Periodic Preventive Maintenance Policy Research Articles

Optimal condition-based maintenance policy for leased equipment considering hybrid preventive maintenance and periodic inspection

Innovations in technology have made the structure of leased equipment more complex, which poses a challenge for lessors to develop maintenance policies. In view of the situation that the single periodic preventive maintenance (PM) policy during leasing activities may cause excessive or insufficient maintenance on the leased equipment, a condition-based maintenance (CBM) policy considering hybrid preventive maintenance (HPM) and periodic inspections is proposed. This policy contains imperfect preventive maintenance (IPM), preventive replacement (PR) and corrective maintenance (CM). The lessor can decide to take maintenance actions depending on whether the state of the equipment reaches the corresponding maintenance threshold. The warranty period of the leased equipment is also considered. To seal the deal, the lessor will give a discount on the rental to cover the CM costs and penalties out of the warranty period. To minimize the lessor's costs, we propose a CBM decision model to determine the optimal inspection period, PM threshold and PR period. The results show that the HPM policy can reduce leasing costs by about 5 –15 % for the lessor compared to that of the single PM policy.

Non-periodic preventive maintenance policies for complex multi-component products sold with loss-based two-dimensional warranties

Multi-component characteristics of complex industrial equipment, such as complex structures and stochastic dependencies, complicate analyzing the failure characteristics of such products and developing effective strategies to reduce warranty costs. In addition, a substantial customer loss or service interruption owing to the shutdown of these products forces manufacturers to formulate warranty contracts while considering customer loss. From the manufacturer’s perspective, with the aim of reducing the warranty costs while restraining the costs of customer loss, we propose the following two novel types of non-periodic imperfect preventive maintenance (PM) policies: unified and customized. The proposed PM policies simultaneously take into account the effects of customer usage rate heterogeneity and product deterioration on product failure. We characterize the failure relationship between the product and corresponding components based on the reliability block diagram and the Type I failure dependency model, and further construct the decision models for the proposed PM policies. The properties of the decision models are provided for certain special cases and are further used to design an algorithm for a general case. A comparison of the results of the numerical examples reveals the following: (1) Providing PM policies is beneficial for both the warranty providers and customers. The proposed PM policies are better than traditional periodic PM policies when shutdown loss costs are considered. (2) The stochastic dependencies will increase the costs of both the warranty and shutdown loss. It is necessary to take into account the stochastic dependencies of multi-component products when analyzing the warranty costs and formulating relevant decisions. (3) Beyond formulating effective PM policies, the manufacturer can mitigate the warranty cost pressure by adjusting the warranty coverage based on market information, or improving product reliability.

Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times

We consider in this work a bicriteria scheduling problem on two different parallel machines with a periodic preventive maintenance policy. The two objectives considered involve minimization of job rejection costs and weighted sum of completion times. They are handled through a lexicographic approach, due to a natural hierarchy among the two objectives in the applications considered. The main contributions of this paper are first to present a new problem relevant to practice, second, to develop a mixed-integer-linear-program model for the problem, and third, to introduce two generalizable tabu-search metaheuristics relying on different neighborhood structures and solution spaces. Computational results for 120 instances (generated from a real case) are reported to empirically demonstrate the effectiveness of the proposed metaheuristics.

Optimal periodic preventive maintenance policies for systems subject to shocks

External shock process, known as the shot-noise process, will lead to the failure rate increasing of systems operating under random environment. In this paper, assuming that each shock may cause a random increment of the system failure rate, the optimal periodic preventive maintenance (PM) policy for the system is investigated. The system is preventively maintained at periodic time points nT,n=1,2,…,N−1, and is preventively replaced at time point NT. The PM is not perfect, however, it can remove the accumulated failure rate increments caused by external shocks occurred during the last PM interval. When the system fails during the PM intervals, a minimal repair is performed to restore the function of the system. The expression of the average cost rate of the system is derived explicitly. The existence and uniqueness of the optimal bivariate PM policy (N,T) that minimizes the average cost rate are proved theoretically. Numerical examples are presented to illustrate the maintenance model and show the effectiveness of the proposed method.

