Imperfect Preventive Maintenance Model Research Articles

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.

Multiobjective Flexible Job-Shop Rescheduling With New Job Insertion and Machine Preventive Maintenance.

In the actual production, the insertion of new job and machine preventive maintenance (PM) are very common phenomena. Under these situations, a flexible job-shop rescheduling problem (FJRP) with both new job insertion and machine PM is investigated. First, an imperfect PM (IPM) model is established to determine the optimal maintenance plan for each machine, and the optimality is proven. Second, in order to jointly optimize the production scheduling and maintenance planning, a multiobjective optimization model is developed. Third, to deal with this model, an improved nondominated sorting genetic algorithm III with adaptive reference vector (NSGA-III/ARV) is proposed, in which a hybrid initialization method is designed to obtain a high-quality initial population and a critical-path-based local search (LS) mechanism is constructed to accelerate the convergence speed of the algorithm. In the numerical simulation, the effect of parameter setting on the NSGA-III/ARV is investigated by the Taguchi experimental design. After that, the superiority of the improved operators and the overall performance of the proposed algorithm are demonstrated. Next, the comparison of two IPM models is carried out, which verifies the effectiveness of the designed IPM model. Last but not least, we have analyzed the impact of different maintenance effects on both the optimal maintenance decisions and integrated maintenance-production scheduling schemes.

Reliability-based optimization of imperfect preventive maintenance with Bayesian estimation

In this study, we present a sequential imperfect preventive maintenance model for a component subject to degradation. We use an age reduction reliability model for scheduling preventive maintenance, which is performed whenever the component’s reliability falls below the reliability threshold level, R. The problem is considered under lack of data, in which the Bayesian methodology is more appropriate than the frequentist view for estimating the unknown parameters of the model. We assume a fixed duration for preventive maintenance, whereas the duration of corrective maintenance is an exponential random variable. We model the total expected cost over all cycles and find the optimal preventive maintenance plan until a replacement based on the reliability threshold value. We also conducted a numerical study for sensitivity analysis of the developed model.

Two-Dimensional Extended Warranty Strategy for an Economic Dependence Multi-Component Series System With Grid Search Algorithm

Extended warranty is an optional contract that often provides additional protection for users after the basic warranty expires. Considering the high warranty cost borne by manufacturers and the lack of system availability guarantee, the present study proposes a two-dimensional extended warranty approach for a multi-component series system considering economic dependence. Based on the imperfect preventive maintenance model and the combination of free warranty and pro-rata warranty policies, the manufacturer’s and user’s warranty cost model and availability model for a single component are established. Considering the economic dependence between multi-components, the preventive maintenance of each component is combined using the grouping maintenance approach. In the case study, we consider the reconnaissance equipment as the research object and use the grid search method to obtain the two-dimensional extended warranty scheme of reconnaissance equipment considering economic dependence. Comparative and sensitivity analyses verify that the approach can effectively reduce the extended warranty cost of the manufacturer and improve the availability of the multi-component system. Additionally, the approach can provide support for warranty cost calculation and system availability estimation under different extended warranty periods.

Geometric imperfect preventive maintenance and replacement (GIPMAR) model for aging repairable systems

PurposeThis work seeks to develop a geometric imperfect preventive maintenance (PM) and replacement model (GIPMAR) for aging repairable systems due to age and prolong usage that would meet users need in three phases: within average life span, beyond average life span and beyond initial replacement age of system.Design/methodology/approachThe authors utilized the geometric process (GP) as the hazard function to characterize the increasing failure rate (IFR) of the system. The GP hazard function was incorporated into the hybridized preventive and replacement model of Lin et al. (2000). The resultant expected cost rate function was optimized to obtain optimum intervals for PM/replacement and required numbers of PM per cycle. The proposed GIPMAR model was applied to repairable systems characterized by Weibull life function and the results yielded PM/replacement schedules for three different phases of system operation.FindingsThe proposed GIPMAR model is a generalization of Lin et al. (2000) PM model that were comparable with results of earlier models and is adaptive to situations in developing countries where systems are used across the three phases of operation depicted in this work. This may be due to economic hardship and operating environment.Practical implicationsThe proposed model has provided PM/Replacement schedules for different phases of operation which was never considered. This would provide a useful guide to maintenance engineers and end-users in developing countries with a view to minimizing the average cost of maintenance as well as reducing the number of down times of systems.Social implicationsA duly implemented GIPMAR model would ensure efficient operation of systems, optimum man-hour need in the organization and guarantee customer's goodwill in a competitive environment.Originality/valueIn this work, the authors have extended Lin et al. (2000) PM model to provide PM/replacement schedules for aging repairable systems which was not provided for in earlier existing models and literature.

