Sequential imperfect preventive maintenance policy with random maintenance quality under reliability limit

2011 ◽  
Vol 225 (8) ◽  
pp. 1926-1935 ◽  
Author(s):  
Z Wang ◽  
J Yang ◽  
G Wang ◽  
G Zhang
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Average Cost ◽  
Numerical Control ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Proposed Model ◽  
Optimal Maintenance ◽  
Average Cost Rate ◽  
Optimal Maintenance Policy

To determine the optimal maintenance number for a system with random maintenance quality in infinite time horizon, a sequential imperfect preventive maintenance model considering reliability limit is proposed. The proposed model is derived from the combination of the Kijima type virtual age model and the failure rate adjustment model. Maintenance intervals of the proposed model are obtained through an iteration method when both failure rate increase factor and maintenance restoration factor are random variables with a uniform distribution. The optimal maintenance policy is presented by minimizing the long-run average cost rate. A real numerical example for the failures of numerical control equipment is given to demonstrate the proposed model. Finally, a discussion is presented to show how the optimal average cost rate depends on the different cost parameters. The results show that in order to satisfy the practical requirements of high reliability, it is necessary and worthwhile to consider the system's reliability limit in preventive maintenance practice.

scholarly journals A model for a dynamic preventive maintenance policy

2000 ◽  
Vol 13 (4) ◽  
pp. 321-346 ◽  
Author(s):  
Christiane Cocozza-Thivent
Keyword(s):  
Simulated Annealing ◽  
Stochastic Model ◽  
Preventive Maintenance ◽  
Average Cost ◽  
Simulated Annealing Algorithm ◽  
Maintenance Policy ◽  
Optimal Maintenance ◽  
Annealing Algorithm ◽  
Optimal Maintenance Policy ◽  
Preventive Maintenance Policy

This paper exhibits a stochastic model which describes the evolution of a material submitted to inspections. When an inspection takes place, a decision depending on the observed state of the material is taken. If the material is in “not too bad” state, no service is rendered, only the date of the next inspection is chosen. If the material is in a “bad” working state, a service takes place. Roughly speaking, the failure rates of the material are constant, the inspection and repair rates are general. We define the average cost function corresponding to the utilization of this material and we show how it can be computed. Then we determine the inspection rates which give the optimal maintenance policy using a simulated annealing algorithm. We observe experimentally that the best durations between inspections are deterministic ones.

scholarly journals Reliability modelling and maintenance policy optimization for a repairable parallel system

2021 ◽  
Author(s):  
Reza Ahmadi ◽  
Shaomin Wu ◽  
Amirhossein Sobhani
Keyword(s):  
Integrated Approach ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Preventive Replacement ◽  
State Process ◽  
Reliability Modelling ◽  
Proposed Model ◽  
Average Cost Rate ◽  
Policy Optimization ◽  
Hidden Failures

This paper proposes an integrated approach for reliability modelling and maintenance scheduling of repairable parallel systems subject to hidden failures. The system consists of heterogeneous redundant subsystems whose failures are revealed only by inspections. Inspections at periodic times reveal the components state and repair actions are decided by the excursion of a basic state process describing the total number of failed components in each subsystem. Using the standard renewal arguments, the paper aims at minimizing the average cost rate by the joint determination of the optimal inspection interval, the partial repair threshold and the preventive replacement threshold. We illustrate the procedure for the case as the components' lifetimes conform to the Weibull distribution. Numerical examples are used to illustrate the proposed model and the response of the optimal solutions to the model's parameters.

Optimal CBM policy with two sampling intervals

2017 ◽  
Vol 23 (1) ◽  
pp. 95-112 ◽  
Author(s):  
Farnoosh Naderkhani ◽  
Leila Jafari ◽  
Viliam Makis
Keyword(s):  
Average Cost ◽  
Hazard Function ◽  
Sampling Interval ◽  
Mean Residual Life ◽  
Maintenance Policy ◽  
Economic Point ◽  
Content Type ◽  
Proposed Model ◽  
Sampling Intervals ◽  
Optimal Maintenance Policy

