A two-dimensional preventive maintenance strategy for items sold with warranty

Conventional preventive maintenance (PM) strategies under two-dimensional (2D) warranties are usually age-based or usage-based, which means that the implementation of PM activities is based solely on item age or usage. In this paper, a new PM strategy, called 2D PM strategy, is proposed for items sold with a 2D warranty. Under this strategy, the item is preventively maintained every K units of age or L units of usage, whichever occurs first. The marginal approach is used to describe the effect of age and usage on item reliability by treating usage as a random function of age. Besides, the effect of PM is characterised by the reduction of virtual age. The objective of this study is to identify the optimal 2D PM strategy under fixed warranty terms so as to minimise the total expected warranty servicing cost from the manufacturer’s perspective. A numerical example is provided to demonstrate the effectiveness of the proposed PM strategy. It is shown that the 2D PM strategy contains the age-based and usage-based strategies as special cases, and outperforms them in terms of warranty servicing cost. Finally, how to implement the proposed PM strategy in practice is discussed with an illustrative case.     

Optimal burn-in time under cumulative free replacement warranty

In this paper, optimal burn-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is studied. When the products with cumulative warranty have high failure rate in the early period (infant mortality period), burn-in procedure is considered to eliminate the early product failures. After burn-in, the posterior product life distribution and the cumulative warranty-related cost are dependent on burn-in time; long burn-in period decreases the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain the total mean cost under burn-in and cumulative warranty. Properties of the optimal burn-in time are analyzed here. Numerical examples and sensitivity analysis are used to demonstrate the applicability of the methodology derived in the paper.     

Investigating reliability improvement of second-hand production equipment considering warranty and preventive maintenance strategies

A cost model for optimal reliability improvement of warranted second-hand production equipment is developed. The second-hand production equipment of age x is subjected to an upgrade action of a certain level u before it is sold with a Free Repair Warranty. We look at determining the optimal upgrade level when not performing and when performing periodic preventive maintenance (PM) during the warranty period. Two different PM strategies are considered: (a) periodic PM actions having the same efficiency level; (b) periodic multi-phase PM actions with a maintenance efficiency level which varies according to the phase. The proposed model aims at helping the dealer to find the optimal upgrade level to perform before selling the second-hand equipment, and to assess whether performing PM actions during the warranty period, according to a specific maintenance strategy, is worthwhile in terms of cost reduction. Numerical experimentations considering each PM scenario are performed in order to investigate how each PM strategy impacts the improvement level to be performed and the associated total expected cost. The obtained results showed that the expected total cost incurred by the dealer is governed by a sensitive trade-off between the warranty servicing cost and the costs associated with the reliability improvement, and with the PM performed during the warranty period. It is also found that the proposed new periodic multi-phase PM policy with an increasing maintenance efficiency level yields lower upgrade levels, inducing lower costs for the dealer.     

Optimal imperfect preventive maintenance policy for equipment leased during successive periods

In this paper, we consider randomly failing equipment leased several times during their life cycle with a given warranty period. A mathematical model is developed to determine the optimal efficiency levels of preventive maintenance (PM) to be performed on the equipment between successive lease periods, maximising the expected total profit of the lessor over the equipment life cycle. The model considers the expected leasing revenue as well as the equipment acquisition cost and the average PM and repair costs. PM actions allow reducing the age of the equipment to a certain extent with a corresponding cost depending on the PM level adopted. The efficiency of the PM is determinant of the expected revenue during the next lease period. Given a set of K possible PM levels and the number of lease periods n over the equipment life cycle, K^{n?1 PM} strategies are possible. A genetic algorithm is proposed in order to obtain nearly optimal policies in situations where the number of possibilities K^n?1 is very high. Obtained numerical results are discussed. Small- and big-size instances of the problem are considered in the case of a service company in the oil and gas industry specialised in leasing specific equipment such as separators, to oil companies for production activities with a limited duration of several months like well testing or short production tests.     

Optimal multi-level classification and preventive maintenance policy for highly reliable products

Highly reliable products are widely used in aerospace, automotive, integrated manufacturing and other fields. With increasing market demand and competition, product classification for different segment market segments has become more and more critical. Leading manufacturers are always searching and designing classification policies for highly reliable products. On the other hand, preventive maintenance can improve the operation efficiency of the product, extend the service life and reduce enormous losses brought by failures. These two factors are taken into account by many large enterprises when making sound economical and operational decisions. Therefore, this research proposes a joint multi-level classification and preventive maintenance model (JMCPM model) under age-based maintenance. Different preventive maintenance policies are developed for corresponding level units. Accordingly, the optimal joint policy of multi-level classification and preventive maintenance can be obtained by JMCPM. In this model, degradation-based burn-in is utilised to eliminate defective units and collect degradation data. The degradation data are the basis of classification and can be used to estimate the residual life. Then, for making full use of these data, linear discriminant analysis is employed to design classification rules. The objective of the JMCPM model is to minimise the average cost per unit time by properly choosing the settings of classification and preventive maintenance intervals simultaneously. Finally, a simulation study is carried out for evaluating the performance of the JMCPM model. For an illustration of the proposed model and the methods of inference developed here, a real case involving degradation data from electrical connectors is analysed.     

