Optimal Preventive Maintenance Policy Research Articles

Optimal Preventive Maintenance Policy for Equipment Rented under Free Leasing as a Contributor to Sustainable Development

Leasing has proven to be a business model that is perfectly suited to the circular economy. It significantly contributes to sustainable development by enabling the reuse of machinery and equipment after each lease period and by including preventive maintenance and overhauls within and between lease terms. This helps to extend the life cycle of equipment, promote value recovery, and reduce waste. This paper examines an imperfect preventive maintenance (PM) strategy applied to equipment rented under the terms of “free leasing”. In free leasing, the lessor makes the equipment available to the customer for a specified period of time without charging rent. In return, the customer is required to purchase the equipment’s consumables exclusively from the lessor. The lessor is also responsible for the maintenance of the equipment at the customer’s premises. The greater the quantity of consumables used by the customer, the more the equipment will deteriorate. Consequently, the lessor must be able to determine the most effective approach to preventive maintenance, ensuring that it aligns with the customer’s planned usage rate while maximizing profit. This work proposes a PM strategy to be adopted by the lessor during the free lease period. This strategy involves the performance of imperfect PM actions just before the start of the lease period and then periodically. Different packages of preventive actions can be applied each time, with each package having a different cost depending on the level of effectiveness in terms of rejuvenating the equipment. Minimal repairs are performed in the event of equipment failure. The decision variables are the PM period to be adopted and the maintenance efficiency level to be chosen for each preventive intervention. The objective is to determine, for a given customer with an estimated consumption rate profile of consumables, the optimal values of these decision variables so that the lessor maximizes their profit. A mathematical model is developed to express the lessor’s average profit over each lease period. A solution procedure is developed for small instances of the problem, and an Artificial Bee Colony algorithm is implemented for larger instances. A numerical example and a sensitivity analysis are presented.

Intelligent optimal preventive replacement maintenance policy for non-repairable systems

This paper developed optimal maintenance policies for industrial machines to ensure uninterrupted production. Analytical and intelligent replacement models were constructed using real-time data from a commercial photocopier operator’s expenditure logbook between 2012 and 2023. A goodness-of-fit test affirmed a log-logistic failure distribution with shape and scale parameters of 1.7233 and 763.9220, respectively. Probability functions from this distribution established replacement models, determining optimal preventive maintenance conditions. Through feature engineering additional features crucial for operational and cost optimization were abstracted, with 4,881 unique data points simulated from boundary conditions defined by the original or raw data. Analytical results showed that the failure distribution-based replacement model outperformed the hazard function-based model in minimum replacement time and unit maintenance cost over time, while key parameters such as availability, reliability, and failure occurrence probability remained constant at 96 %, 94 %, and 0.07 %, respectively. Machine learning models (Extreme Gradient Boosting: XGBoost, Support Vector Machine: SVM, and Multilayer Perceptron: MLP) demonstrated very high accuracy in availability (XGBoost = 99.49 %, SVM = 99.18 %, RF = 100 %, MLP = 99.80 %), reliability (XGBoost = 99.49 %, SVM = 99.18 %, RF = 100 %, MLP = 99.80 %), and maintenance cost (XGBoost = 100 %, SVM = 100 %, RF = 100 %, MLP = 100 %), exceeding results of the analytical models.

A copula-based approach to modelling the failure process of items under two-dimensional warranty and applications

Hundreds of scholarly papers on optimisation of preventive maintenance policies for items under warranty have been published in the reliability related literature. They typically have two limitations: they make a simplified assumption on the relationship between age and usage for items under two-dimensional warranty and they assume that it is cost-effective to conduct preventive maintenance (PM) on each sold product item. These assumptions may not reflect the reality. This paper therefore proposes a copula-based approach to modelling the relationship between age and usage of items under two-dimensional (2D) warranty. It investigates the probabilistic properties of the bivariate failure rate functions of age and usage and derives optimal PM policies for users who bought multiple product items. It also proposes approaches to incorporating maintenance effectiveness in bivariate copulas for depicting the dependence between age and usage. A case study and numerical examples are provided to illustrate the findings.

