human knowledge and perception in capturing statistical data, the real data of lifetimes in many systems are both random and fuzzy in nature. Based on the fuzzy random variables that are used to characterize the lifetimes, this paper studies the redundancy allocation problems to a fuzzy random parallel-series system.Two fuzzy random redundancy allocation models (FR-RAM) are developed through reliability maximization and cost minimization, respectively. Some properties of the FR-RAM are obtained, in which an analytical formula of reliability with convex lifetimes is derived and the sensitivity of the reliability is discussed. To solve the FR-RAMs, we first address the computation of reliability. A random simulation method based on the derived analytical formula is proposed to compute the reliability with convex lifetimes. As for the reliability with nonconvex lifetimes, the technique of fuzzy random simulation together with the discretization method of fuzzy random variable is employed to compute the reliability, and a convergence theorem of the fuzzy random simulation is proved. Subsequently, we integrate the computation approaches of the reliability and genetic algorithm (GA) to search for the approximately optimal redundancy allocation of the models. Finally, some numerical examples are provided to illustrate the feasibility of the solution algorithm and quantify its effectiveness.     

Coordinated maintenance in a multi-component system with compound Poisson deterioration

This paper proposes a coordinated maintenance model in a multi-component system with compound Poisson deterioration. The main contribution is a policy-iteration approach for Semi-Markov processes that optimizes the threshold at which the component is eligible for preventive maintenance if another component requires corrective maintenance. The methodology is novel as we develop explicit expressions for the policy evaluation and prove these expressions to satisfy the set of linear equations which characterize traditional policy evaluation. By doing so, long-run average cost savings are achieved, since setup costs can be shared.     

A polynomial expression for the Owen value in the maintenance cost game

The class of maintenance cost games was introduced in 2000 to deal with a cost allocation problem arising in the reorganization of the railway system in Europe. The main application of maintenance cost games regards the allocation of the maintenance costs of a facility among the agents using it. To that aim it was first proposed to utilize the Shapley value, whose computation for maintenance cost games can be made in polynomial time. In this paper, we propose to model this cost allocation problem as a maintenance cost game with a priori unions and to use the Owen value as a cost allocation rule. Although the computation of the Owen value has exponential complexity in general, we provide an expression for the Owen value of a maintenance cost game with cubic polynomial complexity. We finish the paper with an illustrative example using data taken from the literature of railways management.     

Equivalences between Data Envelopment Analysis and the theory of redundancy in linear systems

This paper establishes how the non-parametric frontier estimation methodology of Data Envelopment Analysis (DEA) and the classical problem of detecting redundancy in a system of linear inequalities are connected. We present an analysis of the sets generated in two of DEA's models from where the empirical efficient production frontier is established from the point of view of polyhedral set theory. This yields convenient alternative characterizations of these sets which provide new insights about their properties. We use these insights to show how these polyhedral sets connect DEA to redundancy in linear systems. This means that DEA can benefit from a rich and well-established collection of computational and theoretical results which apply directly from redundancy in linear systems.     

Optimal allocation of redundancies in series systems

It is of great interest for the problem of how to allocate redundancies in a system so as to optimize the system performance in reliability engineering and system security. In this paper, we consider the problems of optimal allocation of both active and standby redundancies in series systems in the sense of various stochastic orderings. For the case of allocating one redundancy to a series system with two exponential components, we establish two likelihood ratio order results for active redundancy case and standby redundancy case, respectively. We also discuss the case of allocating K active redundancies to a series system and establish some new results. The results developed here strengthen and generalize some of the existing results in the literature. Specifically, we give an answer to an open problem mentioned in Hu and Wang [T. Hu, Y. Wang, Optimal allocation of active redundancies in r-out-of-n systems, Journal of Statistical Planning and Inference 139 (2009) 3733–3737]. Numerical examples are provided to illustrate the theoretic results established here.     

Scheduling of railway track maintenance activities and crews

Before railway track maintenance crews can undertake any work, the allocation of activities to available time intervals in the train schedule as well as to crews must be undertaken. This paper puts forward a model aimed at determining the best allocation of maintenance activities and crews so as to mininise the disruption to and from scheduled trains and to reduce completion time. The model is subject to constraints such as available budget; maintenance activity precedence; track availability; and minimum travel time between track links. Solution to the model is found using the tabu search heuristic for which the neighbourhood is defined by swapping the order of jobs, maintenance crews, or both. Application to a 300?km track corridor with a four day planning horizon is discussed along with the impacts of modifying the number of maintenance crews. The optimal schedule achieved an 8% reduction in expected interference delay with the train schedule and a 7% reduction in average completion times, relative to the solution which was constructed manually.     

