Machine maintenance with workload considerations

Machine maintenance is modeled in the setting of a single‐server queue. Machine deterioration corresponds to slower service rates and failure. This leads to higher congestion and an increase in customer holding costs. The decision‐maker decides when to perform maintenance, which may be done pre‐emptively; before catastrophic failures. Similar to classic maintenance control models, the information available to the decision‐maker includes the state of the server. Unlike classic models, the information also includes the number of customers in queue. Considered are both a repair model and a replacement model. In the repair model, with random replacement times, fixed costs are assumed to be constant in the server state. In the replacement model, both constant and variable fixed costs are considered. It is shown in general that the optimal maintenance policies have switching curve structure that is monotone in the server state. However, the switching curve policies for the repair model are not always monotone in the number of customers in the queue. Numerical examples and two heuristics are also presented. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

An optimum multiechelon repair policy and stockage model

Currently, sophisticated multiechelon models compute stockage quantities for spares and repair parts that will minimize total inventory investment while achieving a target level of weapon system operational availability. The maintenance policies to be followed are input to the stockage models. The Optimum Allocation of Test Equipment/Manpower Evaluated Against Logistics (OATMEAL) model will determine optimum maintenance as well as stockage policies for a weapon system. Specifically, it will determine at which echelon each maintenance function should be performed, including an option for component or module throwaway. Test equipment requirements to handle work load at each echelon are simultaneously optimized. Mixed-integer programming (MIP) combined with a Lagrangian approach are used to do the constrained cost minimization, that is, to minimize all costs dependent on maintenance and stockage policies while achieving a target weapons system operational availability. Real-life test cases are included.     

Optimal joint preventive maintenance and production policies

We study joint preventive maintenance (PM) and production policies for an unreliable production‐inventory system in which maintenance/repair times are non‐negligible and stochastic. A joint policy decides (a) whether or not to perform PM and (b) if PM is not performed, then how much to produce. We consider a discrete‐time system, formulating the problem as a Markov decision process (MDP) model. The focus of the work is on the structural properties of optimal joint policies, given the system state comprised of the system's age and the inventory level. Although our analysis indicates that the structure of optimal joint policies is very complex in general, we are able to characterize several properties regarding PM and production, including optimal production/maintenance actions under backlogging and high inventory levels, and conditions under which the PM portion of the joint policy has a control‐limit structure. In further special cases, such as when PM set‐up costs are negligible compared to PM times, we are able to establish some additional structural properties. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

MAD: Mathematical analysis of downtime

The MAD model presents a mathematic treatment of the relationship between aircraft reliability and maintainability, system manning and inspection policies, scheduling and sortie length, and aircraft downtime. Log normal distributions are postulated for subsystem repair times and simultaneous repair of malfunctions is assumed. The aircraft downtime for maintenance is computed with the distribution of the largest of k log normal distributions. Waiting time for maintenance men is calculated either by using a multiple-channel queuing model or by generating the distribution of the number of maintenance men required and comparing this to the number of men available to determine the probability of waiting at each inspection.     

Modified discrete preventive maintenance policies

This article proposes a modified preventive maintenance (PM) policy which may be done only at scheduled times nT (n = 1,2, …): The PM is done at the next such time if and only if the total number of failures exceeds a specified number k. The optimal number k^* to minimize the expected cost rate is discussed. Further, four alternative similar PM models are considered, when the system fails due to a certain number of faults, uses, shocks, and unit failures.     

Optimal state-dependent pricing policies for a class of stochastic multiunit service systems

This paper models a k-unit service system (e.g., a repair, maintenance, or rental facility) with Poisson arrivals, exponential service times, and no queue. If we denote the number of units that are busy as the state of the system, the state-dependent pricing model formalizes the intuitive notion that when most units are idle, the price (i.e., the service charge per unit time) should be low, and when most units are busy, the price should be higher than the average. A computationally efficient algorithm based on a nonlinear programming formulation of the problem is provided for determination of the optimal state-dependent prices. The procedure ultimately reduces to the search on a single variable in an interval to determine the unique intersection point of a concave increasing function and a linear decreasing function. The algorithm takes, on the average, only about 1/2 second per problem on the IBM 360/65 (FORTRAN G Compiler). A discrete optimal-control approach to the problem is shown to result in essentially the same procedure as the nonlinear-programming formulation. Several properties of the optimal state-dependent prices are given. Comparisons of the optimal values of the objective function for the state-dependent and state-independent pricing policies show that the former is on the average, only about 0.7% better than the latter, which may explain partly why state-dependent pricing is not prevalent in many service systems. Potential generalizations of the model are discussed.     