Purpose The purpose of this paper is to propose a novel condition-based maintenance (CBM) policy with two sampling intervals for a system subject to stochastic deterioration described by the Cox’s proportional hazards model (PHM). Design/methodology/approach In this paper, the new or renewed system is monitored using a longer sampling interval. When the estimated hazard function of the system exceeds a warning limit, the observations are taken more frequently, i.e., the sampling interval changes to a shorter one. Preventive maintenance is performed when either the hazard function exceeds a maintenance threshold or the system age exceeds a pre-determined age. A more expensive corrective maintenance is performed upon system failure. The proposed model is formulated in the semi-Markov decision process (SMDP) framework. Findings The optimal maintenance policy is found and a computational algorithm based on policy iteration for SMDP is developed to obtain the control thresholds as well as the sampling intervals minimizing the long-run expected average cost per unit time. Research limitations/implications A numerical example is presented to illustrate the whole procedure. The newly proposed maintenance policy with two sampling intervals outperforms previously developed maintenance policies using PHM. The paper compares the proposed model with a single sampling interval CBM model and well-known age-based model. Formulas for the conditional reliability function and the mean residual life are also derived for the proposed model. Sensitivity analysis has been performed to study the effect of the changes in the Weibull parameters on the average cost. Practical implications The results show that considerable cost savings can be obtained by implementing the maintenance policy developed in this paper. Originality/value Unlike the previous CBM policies widely discussed in the literature which use sequential or periodic monitoring, the authors propose a new sampling strategy based on two sampling intervals. From the economic point of view, when the sampling is costly, it is advantageous to monitor the system less frequently when it is in a healthy state and more frequently when it deteriorates and enters the unhealthy state.

scholarly journals A Stochastic Failure Model with Dependent Competing Risks and its Applications to Condition-Based Maintenance

2015 ◽  
Vol 52 (2) ◽  
pp. 558-573 ◽  
Author(s):  
Ji Hwan Cha ◽  
Inma T. Castro
Keyword(s):  
Competing Risks ◽  
Common Source ◽  
Maintenance Strategy ◽  
Failure Model ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Long Run ◽  
Degradation Failure ◽  
Average Cost Rate ◽  
Optimal Maintenance Policy

In this paper a stochastic failure model for a system with stochastically dependent competing failures is analyzed. The system is subject to two types of failure: degradation failure and catastrophic failure. Both types of failure share an initial common source: an external shock process. This implies that they are stochastically dependent. In our developments of the model, the type of dependency between the two kinds of failure will be characterized. Conditional properties of the two competing risks are also investigated. These properties are the fundamental basis for the development of the maintenance strategy studied in this paper. Considering this maintenance strategy, the long-run average cost rate is derived and the optimal maintenance policy is discussed.

scholarly journals Optimal Maintenance Policy for a Technical System Subject to Hidden Faults and Randomly Occurring Hazards

2020 ◽  
Vol 6 (1) ◽  
pp. 396-415
Author(s):  
Jacek Malinowski
Keyword(s):  
Poisson Process ◽  
Preventive Maintenance ◽  
Cost Effective ◽  
Optimal Time ◽  
Maintenance Policy ◽  
Modeling And Analysis ◽  
Optimal Maintenance ◽  
Simple Equations ◽  
Periodic Inspections ◽  
Optimal Maintenance Policy

The paper presents a method of finding the optimal time between inspections for a system subject to degradation-related faults which make the system vulnerable to randomly occurring external hazards that may cause its damage. Since faults are assumed to be hidden, periodic inspections and repairs have to be performed in order to detect and remove them. Otherwise, leaving the faulty system unmaintained would eventually lead to a very costly damage. It is also assumed that the time to occurrence of a fault is exponentially distributed and hazardous events constitute a Poisson process. The fault rate, the intensity of the Poisson process and the probability with which a hazardous event results in the system damage are the known parameters. The author presents two main results achieved by analyzing this maintenance model. First, the criteria to be fulfilled by the system parameters in order that preventive maintenance be cost-effective are given in the form of simple inequalities. These criteria must be met so that operating the system with preventive maintenance in place be less costly than operating it until a damage occurs and replacing it thereafter. Second, fairly simple equations are obtained from which the optimal time between inspections can be found numerically by the Newton-Raphson method. The analytical derivation of both the criteria and the equations is presented in detail and is the author’s original work. To the best of his knowledge the obtained results are new in the area of maintenance modeling and analysis. For better understanding, theoretical considerations are illustrated by an example of a generic explosion prevention system.

scholarly journals A study on an optimal replacement policy for a deteriorating system under partial product process

10.26524/cm65 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Govindaraju P ◽  
Rajendiran R
Keyword(s):  
Explicit Expression ◽  
Average Cost ◽  
Replacement Policy ◽  
Partial Product ◽  
Maintenance Policy ◽  
Optimal Replacement ◽  
Optimal Replacement Policy ◽  
Optimal Maintenance ◽  
Random Shocks ◽  
Optimal Maintenance Policy

In this paper, we consider an optimal maintenance policy for a reparable deteriorating system subject to random shocks. For a reparable deteriorating system, the repair time by a partial product process and the failure mechanism by a generalized δshock process. Develop an explicit expression of the ling run average cost per unit time under N policy is studied.

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