基于灰色Malmquist-DEA的中国粮食生产效率分析

选取全国各省粮食生产指标面板数据,对数据进行灰色拟合处理,采用数据包络分析(DEA)法,测算各区域的粮食生产效率,得到投入产出体系的要素冗余值;同时测算了各区域的全要素生产率,并对Malmquist指数进行分解,分析各区域的效率变化和技术变化趋势.结果显示:东、西部地区粮食生产投入要素大量冗余,要素配置效率不高,中部地区要素利用率较高,要素配置趋于合理;效率变化对全要素生产率的作用不明显,而技术进步是全要素生产率增长的关键驱动因素.     

基于DEA的资源配置状况分析

DEA在经济系统中的应用实质是对资源配置状况的分析，但由于分析结果过于简单，构成了该方法推广应用的障碍，章通过深入分析，发现导致决策单元无效的三大成因，把DEA对决策单元的分析结果由两种增加到四种，并相应的提出价格无效、绝对冗余、相对冗余等新概念，从而为管理改善决策提供明确的指导方向。     

Optimal power allocation for SM-OFDM systems with imperfect channel estimation

This paper analyses the bit error rate (BER) of the spatial modulation orthogonal frequency division multiplex (SM-OFDM) system and derives the optimal power allocation between the data and the pilot symbols by minimizing the upper bound for the BER operating with imperfect channel estimation. Furthermore, we prove the proposed optimal power allocation scheme applies to all generalized linear interpolation techniques with the minimum mean square error (MMSE) channel estimation . Simulation results show that employing the proposed optimal power allocation provides a substantial gain in terms of the average BER performance for the SM-OFDM system compared to its equal-power-allocation counterpart.     

A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components

In this paper, we have considered the problem of constrained redundancy allocation of series system with interval valued reliability of components. For maximizing the overall system reliability under limited resource constraints, the problem is formulated as an unconstrained integer programming problem with interval coefficients by penalty function technique and solved by an advanced GA for integer variables with interval fitness function, tournament selection, uniform crossover, uniform mutation and elitism. As a special case, considering the lower and upper bounds of the interval valued reliabilities of the components to be the same, the corresponding problem has been solved. The model has been illustrated with some numerical examples and the results of the series redundancy allocation problem with fixed value of reliability of the components have been compared with the existing results available in the literature. Finally, sensitivity analyses have been shown graphically to study the stability of our developed GA with respect to the different GA parameters.     

Simulation optimization for an emergency department healthcare unit in Kuwait

This paper integrates simulation with optimization to design a decision support tool for the operation of an emergency department unit at a governmental hospital in Kuwait. The hospital provides a set of services for different categories of patients. We present a methodology that uses system simulation combined with optimization to determine the optimal number of doctors, lab technicians and nurses required to maximize patient throughput and to reduce patient time in the system subject to budget restrictions. The major objective of this decision supporting tool is to evaluate the impact of various staffing levels on service efficiency. Experimental results show that by using current hospital resources, the optimization simulation model generates optimal staffing allocation that would allow 28% increase in patient throughput and an average of 40% reduction in patients’ waiting time.     

A Note on the Power of Personal Identifying Information

The values of names, addresses and dates of birth for identifying individuals uniquely depends on several factors. This note shows how to combine the inherent power of an identifier, its availability and its error rate to give a practical measure for ranking its usefulness. The theory is developed in terms of selecting a number of non-unique identifiers to form a composite key with sufficient redundancy to identify individuals in an automated system. The note concludes with an indication of other classification, allocation and decision processes to which the technique may be applied.     

A model to enhance the reliability of the serial parallel systems with component mixing

System reliability, especially for serial parallel systems, has attracted much attention in recent years. Redundancy allocation is a technique to increase the reliability of the serial parallel systems. Supplying redundant components depends on some restrictions such as available budget, weight, space, etc. This paper proposes a new model for redundancy allocation problems (RAPs) by considering discount policy. The proposed model attempts to maximize the reliability of a system by gathering various components where there are some limitations on budgeting. We present two models with different assumptions including all unit discount and incremental discount strategies. The resulted formulations are nonlinear integer models and categorized as NP-hard. Therefore, some heuristics and meta-heuristics are designed to solve the resulted models, efficiently.     