Spares stocking policies for repairable items with dependent repair times

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.     

A unifying treatment of replacement policies with minimal repair

This article presents the mathematical background for analyzing maintenance policies with minimal repair. Standard maintenance policies are summarized. A general failure model is introduced which allows a unifying treatment of more recent maintenance policies with minimal repair. In particular, repair cost limit maintenance policies are considered. © 1993 John Wiley & Sons, Inc.     

Analyzing availability using transfer function models and cross spectral analysis

If we look at the literature of reliability and life testing we do not see much on the use of the powerful methods of time series analysis. In this paper we show how the methods of multivariate time series analysis can be used in a novel way to investigate the interrelationships between a series of operating (running) times and a series of maintenance (down) times of a complex system. Specifically, we apply the techniques of cross spectral analysis to help us obtain a Box-Jenkins type transfer function model for the running times and the down times of a nuclear reactor. A knowledge of the interrelationships between the running times and the down times is useful for an evaluation of maintenance policies, for replacement policy decisions, and for evaluating the availability and the readiness of complex systems.     

某型武装直升机武器系统故障诊断研究

战时快速准确地查找故障部件和制定排故方案是实施战场抢修的前提和基础。目前武装直升机武器系统结构组成日趋复杂,功能模块高度集成,仅凭人工经验进行维护难度较大。为了提高故障诊断效率,采用故障树分析与专家经验相结合的方法,建立了某型武装直升机武器系统故障模型,设计了一种快速故障诊断与辅助决策系统,有效减少了维修保障人员故障排除时间,提升了故障处置效率与准确度,具有重要的实际应用价值。     

Preventive maintenance and replacement under additive damage

A system deteriorates due to shocks received at random times, each shock causing a random amount of damage which accumulates over time and may result in a system failure. Replacement of a failed system is mandatory, while an operable one may also be replaced. In addition, the shock process causing system deterioration may be controlled by continuous preventive maintenance expenditures. The joint problem of optimal maintenance and replacement is analyzed and it is shown that, under reasonable conditions, optimal maintenance rate is decreasing in the cumulative damage level and that beyond a certain critical level the system should be replaced. Meaningful bounds are established on the optimal policies and an illustrative example is provided.     

装备战损率与损坏率关系研究

装备的损坏率是决定装备维修保障的重要依据,通过对装备战损率及其分布的分析,给出了在维修机构修复能力一定的条件下相应的损坏率及其分布的模型,可为装备维修保障提供决策。     

The reliability of multicomponent systems subject to cannibalization

A reliability model for multicomponent multistate systems is presented. This is a generalization of a model previously studied by Hirsch, Meisner, and Boll. In the earlier model, when a failure occurs for which no replacement spare is available, the locations using the same type of part as that having failed are “cannibalized” so as to allocate the shortages to locations where they are least detrimental to system performance. Here, we permit certain restrictions to be imposed upon the cannibalization procedure, and develop effective techniques for relating the probability laws governing the level of system performance to the system structure, cannibalization policy, kit of spare parts, and part reliabilities.     

A heuristic with tie breaking for certain 0–1 integer programming models

A heuristic for 0–1 integer programming is proposed that features a specific rule for breaking ties that occur when attempting to determine a variable to set to 1 during a given iteration. It is tested on a large number of small- to moderate-sized randomly generated generalized set-packing models. Solutions are compared to those obtained using an existing well-regarded heuristic and to solutions to the linear programming relaxations. Results indicate that the proposed heuristic outperforms the existing heuristic except for models in which the number of constraints is large relative to the number of variables. In this case, it performs on par with the existing heuristic. Results also indicate that use of a specific rule for tie breaking can be very effective, especially for low-density models in which the number of variables is large relative to the number of constraints.     

A bivariate optimal replacement policy for a cold standby repairable system with repair priority

In this article, an optimal replacement policy for a cold standby repairable system consisting of two dissimilar components with repair priority is studied. Assume that both Components 1 and 2, after repair, are not as good as new, and the main component (Component 1) has repair priority. Both the sequence of working times and that of the components'repair times are generated by geometric processes. We consider a bivariate replacement policy (T,N) in which the system is replaced when either cumulative working time of Component 1 reaches T, or the number of failures of Component 1 reaches N, whichever occurs first. The problem is to determine the optimal replacement policy (T,N)* such that the long run average loss per unit time (or simply the average loss rate) of the system is minimized. An explicit expression of this rate is derived, and then optimal policy (T,N)* can be numerically determined through a two‐dimensional‐search procedure. A numerical example is given to illustrate the model's applicability and procedure, and to illustrate some properties of the optimal solution. We also show that if replacements are made solely on the basis of the number of failures N, or solely on the basis of the cumulative working time T, the former class of policies performs better than the latter, albeit only under some mild conditions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