Expected Proportional Hazard Model in Preventive Maintenance

Whether directly in the form of expenses or indirectly, the objective of maintenance in the mining industry is self-evident in time losses and loss of production. In this paper, the reliability-based maintenance is examined with a different insight than before. The system goes back to the Good As New (GAN) state or too Bad As Old (BAO) maintenance state; why so, the maintenance of the system shifts to the midrange state. On the other hand, the implementation of repairs is strongly influenced by the environmental factors that are known as the “risk factors”. Therefore, an analysis requires a model that integrates two basic elements: (1) incompleteness of the maintenance effect and (2) risk factors. Thus, an extensive proportional hazard ratio model (EPHM) is used as a combination of the Proportional Hazard Model (PHM) and the Hybrid Imperfect Preventive Maintenance model (HIPM) in order to analyze these elements. In this regards, four different preventive maintenance strategies are proposed. All four strategies are time-based including constant interval or periodic (the first and second strategies) and cyclic interval (the third and fourth strategies). The proposed method is applied for a Komatsu HD785-5 dump-truck in the Songun copper mine as a case study. The PM intervals with a mean value of risk factors for the four activities to reach the 80% reliability for the first and second strategies are about 5 and 48 hours. These intervals for the third strategy are calculated as 48.36, 11.58, 10.25, and 9.035, and for the fourth strategy are 5.06, 4.078, 3.459, and 1.92.

Sequential imperfect preventive maintenance model with failure intensity reduction with an application to urban buses

Urban buses usually require several distinct types of preventive maintenance. Due to the complexity of urban buses, quantifying the efficiency of preventive maintenance is very important for maintenance management decision-making and optimization. This study presents a sequential imperfect preventive maintenance model to quantify the maintenance efficiency of urban buses. Existing works of sequential imperfect preventive maintenance models are all formulated based on failure intensity reduction. The proposed model in this study defines maintenance efficiency as a proportion of the difference between actual and expected failure intensity increments. Since the proportion of the difference can vary from negative to positive, the proposed model can quantify all kinds of maintenance efficiency given in the existing works. A case study of an urban bus fleet in China is presented to illustrate the effectiveness of the model.

Preventive Maintenance Models Based on the Generalized Geometric Process

For a generalized geometric process (GGP), the geometric ratio changes with the number of repairs rather than a constant. The GGP is a more flexible maintenance model that can reflect the varying of the repair effect to the system. On the basis of the GGP, two imperfect preventive maintenance (PM) models are studied. First, we assume that the system is preventively maintained periodically after every $T$ time unit, and is correctively repaired at failure. The corrective repair is a minimal repair that just restores the system to work, while the PM results in a GGP, i.e., the lifetime sequence of a system after PM constitute a decreasing GGP. The long-run average cost rate $C(N,T)$ of the system is derived, and the optimal bivariate policy $(N^*,T^*)$ is determined by minimizing $C(N,T)$ , where $N$ is the number of PMs before replacement. Next, a sequential PM model is investigated for a system in which a sequential time interval to be determined for PM. An algorithm is given to seek the optimal replacement policy $N^*$ and the optimal time intervals $T_1^*,T_2^*,\ldots, T_N^*$ between PMs. By assuming that the lifetime of the system is Weibull distributed, the optimal policy is obtained explicitly. In both models, numerical examples are provided to verify the effectiveness of the approaches developed.

Joint Optimization of Production Plan and Preventive Maintenance Schedule by Stackelberg Game

This paper considers the situation where the production planning sector has decision making priority over the maintenance sector. The production rate of each production period (PP) varies with different lot size of each PP. An extended imperfect preventive maintenance (PM) model is proposed for a system running with time-varying production rate. The Stackelberg game theory model is adopted to handle the interactive effect between production plan and PM schedule; meanwhile, it embodies the decision priority of the production planning sector. In the Stackelberg game theory model, the production planning sector is assigned to be the leader with the decision variable of production rate of each PP, and the maintenance sector to be the follower with the decision variable of PM schedule. Firstly, the optimal lot size of each item for each PP is obtained for the production planning sector. Then, the optimal production rate of each PP and PM sequences are obtained simultaneously by regarding the total lot size of each PP as the objective. The availability loss caused by maintenance operations and effect of production rate on hazard rate function of system have been considered. An example is studied to illustrate the effectiveness of the model, also the results are fully analyzed.

