考虑老化因素的串联系统不完全维修决策优化

针对Markov过程和虚拟役龄方法难以全面描述系统不完全维修的问题,构建基于准更新过程的串联系统可用度分析模型,提出平均故障间隔时间和平均维修间隔时间确定方法;引入运行时间缩减因子、维修时间增长因子描述考虑老化因素的不完全维修过程,确定系统可用度指标确定方法;根据单位时间维修成本、系统平均运行时间约束条件,确定系统在不同指标下的不完全维修次数.以某控制系统为例,应用传统方法验证不完全维修条件下可用度确定方法的有效性,并以维修成本、运行时间为约束确定不同条件下的不完全维修次数,为维修决策制定提供理论指导.     

Optimal imperfect preventive maintenance policies for a used system

In some practical situations, it may be more economical to work a used system than do a new one. From this viewpoint, this article considers three basic preventive maintenance (PM) policies for a used system: the system with initial variable damage Y ₀ begins to operate at time 0, and suffers damage due to shocks. It fails when the total damage exceeds a failure level K and corrective maintenance is made immediately. To prevent such failure, it undergoes PM at a planned time T, a shock number N and a damage level k, but maintenances are imperfect. However, failure rate of a used system maybe higher than that of a new one, so some maintenance is applied to the policies at each shock in the extended models. Using the theory of cumulative processes, expected cost rate models are obtained, optimal policies which minimise them are derived analytically and discussed numerically.     

Optimal maintenance policies with lead times and repair

Maintenance policies with lead times and repair are discussed. We first discuss ordering policy with repair and refer to inspection-ordering policy. In each policy, as a criterion of optimality, we apply cost effectiveness which balances system effectiveness and cost, and obtain the optimal policies. It is shown that, under certain conditions, there exists a finite and unique optimal policy.     

Optimal maintenance time for imperfect maintenance actions on repairable product

This paper develops a maintenance strategy for repairable products that combines imperfect maintenance actions at pre-scheduled times and minimal repair actions for failures. Under a power law process of failures, an expected total cost is developed that involves the sum of the total cost of imperfect preventive maintenances and the expected total cost of minimal repairs. Moreover, a searching procedure is provided to determine the optimal maintenance schedule within a finite time span of warranty. When the parameters of the power law process are unknown, the accuracy of the estimated maintenance schedule is evaluated based on data through an asymptotic upper bound for the difference of the true expected total cost and its estimate. The proposed method is applied to an example regarding the maintenance of power transformers and the performance of the proposed method is investigated through a numerical study. Numerical results show that the proposed maintenance strategy could save cost whether an imperfect maintenance action or the perfect maintenance action is implemented.     

Optimal lot-sizing problem with imperfect maintenance and imperfect production

In this paper, we develop an integrated model for the joint determination of both economic production quantity and level of preventive maintenance (PM) for an imperfect production process. This process has a general deterioration distribution with increasing hazard rate. The effect of PM activities on the deterioration pattern of the process is modelled using the imperfect maintenance concept. In this concept, it is assumed that after performing PM, the ageing of the system is reduced in proportion to the PM level. After a period of time in production, the process may shift to out-of-control states, either type I or type II. A minimal repair will remove the type I out-of-control state. If a type II out-of-control state occurs, the production process has to stop, and then restoration work is carried out. Examples of Weibull shock models are given to show that the use of PM reduces costs.     

Repair-limit risk-free warranty policies with imperfect repair

The current competitive market environment requires manufacturers to continuously provide better service and support. As a result, warranty considerations emerge as a significant instrument for increasing product marketability. In this paper, we propose a new warranty policy, the repair-limit risk-free warranty with a threshold point on the number of repairs, where replacement is deemed to be more cost effective thereafter. Consumers are better off with this than with a traditional free-repair policy since they could be compensated with a new product in case of premature failures. As for the manufacturers, it not only offers extra marketing incentives, but also reduces the possibility of high-cost lawsuits due to the products with "proven" bad quality. Some useful results of the warranty cost of imperfectly repaired products are derived through a censored quasi-renewal process.     