Investigation of system transient availability under imperfect maintenance

PurposeWhile steady-state analysis is useful, it does not consider the inherent transient characteristics of repairable systems' behavior, especially in systems that have relatively short life spans, or when their transient behavior is of special concern such as the motivating example used in this paper, military systems. Therefore, a maintenance policy that considers both transient and steady-state availability and aims to achieve the best trade-off between high steady-state availability and rapid stabilization is essential.Design/methodology/approachThis paper studies the transient behavior of system availability under the Kijima Type II virtual age model. While such systems achieve steady-state availability, and it has been proved that deploying preventive maintenance (PM) can significantly improve its steady-state availability, this improvement often comes at the price of longer and increased fluctuating transient behavior, which affects overall system performance. The authors present a methodology that identifies the optimal PM policy that achieves the best trade-off between high steady-state availability and rapid stabilization based on cost-availability analysis.FindingsWhen the proposed simulation-based optimization and cost analysis methodology is applied to the motivating example, it produces an optimal PM policy that achieves an availability–variability balance between transient and steady-state system behaviors. The optimal PM policy produces a notably lower availability coefficient of variation (by 11.5%), while at the same time suffering a negligible limiting availability loss of only 0.3%. The new optimal PM policy also provides cost savings of about 5% in total maintenance cost. The performed sensitivity analysis shows that the system's optimal maintenance cost is sensitive to the repair time, the shape parameter of the Weibull distribution and the downtime cost, but is robust with respect to changes in the remaining parameters.Originality/valueMost of the current maintenance models emphasize the steady-state behavior of availability and neglect its transient behavior. For some systems, using steady-state availability as the sole metric for performance is not adequate, especially in systems that have relatively short life spans or when their transient behavior affects the overall performance. However, little work has been done on the transient analysis of such systems. In this paper, the authors aim to fill this gap by emphasizing such systems and applications where transient behavior is of critical importance to efficiently optimize system performance. The authors use military systems as a motivating example.

Optimal rearrangement and preventive maintenance policies for heterogeneous balanced systems with three failure modes

This paper studies a heterogeneous balanced system composed of multiple interchangeable components. The degradation process of components is described by a gamma process, and deterioration rates in different positions are different due to the effect of loading stress or temperature. Three competing failures may occur: a) shock failure caused by environment shocks, b) soft failure when the deterioration level of any component exceeds a critical value, and c) out of balance when the difference value among components reaches the failure threshold. To avoid system failure, a rearrangement action is adopted to change the position of components. Besides, preventive maintenance is considered when a component deteriorates severely. A semi-Markov decision process (SMDP) is developed to obtain the optimal policy by minimizing the average maintenance cost. To facilitate calculation, the data transmission method is used to convert the semi-Markov decision model to the Markov decision model, and a value iteration algorithm is established to obtain the optimal maintenance action at each state. Considering practical implications, an imperfect preventive and opportunistic maintenance model is formulated under the SMDP framework. Finally, a typical tire rotation problem in motorcycles proves that the imperfect maintenance policy outperforms the other policies when replacement fees are more expensive.

Optimal preventive maintenance policy for leased equipment for free with minimum quantity of consumables purchasing commitment by the lessee

PurposeThis paper deals with a particular type of leasing contracts according to which an equipment is leased for free with the condition for the lessee to purchase a predetermined minimum quantity of consumables during each leasing period. Maintenance actions are performed by the lessor and borne by him. Imperfect preventive maintenance is carried out every t time units throughout the leasing period. Minimal repairs are performed following equipment failures. At the end of the leasing period, an overhaul which restores the equipment to “as good as new” state is performed. The equipment is leased many times during its life cycle. The purpose of this paper is to determine the values of the decision variables for the lessor, which are the preventive maintenance (PM) period and the minimum quantity of consumables to be sold to ensure profit.Design/methodology/approachA mathematical model is developed to express the expected maintenance cost per time unit incurred by the lessor as well as his expected profit over the equipment life cycle. The optimal PM period minimizing the maintenance cost is determined first. Then, given the corresponding minimum maintenance cost, the minimum quantity of consumables (the lessor's break-even point) to be purchased by the lessee is computed. A numerical example and a sensitivity study are presented, and the obtained results are discussed.FindingsThe outcome of this work is supposed to help the lessors determining two key values to be included in each leasing contract, namely: (1) the periodicity according to which they will commit to perform preventive maintenance actions such that their average total cost of maintenance is minimized, (2) the minimum quantity of consumables that the lessee must commit to purchasing during the leasing period. This quantity must be between the break-even point and the maximum quantity associated with the capacity of the equipment.Practical implicationsPractically, the objective of this work is first to determine the optimal strategy to be adopted by the lessor in terms of effort relating to PM and second to determine the minimum quantity of consumables that the lessee must purchase during the leasing period such as profit is insured for the lessor.Originality/valueThis type of leasing (for free) has not been addressed in the literature particularly when considering maintenance strategies.