Pruned Pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives

In this paper, a new methodology is presented to solve different versions of multi-objective system redundancy allocation problems with prioritized objectives. Multi-objective problems are often solved by modifying them into equivalent single objective problems using pre-defined weights or utility functions. Then, a multi-objective problem is solved similar to a single objective problem returning a single solution. These methods can be problematic because assigning appropriate numerical values (i.e., weights) to an objective function can be challenging for many practitioners. On the other hand, methods such as genetic algorithms and tabu search often yield numerous non-dominated Pareto optimal solutions, which makes the selection of one single best solution very difficult. In this research, a tabu search meta-heuristic approach is used to initially find the entire Pareto-optimal front, and then, Monte-Carlo simulation provides a decision maker with a pruned and prioritized set of Pareto-optimal solutions based on user-defined objective function preferences. The purpose of this study is to create a bridge between Pareto optimality and single solution approaches.     

Connectivity modeling and optimization of linear consecutively connected systems with repairable connecting elements

Linear consecutively connected systems (LCCSs) are systems containing a linear sequence of ordered nodes. Connection elements (CE) characterized by diverse connection ranges, time-to-failure and time-to-repair distributions are allocated to different nodes to provide the system connectivity, i.e., a connection between the source and sink nodes of the LCCS. Examples of LCCSs abound in practical applications such as flow transmission systems and radio communication systems. Considerable research efforts have been expended in modeling and optimizing LCCSs. However, most of the existing works have assumed that CEs either are non-repairable or undergo a restrictive minimal repair policy with constant repair time. This paper makes new technical contributions by modeling and optimizing LCCSs with CEs under corrective maintenance with random repair time and different repair policies (minimal, perfect, and imperfect). The characteristics of CEs can depend on their location because the distance between adjacent nodes and conditions of CE operation and maintenance at different nodes can be different, which further complicates the problem. We first propose a discrete numerical algorithm to evaluate the instantaneous availability of each CE. A universal generating function based method is then implemented for assessing instantaneous and expected system connectivity for a specific CE allocation. As the CE allocation can have significant impacts on the system connectivity, we further define and solve the optimal CE allocation problem, whose objective is to find the CE allocation among LCCS nodes maximizing the expected system connectivity over a given mission time. Effects of different parameters including repair efficiency, mission time and repair time are investigated. As illustrated through examples, optimization results can facilitate optimal decisions on robust design and effective operation and maintenance managements of LCCSs.     

Optimisation of sinking funds for major repairs in a housing association

Changes to the financial framework regulating housing associations require them to create a sinking fund that will accrue the necessary cash for future maintenance work to their stock. This paper presents an alternative to the conventional methods by using a Linear Programming model to obtain sinking fund strategies. The relevance of such modelling is discussed with reference to the evolving Sinking Fund system in the UK and European Housing Association movements. The methodology is applied to data from a Housing Association in Scotland. The paper concludes that the LP model offers a degree of flexibility not found in existing practice. The work has relevance to the long-term maintenance management of any built asset.     

警车配置及巡逻方案研究

以警车的配置与巡逻方案为研究对象,建立了一套警车巡逻模型,并提出巡逻效果显著度及隐藏性的评价标准,分别针对警车初始位置配置与巡逻方案的制定,提出警车配置优化选址的贪婪算法与基于多Agent的警车巡逻方案设计方法,给出了不同情景下的配置及巡逻方案:①在只考虑警车选址配置的情况下,配置19辆警车可以使全市路网警车覆盖率达到92.8%;②在顾及巡逻效果显著性与隐藏性的情况下,配置25辆警车使全市路网在整个巡逻过程中平均警车覆盖率达到90.9%;③在配置10辆警车的情况下,使得全市路网在整个巡逻过程中平均警车覆盖率达到61.5%.     

汽车修理排队系统数据分析及配置优化

利用排队理论研究汽车修理系统,通过实例对输入过程和服务时间数据的整理进而验证了它们的分布规律,由此指出了应用排队模型类型,得到排队系统的各种基本运行参数,然后从顾客消费心理考虑,以区间估计的方法,在进入修理店时告知需要等待时间,最后给出汽车修理服务台的优化配置数.