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.     

Optimal lot sizing with maintenance actions and imperfect production processes

Porteus (1986) explored an economic order quantity model with imperfect production processes that the approximate lot size is derived. Basically, he dealt with the lot size problem is rather meaningful. However, for mathematical simplicity, he adopted a truncated Taylor series expansion to present the approximate expected total cost function that results in overvalue of expected total cost. In this paper, we extend Porteus (1986) to present the optimal lot size model for defective items with a constant probability when the system is out-of-control and taking the maintenance cost into account. We show that there exists a unique optimal lot size such that the expected total cost is minimised. In addition, the bounds of optimal lot size are provided to develop the solution procedure. Finally, numerical examples are given to illustrate the theoretical results and compare optimal solutions obtained by using our approach and Porteus's approach. Numerical results show that our approach is better.     

Optimal maintenance policies for systems subject to a Markovian operating environment

Many stochastic models of repairable equipment deterioration have been proposed based on the physics of failure and the characteristics of the operating environment, but they often lead to time to failure and residual life distributions that are quite complex mathematically. The first objective of our study is to investigate the potential for approximating these distributions with traditional time to failure distribution. We consider a single-component system subject to a Markovian operating environment such that the system’s instantaneous deterioration rate depends on the state of the environment. The system fails when its cumulative degradation crosses some random threshold. Using a simulation-based approach, we approximate the time to first failure distribution for this system with a Weibull distribution and assess the quality of this approximation. The second objective of our study is to investigate the cost benefit of applying a condition-based maintenance paradigm (as opposite to a scheduled maintenance paradigm) to the repairable system of interest. Using our simulation model, we assess the cost benefits resulting from condition-based maintenance policy, and also the impact of the random prognostic error in estimating system condition (health) on the cost benefits of the condition-based maintenance policy.     

Optimal pricing policies for services with consideration of facility maintenance costs

For survival and success, pricing is an essential issue for service firms. This article deals with the pricing strategies for services with substantial facility maintenance costs. For this purpose, a mathematical framework that incorporates service demand and facility deterioration is proposed to address the problem. The facility and customers constitute a service system driven by Poisson arrivals and exponential service times. A service demand with increasing price elasticity and a facility lifetime with strictly increasing failure rate are also adopted in modelling. By examining the bidirectional relationship between customer demand and facility deterioration in the profit model, the pricing policies of the service are investigated. Then analytical conditions of customer demand and facility lifetime are derived to achieve a unique optimal pricing policy. The comparative statics properties of the optimal policy are also explored. Finally, numerical examples are presented to illustrate the effects of parameter variations on the optimal pricing policy.     

Quasi-optimal integrated production, inventory and maintenance policies for a single-vendor single-buyer system with imperfect production process

In this paper we deal with the integrated supply chain management problem in the context of a single vendor-single buyer system for which the production unit is assumed to randomly shift from an in-control to an out-of-control state. At the end of each production cycle, a corrective or preventive maintenance action is performed, depending on the state of the production unit, and a new setup is carried out. Two different integrated production, shipment and maintenance strategies are proposed to satisfy the buyer’s demand at minimum total cost. The first one suggests that the buyer orders batches of size nQ and the vendor produces nQ and makes equal shipments of size Q. The second policy proposes that to satisfy the same ordered quantity, the vendor produces separately smaller batches of size Q, n times. The total integrated average cost per time unit corresponding to each strategy is considered as the performance criterion allowing choosing the best policy for any given situation.     