On preventive maintenance of k-out-of-n systems subject to fatal shocks

In this paper, we investigate optimal age-based preventive maintenance (PM) policies for an ( n- k + 1)-out-of- n system whose components are exposed to fatal shocks that arrive from various sources. We consider two different scenarios for the system failure. In the first one, it is assumed that the shock process is of the type of Marshall-Olkin where each shock affects one component of the system and puts it down, and one shock affects all components and destroys all of them. In the second scenario, it is assumed that the system is subject to an extended type of Marshall-Olkin shock process where the shocks arriving at random times may cause the breakdown of 1, 2, …, or n components. Under each scenario for the components failure, we investigate an optimal age-based PM model for the system by imposing the related cost function. Then, in each case, we explore the optimal PM time that minimizes the mean cost per unit of time. Some numerical results are presented to illustrate the applications of the proposed models.

Really Ageing Systems Undergoing a Discrete Maintenance Optimization

In general, a complex system is composed of different components that are usually subject to a maintenance policy. We take into account systems containing components that are under both preventive and corrective maintenance. Preventive maintenance is considered as a failure-based preventive maintenance model, where full renewal is realized after the occurrence of every nth failure. It offers an imperfect corrective maintenance model, where each repair deteriorates the component or system lifetime, the probability distribution of which gradually changes via increasing failure rates. The reliability mathematics for unavailability quantification is demonstrated in the paper. The renewal process model, involving failure-based preventive maintenance, arises from the new corresponding renewal cycle, which is designated a real ageing process. Imperfect corrective maintenance results in an unwanted rise in the unavailability function, which can be rectified by a properly selected failure-based preventive maintenance policy; i.e., replacement of a properly selected component respecting both cost and unavailability after the occurrence of the nth failure. The number n is considered a decision variable, whereas cost is an objective function in the optimization process. The paper describes a new method for finding an optimal failure-based preventive maintenance policy for a system respecting a given reliability constraint. The decision variable n is optimally selected for each component from a set of possible realistic maintenance modes. We focus on the discrete maintenance model, where each component is realized in one or several maintenance mode(s). The fixed value of the decision variable determines a single maintenance mode, as well as the cost of the mode. The optimization process for a system is demanding in terms of computing time because, if the system contains k components, all having three maintenance modes, we need to evaluate 3k maintenance configurations. The discrete maintenance optimization is shown with two systems adopted from the literature.

Design and pricing of usage-driven customized two-dimensional extended warranty menus

In this article, we study the design and pricing of customized two-dimensional extended warranty menus from the provider’s perspective, where each consumer is presented with a tailored warranty menu based on her usage rate. We propose to design such usage-driven customized menus in two steps. First, for a fixed usage rate, we design the corresponding menu by seeking optimal prices for given warranty limits. Then, the menu for any other usage rate is designed by fixing the optimal prices and determining the associated warranty limits. We prove that under the multinomial logit choice framework, if the product failure probabilities for respective options in two customized menus are the same, then the menus will have identical expected profits and attach rates. A case study on commercial vehicles is presented to demonstrate the customization methodology. We find that customized menus can generate a higher profit and attach rate than a uniform menu without customization, indicating the benefit of customization. In addition, we extend the original model to incorporate ancillary preventive maintenance programs. Our analysis reveals that the optimal preventive maintenance policy for each option is independent of those for other options; moreover, bundling preventive maintenance programs can increase profit and attach rate.