有限维修能力下多级保障系统装备时变可用度评估及保障方案优化

备件库存和站点维修能力是影响备件维修周转的重要因素，制约装备使用效果。针对备件需求随任务阶段动态变化的装备保障方案评估和优化问题，考虑站点维修能力对备件维修过程的影响，结合METRIC建模方法和动态排队理论，建立了有限维修能力下多级保障系统装备时变可用度评估模型。在评估模型基础之上，以保障费用为优化目标，装备可用度为约束条件，建立了任务期内多级保障系统保障方案优化模型。以任务期内的最低可用度所对应的备件短缺数为观测值，分析了各项资源的边际效益值，采用边际优化算法对各项资源进行优化计算。算例分析表明，评估模型能够计算多级保障系统任务期内各阶段装备可用度；保障方案优化模型和方法能够得到各项保障资源的优化配置方案。提出的模型和优化方法能够为装备保障人员制定合理的保障方案提供决策支持。     

有限维修能力下多级保障系统装备时变可用度评估及保障方案优化

备件库存和站点维修能力是影响备件维修周转的重要因素,制约着装备的使用效果。针对备件需求随任务阶段动态变化时装备保障方案的评估和优化问题,考虑站点维修能力对备件维修过程的影响,结合METRIC建模方法和动态排队理论,建立了有限维修能力下多级保障系统装备时变可用度评估模型。在评估模型基础之上,以保障费用为优化目标、装备可用度为约束条件,建立任务期内多级保障系统保障方案优化模型。以任务期内的最低可用度所对应的备件短缺数为观测值,分析各项资源的边际效益值,采用边际优化算法对各项资源进行优化计算。算例分析表明,评估模型能够计算多级保障系统任务期内各阶段装备可用度;保障方案优化模型和方法能够得到各项保障资源的优化配置方案。提出的模型和优化方法能够为装备保障人员制订合理的保障方案提供决策支持。     

Generalized multicomponent systems under cannibalization

Using the theory of Hirsch, Meisner, and Boll, we study the consequences of interchanging parts within a generalized coherent structure. This procedure has been termed “cannibalization.” The theory of cannibalization is extended to the case where each component can operate at several levels of partial performance and a representation theorem is derived, which expresses the state of a system as a function of the number of working parts at each level. The stochastic theory of these systems is then investigated.     

Stochastic scheduling subject to machine breakdowns: The preemptive‐repeat model with discounted reward and other criteria

We consider the problem of scheduling a set of jobs on a single machine subject to random breakdowns. We focus on the preemptive‐repeat model, which addresses the situation where, if a machine breaks down during the processing of a job, the work done on the job prior to the breakdown is lost and the job will have to be started from the beginning again when the machine resumes its work. We allow that (i) the uptimes and downtimes of the machine follow general probability distributions, (ii) the breakdown process of the machine depends upon the job being processed, (iii) the processing times of the jobs are random variables following arbitrary distributions, and (iv) after a breakdown, the processing time of a job may either remain a same but unknown amount, or be resampled according to its probability distribution. We first derive the optimal policy for a class of problems under the criterion to maximize the expected discounted reward earned from completing all jobs. The result is then applied to further obtain the optimal policies for other due date‐related criteria. We also discuss a method to compute the moments and probability distributions of job completion times by using their Laplace transforms, which can convert a general stochastic scheduling problem to its deterministic equivalent. The weighted squared flowtime problem and the maintenance checkup and repair problem are analyzed as applications. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Optimal design of a multi-item,multi-location,multi-repair type repair and supply system

The design of a system with many locations, each with many items which may fail while in use, is considered. When items fail, they require repair; the particular type of repair being governed by a probability distribution. As repairs may be lengthy, spares are kept on hand to replace failed items. System ineffectiveness is measured by expected weighted shortages over all items and locations, in steady state. This can be reduced by either having more spares or shorter expected repair times. Design consists of a provisioning of the number of spares for each item, by location; and specifying the expected repair times for each type of repair, by item and location. The optimal design minimizes expected shortages within a budget constraint, which covers both (i) procurement of spares and (ii) procurement of equipment and manning levels for the repair facilities. All costs are assumed to be separable so that a Lagrangian approach is fruitful, yielding an implementable algorithm with outputs useful for sensitivity analysis. A numerical example is presented.