Optimal design of lock-down and reopening policies for early-stage epidemics through SIR-D models

The diffusion of COVID-19 represents a real threat for the health and economic system of a country. Therefore the governments have to adopt fast containment measures in order to stop its spread and to prevent the related devastating consequences. In this paper, a technique is proposed to optimally design the lock-down and reopening policies so as to minimize an aggregate cost function accounting for the number of individuals that decease due to the spread of COVID-19. A constraint on the maximal number of concomitant infected patients is also taken into account in order to prevent the collapse of the health system. The optimal procedure is built on the basis of a simple SIR model that describes the outbreak of a generic disease, without attempting to accurately reproduce all the COVID-19 epidemic features. This modeling choice is motivated by the fact that the containing measurements are actuated during the very first period of the outbreak, when the characteristics of the new emergent disease are not known but timely containment actions are required. In fact, as a consequence of dealing with poor preliminary data, the simplest modeling choice is able to reduce unidentifiability problems. Further, the relative simplicity of this model allows to compute explicitly its solutions and to derive closed-form expressions for the maximum number of infected and for the steady-state value of deceased individuals. These expressions can be then used to design static optimization problems so to determine the (open-loop) optimal lock-down and reopening policies for early-stage epidemics accounting for both the health and economic costs.     

Optimal measurement policies for control purposes

A method is presented for off-line calculation of optimal measurement subsets to be used during implementation of optimal feedback control for linear stochastic systems. It is seen that feedback control imposes a penalty on noisy measurements which must be included with measurement cost in the optimization. The combinatorial problem involved with subset selection is avoided by creating a non-linear ‘ optimal control ’ problem which can be solved using available algorithms. Results for a scalar example show that, with costly measurements, it is most economical to use a number of short measurement periods.     

Optimum preventive maintenance policies for systems subject to random working times,replacement, and minimal repair

This paper proposes, from the economical viewpoint of preventive maintenance in reliability theory, several preventive maintenance policies for an operating system that works for jobs at random times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of two types of failure based on a specific random mechanism: type-I (repairable) failure is rectified by a minimal repair, and type-II (non-repairable) failure is removed by a corrective replacement. First, a modified random and age replacement policy is considered in which the system is replaced at a planned time T, at a random working time, or at the first type-II failure, whichever occurs first. Next, as one extended model, the system may work continuously for N jobs with random working times. Finally, as another extended model, we might consider replacing an operating system at the first working time completion over a planned time T. For each policy, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented analytically and discussed numerically. Because the framework and analysis are general, the proposed models extend several existing results.     

An optimal production lot-sizing problem for an imperfect process with imperfect maintenance and inspection time length

This article develops an integrated model in considering the situations of an imperfect process with imperfect maintenance and inspection time for the joint determination of both economic production quantity (EPQ) and preventive maintenance (PM). This imperfect process has a general deterioration distribution with increasing hazard rate. Even with periodic PM, such a production system cannot be recovered as good as new. This means that the system condition depends on how long it runs. Also, the PM level can be distinct due to the maintenance cost. For convenience, it is assumed the age of system is reduced in proportional to the PM level. Further, during a production cycle, we need an inspection to see if the process is in control. This inspection might demand a considerable amount of time. In this article, we take PM level and inspection time into consideration to optimise EPQ with two types of out-of-control states. To see how the method works, we use a Weibull shock model to show the optimal solutions for the least costs.     

Performance evaluation of subsea BOP control systems using dynamic Bayesian networks with imperfect repair and preventive maintenance

The work presents a dynamic Bayesian networks (DBN) modeling of series, parallel and 2-out-of-3 (2oo3) voting systems, taking account of common-cause failure, imperfect coverage, imperfect repair and preventive maintenance. Seven basic events of one, two or three component failure are proposed to model the common-cause failure of the three-components-systems. The imperfect coverage is modeled in the conditional probability table by defining a coverage factor. A multi-state degraded component is used to model the imperfect repair and preventive maintenance. Using the proposed method, a DBN modeling of a subsea blowout preventer (BOP) control system is built, and the reliability and availability are evaluated. The mutual information is researched in order to assess the important degree of basic events. The effects of degradation probability, failure rate and mean time to repair (MTTR) on the performances are studied. The results show that the repairs and maintenance can improve the system performance significantly, whereas the imperfect repair cannot degrade the system performance significantly in comparison with the perfect repair, and the preventive maintenance can improve the system performance slightly in comparison with the imperfect repair. In order to improve the performance of subsea BOP control system, the single surface components and the components with all-common-cause failure should given more attention. The influence of degradation probability on the performance is in the order of PLC, PC and ES. The influence of failure rate and MTTR on the performance is in the order of PLC, ES, PC, DO, DI and AI.     