Optimal periodic preventive maintenance policy for leased equipment

For leased equipment the lessor incurs penalty costs for failures occurring over the lease period and for not rectifying such failures within a specified time limit. Through preventive maintenance actions the penalty costs can be reduced but this is achieved at the expense of increased maintenance costs. The paper looks at a periodic preventive maintenance policy which achieves a tradeoff between the penalty and maintenance costs.     

Optimal preventive maintenance strategy using two repair crews having different efficiencies: a quasi renewal process based modelling approach

This paper considers randomly failing, single-unit equipment subject to a periodic preventive maintenance (PM) policy. In case of failure between successive perfect PM actions (renewals), imperfect repairs are performed following a decreasing quasi-renewal process. One of two different maintenance crews can perform the repairs. One team is more experienced, and consequently more efficient than the other, but more costly. A mathematical model is developed in order to determine the PM period, T, and the kth repair, during a PM period, after which the repair team should be changed, minimising the average total cost per time unit over an infinite time span. It is also proved that an optimal solution in terms of the PM period always exists for any given system lifetime distribution and any set of maintenance costs. Numerical examples are presented and the obtained results are discussed.     

Optimal maintenance policies during the post-warranty period

This paper develops the optimal periodic preventive maintenance policies following the expiration of warranty. We consider two types of warranty policies to discuss such optimum maintenance policies: renewing warranty and non-renewing warranty. From the user's perspective, the product is maintained free of charge or with prorated cost on failure during the warranty period. However, the users will have to repair or replace the failed product at their own expenses during the post-warranty period. Given the cost structure to the user during the cycle of the product, we derive the expressions for the expected maintenance costs for the periodic preventive maintenance following the expiration of warranty when applying two types of warranty policies and obtain the optimal number and the optimal period for such post-warranty maintenance policies by minimizing the expected long-run maintenance cost per unit time. Explicit solutions for the optimal periodic preventive maintenance are presented for illustrative purposes.     

Control-limit preventive maintenance policies for components subject to imperfect preventive maintenance and variable operational conditions

This paper develops two component-level control-limit preventive maintenance (PM) policies for systems subject to the joint effect of partial recovery PM acts (imperfect PM acts) and variable operational conditions, and investigates the properties of the proposed policies. The extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors. Several numerical experiments are conducted for policy property analysis, using real lifetime and operational condition data and typical characterization of imperfect PM acts and maintenance durations. The experimental results demonstrate the necessity of considering both factors when they do exist, characterize the joint effect of the two factors on the performance of an optimized PM policy, and explore the influence of the loading sequence of time-varying operational conditions on the performance of an optimized PM policy. The proposed policies extend the applicability of PM optimization techniques.     

A full history proportional hazards model for preventive maintenance scheduling

This paper is concerned with the development of a realistic preventive maintenance (PM) scheduling model. A heuristic approach for implementing the semi-parametric proportional-hazards model (PHM) to schedule the next preventive maintenance interval on the basis of the equipment's full condition history is introduced. This heuristic can be used with repairable systems and does not require the unrealistic assumption of renewal during repair, or even during PM. Two PHMs are fitted, for the life of equipment following corrective work and the life of equipment following PM, using appropriate explanatory variables. These models are then used within a simulation framework to schedule the next preventive maintenance interval. Optimal PM schedules are estimated using two different criteria, namely maximizing availability over a single PM interval and over a fixed horizon. History data from a set of four pumps operating in a continuous process industry is also used to demonstrate the proposed approach. The results indicate a higher availability for the recommended schedule than the availability resulting from applying the optimal PM intervals as suggested by using the conventional stationary models. © 1997 John Wiley & Sons, Ltd.     

Joint optimization of preventive maintenance and flexible flowshop sequence-dependent group scheduling considering multiple setups

This study focuses on a joint optimization problem regarding preventive maintenance (PM) and non-permutation group scheduling for a flexible flowshop manufacturing cell in order to minimize makespan. A mixed-integer linear programming model for the investigated problem is developed, which features the consideration of multiple setups, the relaxation of group technology assumptions, and the integration of group scheduling and PM. Based on the model, a lower bounding technique is presented to evaluate the quality of solutions. Furthermore, a genetic algorithm (GA) is proposed to improve computational efficiency. In the GA, a threshold-oriented PM policy, a hybrid crossover and a group swap mutation operator are applied. Numerical experiments are conducted on 45 test problems with various scales. The results show that the proposed model can remarkably reduce makespan. Comparative experiments reveal that the GA outperforms CPLEX, particle swarm optimization and cuckoo search with respect to effectiveness and efficiency.     