A dynamic maintenance policy for production system with variable operational condition

This paper proposes a dynamic opportunistic preventive maintenance (PM) policy for a multi-machine system with batch production of pull pattern. The situation that the operational condition (OC) between each batch is variable and the information of next batch cannot be confirmed until the completion of current batch is studied. One objective of this study is to present the evolution model of reliability and hazard rate when OC changes, and develop a novel imperfect PM model of machine operating under variable OC. Setting that PM can be implemented only at the shift point of each batch, minimal repair is adopted to restore the machine back to work without altering hazard rate when failure happens during PM intervals, another objective is to propose a dynamic opportunistic PM policy to optimize the PM machine group at each batch shift point. A numerical example is finally introduced to validate the necessity of taking into account OC and to verify the effectiveness of our model.

Imperfect Preventive Maintenance Model Study Based On Reliability Limitation

Effective maintenance is crucial for equipment performance in industry. Imperfect maintenance conform to actual failure process. Taking the dynamic preventive maintenance cost into account, the preventive maintenance model was constructed by using age reduction factor. The model regards the minimization of repair cost rate as final target. It use allowed smallest reliability as the replacement condition. Equipment life was assumed to follow two parameters Weibull distribution since it was one of the most commonly adopted distributions to fit cumulative failure problems. Eventually the example verifies the rationality and benefits of the model.

A model for optimizing maintenance policy for power equipment

• A new maintenance model for making optimal maintenance decisions. • The model was developed as a function of maintenance interval. • The model does not need of estimating parameters subjectively. • The model demonstrates its applicability and simplicity. Electrical utilities have the problem of applying complex mathematical models for maintenance optimization of power equipment. This is because the models presented in the literature lack the simplicity desired to carry out evaluations, and some others require a great number of input data, which may not be easily available. In order to overcome these difficulties, a new analytical optimization method for preventive maintenance (PM) policy with minimal repair at failure, periodic overhaul, and replacement is proposed for power equipment 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 overhaul interval T 0 and the optimal overhaul interval T to be found. The Weibull parameters are estimated using a new analytical method. Based on this model, the optimal number of overhauls and the optimal overhaul interval for minimizing the expected total maintenance cost are also analytically determined. Several study cases were designed in order to test the proposed model, demonstrating its applicability and simplicity to determine an optimal maintenance 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.

Optimal Age Policy for a Used System with Imperfect Preventive Maintenance and Cumulative Damage Model

In this article, the concept of imperfect preventive maintenance is discussed and an age maintenance policy is developed based on the cumulative damage model for a used system with initial variable damage. The deterioration of the system is assumed to suffer the non-homogeneous Poisson shocks which can be divided into two types with stochastic probability: Type-I shock (minor) yields a random amount of additive damage of the system, or Type-II shock (catastrophic) causes the system to fail. An age preventive maintenance policy T is presented in which the system undergoes preventive maintenance at a scheduled lifetime T, or corrective maintenance at first Type-II shock and the total damage exceeds a threshold level, whichever occurs first. The objective is to determine the optimal preventive maintenance schedule such that the expected cost rate is minimized. The optimal solution is derived analytically and discussed numerically.

Reliability for multiple units adopting sequential imperfect maintenance policies

Preventive maintenance literature provides so many models that address single unit systems. However, many real life applications deal with multiple-unit systems. This work deals with a sequential imperfect preventive maintenance model and extends it to consider multiple units. The model targets specific system reliability by determining the maintenance timing for each unit in the system. The model helps to optimize the maintenance management process for multiple-unit systems.

Optimizing Bi-Objective Imperfect Preventive Maintenance Model for Multi-Component System Using a Proposed Improved PSO Algorithm

This study aims to establish a bi-objective imperfect preventive maintenance (BOIPM) model in which the total maintenance cost and the mean system reliability are optimized by determining the maintenance periods and maintenance activities simultaneously. To efficiently solve the established BOIPM model, this study proposes an improved particle swarm optimization (IPSO) algorithm. The IPSO extends the practicability of the conventional PSO originally designed to solve an optimization problem with continuous decision variables. Furthermore, time-varying mechanisms associated with search parameters of the PSO are utilized to enhance the particles search capability. An adjustment mechanism addressing the issue of particles falling into the infeasible area is constructed to enhance the exploring ability of the IPSO. A case verifies the effectiveness of the proposed approach.