A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process

Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover this important in-practice setting. Therefore, our paper is the first to deal with these issues by modeling dependence in the bivariate set up when a system consists of two dependent parts. We employ the bivariate generalized Polya process to model the corresponding failure and repair process. Relevant stochastic properties of this process have been obtained in order to propose and further discuss the new optimal bivariate preventive maintenance policy with two decision parameters: age and operational history. Moreover, introducing these two parameters in the considered context is also a new feature of the study. Under the proposed policy, the long-run average cost rate is derived and the optimal replacement policies are investigated. Detailed numerical examples illustrate our findings and show the potential efficiency of the obtained results in practice.

Optimal preventive maintenance policies for products with multiple failure modes after geometric warranty expiry

In this paper, the optimal maintenance strategy for the warranty product subject to multiple failure modes and repair time limit is studied from the customer’s perspective. When the product fails, a minimal repair based on the failure type is conducted. If the product can not be repaired within a given time limit, it will be replaced with a new one by the manufacturer during the warranty period. Different from the traditional renewing warranty policy, a geometric warranty policy is adopted in this work, under which once the warranty product is replaced; the length of warranty period is geometrically renewed. After the warranty expires, the product undergoes preventive maintenance (PM) periodically and the PM effect is modeled by reducing the virtual age of different failure modes by different degree. The objective is to determine the optimal interval time for PM and the optimal number of PMs by minimizing the expected life cycle cost rate of product. The existence and uniqueness of the optimal PM policy are proved theoretically, and the optimal bivariate policy can be obtained by using a recursive seeking algorithm. Numerical examples illustrate the effectiveness of geometric warranty policy and the proposed PM model.

Optimal preventive maintenance for repairable products with three types of failures sold under a renewable hybrid FRW/PRW policy

This paper proposes the optimal preventive maintenance policy for products under a warranty policy, which combines fully renewable free replacement warranty (FRW) and pro-rata warranty (PRW). Replacement age is divided into three separate periods: within FRW, during PRW and post-warranty. Moreover, it is assumed the product is subject to three types of failures arriving according to a non-homogeneous Poisson process. The first type can be fixed by minimal repair, and the third type is a catastrophic failure that results in product replacement. If the failure is of the second type and the product is at age t, it is either minimally repaired with probability p(t) or replaced by a new one with probability 1−p(t). The aim of this study is to develop the long-run expected cost rate for both warranted and non-warranted repairable products as well as to derive the optimal replacement time such that the incurred costs are minimized. The proposed approach provides valuable information for the product customers, managers, or engineers to make better decisions about the preventive replacement time of such products. The proposed model covers some preventive maintenance policies in the existing literature. Numerical computations are also performed to investigate the effect of the model’s parameters on the optimal solutions. Eventually, a real-life application is discussed to demonstrate the applicability of the proposed policy.

Optimal Preventive Maintenance Policy Considering Imperfect Inspection and Limiting the Number of Minimal Repairs for Degradation System

Optimal Preventive Maintenance Policy Considering Imperfect Inspection and Limiting the Number of Minimal Repairs for Degradation System

Energy Consumption-Based Maintenance Policy Optimization

The optimal predictive, preventive, corrective and opportunistic maintenance policies play an important role in the success of sustainable maintenance operations. This study discusses a new energy efficiency-related maintenance policy optimization method, which is based on failure data and status information from both the physical system and the digital twin-based discrete event simulation. The study presents the functional model, the mathematical model and the solution algorithm. The maintenance optimization method proposed in this paper is made up of four main phases: computation of energy consumption based on the levelized cost of energy, computation of GHG emission, computation of value determination equations and application of the Howard’s policy iteration techniques. The approach was tested with a scenario analysis, where different electricity generation sources were taken into consideration. The computational results validated the optimization method and show that optimized maintenance policies can lead to an average of 38% cost reduction regarding energy consumption related costs. Practical implications of the proposed model and method regard the possibility of finding optimal maintenance policies that can affect the energy consumption and emissions from the operation and maintenance of manufacturing systems.