A study of maintenance policies for second-hand products

This paper proposes two maintenance schemes for reused products. In order to reduce the purchasing cost or conform to the concept of environmental protection, reuse is considered as one of the most efficient strategies. However, the initial quality of reused product is often inferior to the new one and then product failures will occur frequently during usage period. Therefore, two periodical preventive maintenance (PM) policies in this paper are developed to decrease the high failure rate of the second-hand products. When a second-hand product with Weibull life time distribution of known age is intended to be used for a pre-specified period of time, the optimal number of PM actions and the corresponding maintenance degree are derived such that the expected total maintenance cost is minimized. The impact of providing preventive maintenance is illustrated through numerical examples.     

Multi-objective imperfect maintenance optimization for production system with an intermediate buffer

In several production systems, buffer stocks are built between consecutive machines to ensure the continuity of supply during interruptions of service caused by breakdowns or planned maintenance actions. However, in previous research, maintenance planning is performed individually without considering buffer stocks. In order to balance the trade-offs between them, in this study, an integrated model of buffer stocks and imperfective preventive maintenance for a production system is proposed. This paper considers a repairable machine subject to random failure for a production system by considering buffer stocks. First, the random failure rate of a machine becomes larger with the increase of the number of random failures. Thus, the renewal process is used to describe the number of random failures. Then, by considering the imperfect maintenance action reduced the age of the machine partially, a mathematical model is developed in order to determine the optimal values of the two decision variables which characterize the proposed maintenance strategy and which are: the size of the buffer stock and the maintenance interval. The optimal values are those which minimize the average total cost per time unit including maintenance cost, inventory holding cost and shortage cost, and satisfy the availability constraint. Finally, a heuristic procedure is used to solve the proposed model, and one experiment is used to evaluate the performance of the proposed methods for joint optimization between buffer stocks and maintenance policy. The results show that the proposed methods have a better performance for the joint optimization problem and can be able to obtain a relatively good solution in a short computation time.     

Joint quality control and preventive maintenance strategy for imperfect production processes

In this paper, we develop a joint quality control and preventive maintenance policy for a production system producing conforming and nonconforming units. The considered system consists of one machine which must supply another production line operating on a just-in-time basis. Each lot produced by the machine is subject to a quality control. According to the proportion l of nonconforming units observed and compared to a threshold value l _m , one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine for preventive and corrective maintenance actions of random durations, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. The proposed strategy is modelled using simulation and experimental design. This approach allows to generate a second order response surface allowing to easily determine the optimal rate, l_m^*{l_{m}^*}, of nonconforming units on the basis of which preventive maintenance actions should be performed, and the optimal size, h*, of the buffer stock to be built. These values minimize the total cost per time unit which includes the costs related to maintenance, quality and inventory.     

Analysis of maintenance policies for finite life-cycle multi-state systems

Maintenance policies for multi-state systems (MSS) are often analyzed under infinite horizon assumptions. In practice, it is important to consider maintenance policies under a finite horizon because the life cycles of most systems are finite. In this paper, we consider a finite life-cycle MSS that is subject to both degradation and Poisson failures. We study two classes of maintenance policies – preventive replacements and corrective replacements, and their effectiveness in controlling the customer’s expected discounted maintenance cost (EDMC). For both policies, replacement decisions are modelled via two control parameters – a threshold on the current system state and a threshold on the residual life cycle, which is measured as the time span from present to the end of life cycle. We derive close-to-explicit forms of the cost models under each of the policy. Methodologies for optimizing the maintenance thresholds are further proposed. Computational results verify that preventive replacements outperform corrective replacements typically when the downtime cost per failure is relatively high compared to the repair cost.