Optimizing bi-objective imperfect preventive maintenance model for series-parallel system using established hybrid genetic algorithm

This study establishes a bi-objective imperfect preventive maintenance (BOIPM) model of a series-parallel system. The improvement factor method is used to evaluate the extent to which repairing components can restore the system reliability. The total maintenance cost and mean system reliability are optimized simultaneously through determining the most appropriate maintenance alternative. A bi-objective hybrid genetic algorithm (BOHGA) is established to optimize the BOIPM model. The BOHGA utilizes a Pareto-based technique to determine and retain the superior chromosomes as the GA chromosome evolutions are performed. Additionally, a unit-cost cumulative reliability expectation measure (UCCREM) is developed to evaluate the extent to which maintaining each individual component benefits the total maintenance cost and system reliability over the operational lifetime. This UCCREM is then incorporated into the genetic algorithm to construct a superior initial chromosome population and thereby enhance its solution efficiency. In order to obtain diverse bi-objective solutions as the Pareto-efficient frontier is approached, the closeness metric and diversity metric are employed to evaluate the superiority of the non-dominated solutions. Accordingly, decision makers can easily determine the most appropriate maintenance alternative. Three simulated cases verify the efficacy and practicality of this approach for determining an imperfect preventive maintenance strategy.

Exact Results on the Statistically Expected Total Cost and Optimal Solutions for Extended Periodic Imperfect Preventive Maintenance

Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) presented an interesting extended periodic imperfect preventive maintenance (EPIPM) model for a system with age-dependent failure type. Many cases studied previously are special cases of the EPIPM model. In the Errata (IEEE Trans. Rel., vol. 60, no. 2, 2011), Sheu and Chang showed that the proposed effective age and the proposed hazard rate function after the PM are incorrect. In this paper, based on the correct failure characteristics (effective age and hazard rate function after PM), the correct s -expected total cost per unit time for the EPIPM model is presented. By assigning three types of failure characteristics for the EPIPM model, we analyse and compare the corresponding s -expected total costs per unit time. We find that the s-expected total cost per unit time developed by Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) is only one upper bound of the exact s-expected total cost per unit time. In addition, we also give some results on the existence of the optimal solution for the exact s -expected total cost.

Optimal Imperfect Periodic Preventive Maintenance for Systems in Time-Varying Environments

Manufacturing systems run in time-varying environmental and operational conditions. For the effective manager to make a long-term preventive maintenance decision, it is necessary to integrate the time-varying environment into preventive maintenance (PM) policies. This paper considers PM for systems running in the time-varying environment, modeled as a two-state homogeneous Markov process, where one state represents a typical condition, and the other represents a severe condition. Environmental conditions affect the hazard rate function through a proportional hazard model. To avoid sudden failures in a system due to either minor failures or catastrophic failures, an extended periodic imperfect preventive maintenance model is carried out, and the maintenance effect is modeled with an age reduction factor, and a hazard improvement factor. We prove the discontinuity of the hazard rate function of the system in a time-varying environment through a Markov additive process. We also give a method to compute the probability density function of failure at any time. Further, the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$s$</tex></formula> -expected cost rate of the system in the time-varying environment is compared with the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$s$</tex></formula> -expected cost rates of the system always working in typical, and severe conditions. Finally, numerical examples fully verify our main results.

An Extended Sequential Imperfect Preventive Maintenance Model with Improvement Factors

This article presents a generalization of the imperfect sequential preventive maintenance (PM) policy with minimal repair. As failures occur, the system experiences one of two types of failures: a Type-I failure (minor), rectified by a minimal repair; or a Type-II failure (catastrophic) that calls for an unplanned maintenance. In each maintenance period, the system is maintained following the occurrence of a Type-II failure or at age, whichever takes place first. At the Nth maintenance, the system is replaced rather than maintained. The imperfect PM model adopted in this study incorporates with improvement factors in the hazard-rate function. Taking age-dependent minimal repair costs into consideration, the objective consists of finding the optimal PM and replacement schedule that minimize the expected cost per unit time over an infinite time-horizon.