Optimal Age-Based Preventive Maintenance Policy for a System Subject to Cumulative Damage Degradation and Random Shocks

This research investigates the problem of cumulative degradation and random shocks a system like a centrifugal pump may experience during normal and adverse operating conditions. An accelerated life testing method was employed to determine the degradation of the pump under cumulative damage degradation and random shocks conditions. An age- Based policy was used to determine the optimum time interval that will minimize the total expected cost of the system. The random shock increases the number of failures and hence reduces the reliability of the system. The total expected preventive maintenance cost obtained varies from N1700.00 (One thousand seven hundred naira) to N16,000.00 (sixteen thousand naira), depending on the shock and shock duration. The methodology presented is useful and thus recommended for use to study cumulative damage degradation and random shocks for similar systems.

Optimal Maintenance Probabilities and Preventive Replacement Maintenance Policy for Photocopy Machines

The need for suitable replacement policies are essential to minimize down time, maintenance cost and maximize the availability and reliability of equipment. On this premise, this work models the failure rate of Photocopy machines and obtain its optimal preventive maintenance policy that would prevent damage and its attendant losses to both users and end-product consumers. The failure distribution of the machine was shown to follow the Log-Logistic distribution with shape parameter, ˆα=1.723339368 and scale parameter, ˆβ=763.9219635. Optimal probabilities of the distribution were obtained and utilized in both the cumulative failure function and cumulative hazard function-based replacement models to formulate a replacement maintenance policy for the machine. The failure cumulative function-based replacement model was found to be a better model which yields optimal replacement maintenance time of 166 hours at a minimum cost of 113 Naira for maintaining the machine per cycle time with 96% availability, 94% reliability and 0.07% chance of failure occurrence in the machine.

Optimal preventive maintenance policy of the balanced system under the semi-Markov model

Reliability problems of new systems such as balanced systems have received more attention in recent years due to the rapid development of technology. However, the research on maintenance optimization for balanced systems is still underexplored, and the existing policies for orthodox systems cannot solve the maintenance problem of balanced systems. Thus, an optimal preventive maintenance optimization model is formulated under the semi-Markov model for a balanced system with n identical units, where each unit is subject to degradation failure and sojourn times in different function zones follow Erlang distribution with different parameters, respectively. Different from orthodox systems, the failure criterion of the balanced system is given according to the system balance degree. Namely, when any two symmetric components do not perform the same function, the system is out of balance. To avoid system unbalance, a preventive maintenance action is performed once the state difference on any two symmetric units exceeds the maintenance threshold. Finally, some numerical examples are used to demonstrate the priority of the proposed preventive maintenance policy, and the obtained results provide a good insight for repairmen to maintain components on the balanced system.

Optimal condition-based preventive maintenance policy for balanced systems

Reliability evaluation of balanced systems has been extensively studied in recent years. However, the research on maintenance optimization for balanced systems is still underexplored. This paper makes a novel contribution to existing literature by proposing a condition-based preventive maintenance (PM) policy for balanced systems with identical components. Each component is subject to continuous degradation and the states of all components are simultaneously detected at discrete time epochs. The system state is evaluated based on the deterioration levels of all components. The system is out of balance once the deterioration level of any component reaches a critical value or the difference between the deterioration levels of two components on the symmetric positions exceeds a specific threshold, whichever occurs first. In this research, PM activities are employed to avoid competing failures. The optimal PM thresholds are determined by minimizing the system maintenance cost within the framework of semi-Markov decision process. An illustrative example is provided to demonstrate the application of the proposed PM policy for balanced systems.

An optimal preventive maintenance policy for a two-stage competing-risk system with hidden failures

In many complex industrial systems, failures are not always evident to the operating crew, thus inspections are used to identify such hidden failures and then make necessary maintenance actions. In this paper, we study a two-stage system that is subject to two competing risks of degradation and random shocks. Failures of this two-stage competing-risk system are hidden and could only be detected by periodic inspections. For such a system, a delay-time model is introduced to describe the evolution of the system behavior. Random shocks are assumed to follow a homogeneous Poisson process. A preventive maintenance policy is presented in response to the observed system state, based on which the expected cost rate of the system is derived. This paper aims to find the minimal expected cost rate by determining the optimal inspection interval. A numerical example is presented to demonstrate the applicability of the proposed method and results.

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.