Optimal periodic preventive maintenance policy for a system subject to failures/repairs which follow the non-homogeneous pure birth process

ABSTRACT This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the reliability, at periodic times iT (i = 1, 2, … N–1), the system is preventively maintained (PM). At the time NT the system is replaced. The failure/repair process between two PMs follows the Non-Homogeneous Pure Birth Process (NHPBP) which is a generalized version of the Non-homogeneous Poisson process (NHPP). The reliability improvement made by a PM action is stochastically modeled based on the properties of NHPBP. The cost for each PM depends on the reliability condition of the system at that PM time. The PM policy is characterized by the two parameters (N, T). We develop a two-stage procedure to find the optimal (N*, T*) which minimizes the long-run expected cost rate. Numerical examples are presented to illustrate the properties of the optimal policies. Abbreviations: NHPBP: Non-homogeneous pure birth process; NHPP: Non-homogeneous Poisson process; PM: Preventive maintenance; CM: Corrective maintenance; RM: Replacement maintenance

Optimization of Condition-Based Maintenance of Wood Utility Pole Network Subjected to Hurricane Hazard and Climate Change

Electric power distribution systems that link the bulk power grid (generation and transmission systems) to customers are the leading cause of power outages due to their vulnerability to extreme wind events, especially hurricanes. The strength of the wood poles that typically support the distribution lines also deteriorate over time. The vulnerability of the poles is expected to increase due to the potential impact of climate change on both hurricane hazard and wood decay rate. As such, an effective maintenance planning method is required for the vast number of poles supporting distribution lines. This paper presents a framework to optimize the maintenance of a network of wood utility poles. Corrective replacement due to failure caused by hurricanes and preventive replacement due to excessive decay are considered. The objective is to find the optimal inspection interval for the preventive replacement to minimize the long-term maintenance cost. To solve the optimization problem, the decay of the poles is modeled as a stationary gamma process. The impact of climate change on the rate of pole failure and replacement is also investigated. Two locations are considered as case studies: Miami, Florida, and New York City, New York. The period from 2010 to 2099 is considered for the study. The results of the case study show that the optimal inspection/replacement cycle determined using the developed framework results in lower total maintenance costs compared to current typical utility practice. Based on the inspection and replacement costs used in the study, the results show that adopting a periodic preventive maintenance policy decreases the failure rate of the poles but increases the total maintenance cost. However, only the cost of replacing the poles is considered here. Other considerations, such as indirect costs due to power outages and the impact of pole failure on system reliability, can render the adoption of a preventive replacement policy cost-effective. The results also show that climate change can increase the total maintenance cost. Based on current typical utility maintenance practice, climate change can increase the total maintenance cost by up to 8% in Miami and 6% in NYC, depending on the emission scenario considered.

Periodic preventive maintenance planning for systems working under a Markovian operating condition

Systems commonly work under time-varying operating condition. Operating condition can influence the failure time of systems, which should be taken into account when do preventive maintenance (PM) planning. This study considers a one-component system working under time-varying operating condition, where the evolution process of the operating condition is governed by a Markov process. We assume that the failure time distribution of systems working under different operating condition can be modeled by an accelerated failure time model. A periodic PM policy is proposed to mitigate the increasing failure risk, where both imperfect maintenance (IM) and replacement are considered. The optimal combination of PM interval and number of IM actions before each replacement are determined by minimizing the long-term average cost, which is formulated based on the semi-regenerative properties of the system state. We also consider a special case where only two operating conditions exist. Numerical studies are conducted to validate the proposed maintenance policy.

Bi-objective optimization of non-periodic preventive maintenance strategy by considering time value of money

Recently, design of preventive maintenance (PM) policies during the warranty period has attracted the attention of researchers. The methods mainly design warranty servicing strategies in a way that reduce the cost imposed on the manufacturer without considering the impact of customer dissatisfaction. While dissatisfaction with a product is an important issue which may result in the loss of potential buyers and switching existing buyers to competitors. Therefore, this study develops a bi-objective model which simultaneously minimizes the manufacturer and the buyer cost under a Non-homogeneous Poisson Process framework. Also, a non-periodic preventive maintenance strategy is presented in which PM actions are performed at discrete time instants in a way that the expected number of failures remains a constant value over all PM intervals. Furthermore, it is a known fact that the value of money reduces over time due to different reasons and has a significant impact on long-term contracts. Since PMs and repairs are conducted at different times, the time value of money is considered to estimate the cost more accurately. A comparative study is conducted to support this claim that the presented non-periodic reliability-based PM policy has a better performance in comparison with a periodic PM policy.

Joint optimization of capacity, production and maintenance planning of leased machines

This paper deals with capacity design, production and preventive maintenance planning of a production system made of parallel leased machines. The production system must satisfy a random demand over a finite number of periods. The number of machines to be leased, the quantity to produce by each one and customer demand are variable. A joint optimization approach of a maintenance strategy and an economical production plan is developed by considering the influence of usage rates on the degradation of machines. Firstly, we determine a nearly optimal number of machines to be leased as well as the quantities to produce during each period. Secondly, given the obtained production plan, a periodic preventive maintenance policy with minimal repairs at failure is determined for each machine. Branch and bound and random exploration methods are used to obtain an optimal solution.