Integrated reconfiguration and age-based preventive maintenance decision making

The use of manufacturing system reconfiguration in conjunction with maintenance operations has not been previously reported in the literature. This research attempts to incorporate reconfiguration into Preventive Maintenance (PM) actions for improved system performance in terms of reduced total cost. This paper presents an Integrated Reconfiguration and Age-Based Maintenance (IRABM) policy and applies it to a parallel-serial manufacturing system. The expected total cost of implementing the IRABM policy is estimated and minimized through a simulation-based heuristic optimization procedure. Using this method, it is possible to systematically identify the conditions under which the integration of reconfiguration into maintenance is cost effective. In addition, numerical examples demonstrate that the manufacturing system could have a higher probability of fulfilling production requirements at a lower cost under the IRABM policy compared to the conventional age-based PM policy. The influences of the input parameters associated with reconfiguration, production, and reliability on the performance of IRABM policy also are studied.     

Optimal reliability, warranty and price for new products

The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about product reliability. Product warranty is one such tool to signal reliability with a longer warranty period indicating better reliability. Better warranty terms result in increased sales and also higher expected warranty servicing costs. Warranty costs are reduced by improvements in product reliability. Learning effects result in the unit manufacturing cost decreasing with total sales volume and this in turn impacts on the sale price. As such, reliability, price and warranty decisions need to be considered jointly. The paper develops a model to determine the optimal product reliability, price and warranty strategy that achieve the biggest total integrated profit for a general repairable product sold under a free replacement-repair warranty strategy in a market and looks at two scenarios for the pricing and warranty of the product. The model assumes that the sale rate increases as the warranty period increases and decreases as the price increases. The maximum principle method is used to obtain optimal solutions for dynamic price and warranty situations. Finally, numerical examples are given to illustrate the proposed model.     

Analysing event data from a repairable machine subject to imperfect preventive maintenance

A machine is minimally repaired on failure and imperfect preventive maintenance (PM) is also carried out from time to time, not necessarily at regular intervals. A simple point process model is proposed for the sequence of corresponding failure times, and estimates of the machine lifetime parameters and the degree of age rejuvenation at PMs are obtained using maximum likelihood techniques. These results are then applied to real event data. © 1997 John Wiley & Sons, Ltd.     

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.     

On a dynamic preventive maintenance policy for a system under inspection

The purpose of this article is to propose both state and time-dependent preventive maintenance policy for a multi-state deteriorating system, which is equipped with inspection equipment(s) connected to a computer center. After the system being identified as state x at nd through computation by the computer center after inspection (or measurement) via equipment(s), one maintenance action with the minimum expected total cost since nd till Nd (where N=n+K for a fixed integer 0<K<∞) will be chosen from the set A_x of alternatives also with the help of the computer center. In real case, the expected total costs since nd till Nd will be time-dependent and so is the maintenance action chosen at nd. A numerical example is given to illustrate such a maintenance policy for a Markovian deteriorating system to describe its state dependent aspect only for simplicity reason. Due to the fact that both equipment measurement and computer computation take time, the preventive maintenance policy for a sufficiently small d may be used in fact as the one under continuous inspection.     

Modelling and optimizing sequential imperfect preventive maintenance

This paper deals with the problem of scheduling imperfect preventive maintenance (PM) of some equipment. It uses a model due to Kijima in which each application of PM reduces the equipment's effective age (but without making it as good as new). The approach presented here involves minimizing a performance function which allows for the costs of minimal repair and eventual system replacement as well as for the costs of PM during the equipment's operating lifetime. The paper describes a numerical investigation into the sensitivity of optimum schedules to different aspects of an age-reduction model (including the situation when parts of a system are non-maintainable—i.e., unaffected by PM).     

A variable neighbourhood search for integrated production and preventive maintenance planning in multi-state systems

This paper presents a variable neighbourhood search (VNS) to the integrated production and maintenance planning problem in multi-state systems. VNS is one of the most recent meta-heuristics used for problem solving in which a systematic change of neighbourhood within a local search is carried out. In the studied problem, production and maintenance decisions are co-ordinated, so that the total expected cost is minimised. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimise the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-state components. The formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. The proposed VNS deals with the preventive maintenance selection task. Results on test instances show that the VNS method provides a competitive solution quality at economically computational expense in comparison with genetic algorithms.     

Optimal major and minimal maintenance policies for deteriorating systems

We present a maintenance model for a multi-state semi-Markovian deteriorating system. Our model allows one of three maintenance decisions (do-nothing, minimal maintenance or replacement) to be taken at each state of the system. We use control limit policy and the policy-iteration algorithm to find the optimal maintenance policies that minimizes the expected long-run cost rate of the system. Numerical examples are given to illustrate the proposed policies.     

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.