Optimal design of sales and maintenance under the renewable warranty

This paper presents an integrated model to determine the optimal sales price, preventive maintenance (PM) interval and warranty period with the objective of maximizing the total profit. It is assumed that the sales growth can be featured by NHPP-Bass model over the time. Production cost, R&D cost and warranty cost involving product reliability are considered in this integrated profit model. Then, we consider a periodic PM policy, minimal repair and replacement policy in this paper and the product is deteriorated with the time goes. We also consider effects of the repair time of the repairable product. During the warranty period, manufacturer conducts the PM periodically, and if the repair time is beyond the limited repair time, the failure is replaced with a new product attached renewed warranty period. If not, the failed product is conducted with only minimal repair. Moreover, we give the numerical example and the sensitive analysis to provide insights into the influence of sales price, warranty period and PM interval.

A hybrid condition-based maintenance policy for continuously monitored components with two degradation thresholds

Condition-based maintenance (CBM) makes use of the actual condition of the component to decide when to maintain and/or replace the component, thereby maximising the lifetime of the machine, while minimising the number of service interventions. In this paper we combine CBM on one (monitored) component, with periodic preventive maintenance (PM) and corrective maintenance (CM) on the other components of the same machine/system. We implement two thresholds on the degradation level to decide when to service the monitored component: when the degradation level of the monitored component surpasses a first ‘opportunistic’ threshold, the monitored component will be serviced together with other components, for instance with a (planned) PM intervention, or upon breakdown of another component, requiring CM. In case none of these opportunities have taken place, and the degradation level surpasses a second ‘intervention’ threshold, an additional maintenance intervention is planned for the monitored component in order to prevent a failure. Both thresholds are optimised to minimise the total expected maintenance costs of the monitored component, or to minimise the downtime of the machine due to maintenance on the monitored component. We perform an extensive numerical experiment to demonstrate the potential gains of this hybrid policy with two thresholds compared to using a traditional PM policy, and we identify its key drivers of performance. We also benchmark our results when only one threshold is implemented. Our model is validated and applied at an OEM in the compressed air and generator industry.

Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty

This paper considers an optimal periodic preventive maintenance policy after the expiration of two-dimensional warranty. During the two-dimensional warranty period, both renewal warranty and nonrenewal warranty are considered and a repair time threshold is pre-specified so that the failed system is either minimally repaired or is replaced depending on whether the length of repair time exceeds the repair time threshold or not. After the warranty expires, the system undergoes the preventive maintenance periodically a fixed number of times by the user to prolong the life of the system and then the system is replaced preventively by a new one. In this study, we develop an optimal post-warranty periodic preventive maintenance strategy by minimizing the expected cost rate incurred during the life cycle of the system. From the user's perspective, the system is maintained free of charge or with prorated charge on the failed system during the warranty period. Once the warranty expires, the maintenance cost of the system is entirely charged to the user. Subject to such a cost structure, we derive the formula to evaluate the expected cost rate, which is used as an objective function for the optimality. The main goal of this paper is to determine an optimal preventive maintenance cycle after the warranty expires and thus to propose an optimal post-warranty strategy for the user. The effect of several parameters on the optimal strategy is also investigated numerically in this study. For the purpose of illustration of our proposed model, we present and discuss some numerical examples.

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.

New stochastic models for preventive maintenance and maintenance optimization

This paper considers periodic preventive maintenance policies for a deteriorating repairable system. On each failure the system is repaired and, at the planned times, it is periodically maintained to improve its reliability performance. Most of periodic preventive maintenance (PM) models for repairable systems have been studied assuming that the failure process between two PMs follows the nonhomogeneous Poisson process (NHPP), implying the minimal repair on each failure. However, in this paper, we assume that the failure process between two PMs follows a new counting process which is a generalized version of the NHPP. We develop two types of PM models and study detailed properties of the optimal policies which minimize the long-run expected cost rates. Numerical examples are also provided.

Joint reliability based design and periodic preventive maintenance policy for systems sold with warranty

Purpose – The authors consider a system which is a part of a complex equipment (e.g. aircraft, automobile, medical equipment, production machine, etc.), and which consists of N independent series subsystems. The purpose of this paper is to determine simultaneously the system design (reliability) and its preventive maintenance (PM) replacements periodicity which minimize the total average cost per time unit over the equipment useful life, taking into account a minimum required reliability level between consecutive replacements. Design/methodology/approach – The problem is tackled in the context of reliability-based design (RBD) considering at the same time the burn-in of components, the warranty commitment and the maintenance strategy to be adopted. A mathematical model is developed to express the total average cost per time unit to be minimized under a reliability constraint. The total average cost includes the cost of acquiring and assembling components, the burn-in of each component, preventive and corrective replacements performed during the warranty and post-warranty periods. A numerical procedure is proposed to solve the problem. Findings – For any given set of input data including components reliability, their cost and the costs of their preventive and corrective replacements, the system design (reliability) and the periodicity of preventive replacement during the post-warranty period is obtained such as the system’s total average cost per time unit is minimized. The obtained results clearly indicate that a decrease in the number of PM actions to be performed during the post-warranty period increases the number of components to be added at each subsystem at the design stage. Research limitations/implications – Given that the objective function (cost rate function) to be minimized is non-linear and involves several integer variables, it has not been possible to derive the optimal solution. A numerical procedure based on a heuristic approach has been proposed to solve the problem finding a nearly optimal solution for a given set of input data. Practical implications – This paper offers to manufacturers a comprehensive approach to look for the most economical combination of the reliability level to be given to their products at the design stage, on one hand, and the PM policy to be adopted, on the other hand, given the offered warranty and service for the products and reliability requirements during the life cycle. Originality/value – While the RBD problem has been largely treated, most of the published works have focussed on the development or the improvement of solving techniques used to find the optimal configuration. In this paper the authors provide a more comprehensive approach that considers simultaneously RBD, the burn-in and warranty periods, along with the maintenance policy to be adopted. The authors also consider the context of products whose component failures cannot be rectified through repair actions. They can only be fixed by replacement.

Multi-phase preventive maintenance policy for leased equipment

This paper proposes a multi-phase preventive maintenance (PM) policy for leased equipment by combining the advantages of both periodic PM and sequential PM. The lease period of the equipment is divided into multiple PM phases. The PM activities within each phase are performed periodically with the convenience of implementation, while the frequency of PM for each phase is different and it gives a gradual increase because of the imperfect effect of PM. A multi-phase PM model is built up based on the age reduction method for imperfect PM with the penalty for equipment failures and overtime of repair involved. The optimal PM intervals for every PM phases are achieved by minimising the cumulative maintenance cost throughout the lease period from the perspective of the lessor. Numerical example shows that the cumulative maintenance cost under the proposed multi-phase PM policy is lower than that under periodic PM policy.

Analytical method for optimization of maintenance policy based on available system failure data

An analytical optimization method for preventive maintenance (PM) policy with minimal repair at failure, periodic maintenance, and replacement is proposed for systems with historical failure time data influenced by a current PM policy. The method includes a new imperfect PM model based on Weibull distribution and incorporates the current maintenance interval T0 and the optimal maintenance interval T to be found. The Weibull parameters are analytically estimated using maximum likelihood estimation. Based on this model, the optimal number of PM and the optimal maintenance interval for minimizing the expected cost over an infinite time horizon are also analytically determined. A number of examples are presented involving different failure time data and current maintenance intervals to analyze how the proposed analytical optimization method for periodic PM policy performances in response to changes in the distribution of the failure data and the current maintenance interval.

A Failure-rate-reduction Periodic Preventive Maintenance Model with Delayed Initial Time in a Finite Time Period

HeA new machine will not fail easily in the early stage of its useful life. This phenomenon is consistent with the fact that the optimal sequential preventive maintenance (PM) policy which has longer PM intervals in its earlier stage of lifetime. In this paper, we propose a failure-rate-reduction periodic PM model with delayed initial time in a finite time span. Then, the optimal periodic PM policy is developed by minimizing the expected total maintenance cost, which can have smaller expected total maintenance cost than the optimal policy of the original failure-rate-reduction periodic PM model. The algorithm of finding the optimal PM policy for the proposed PM model is developed. Finally, examples are illustrated to verify the optimal policies of the proposed new PM model.

Warranty Cost Analysis for $k\hbox{-}out\hbox{-}of\hbox{-}n$ Systems With 2-D Warranty

This paper presents new warranty cost models subject to two types of warranty periods (warranty and postwarranty periods), minimal repairs, and various types of warranty policies including free repair/replacement warranty and prorata warranty for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -out-of- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> systems. Two-dimensional warranty is applied to investigate the warranty cost using repair times and failure times. We obtain the long-run expected cost functions per unit time with respect to both the warranty and postwarranty periods by considering the aspects of both the manufacturer and the customer. This paper considers a periodic preventive maintenance (PM) policy with both corrective maintenance and PM and also determines three decision variables including warranty period, repair time limit, and periodical maintenance cycles, which minimize the long-run expected cost. Numerical examples are discussed to demonstrate the applicability of the methodologies, and results including the three optimum decision-variable solution and their corresponding long-run expected cost per unit are derived.

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.