MAINTENANCE OPTIMIZATION OF EQUIPMENT BY LINEAR PROGRAMMING

2005 ◽  
Vol 20 (1) ◽  
pp. 183-193 ◽  
Author(s):  
Archana Jayakumar ◽  
Sohrab Asgarpoor
Keyword(s):  
Linear Programming ◽  
Preventive Maintenance ◽  
Mathematical Optimization ◽  
Optimal Solution ◽  
Cost Effective ◽  
Maintenance Policy ◽  
Markov Decision ◽  
Random Failure ◽  
Optimal Maintenance ◽  
Optimal Maintenance Policy

Optimal levels of preventive maintenance performed on any system ensures cost-effective and reliable operation of the system. In this paper a component with deterioration and random failure is modeled using Markov processes while incorporating the concept of minor and major preventive maintenance. The optimal mean times to preventive maintenance (both minor and major) of the component is determined by maximizing its availability with respect to mean time to preventive maintenance. Mathematical optimization programs Maple 7 and Lingo 7 are used to find the optimal solution, which is illustrated using a numerical example. Further, an optimal maintenance policy is obtained using Markov Decision Processes (MDPs). Linear Programming (LP) is utilized to implement the MDP problem.

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.

An Optimal Maintenance Policy for a Queueing System Server Under Periodic Observation

1997 ◽  
Vol 04 (04) ◽  
pp. 357-367 ◽  
Author(s):  
Junji Koyanagi ◽  
Hajime Kawai
Keyword(s):  
Preventive Maintenance ◽  
Queueing System ◽  
Observation Time ◽  
Maintenance Policy ◽  
Corrective Maintenance ◽  
Markov Decision ◽  
Poisson Stream ◽  
Optimal Maintenance ◽  
Optimal Maintenance Policy ◽  
Time Of Failure

This paper describes an optimal maintenance policy for an M/M/1 queueing system server. Customers arrive at the system in a Poisson stream and are served by the exponential server. After a random time, the server is interrupted by a failure and this failure is detected through regularly timed observations. We begin corrective maintenance when we detect the failure. Through the failure of the server, we lose the customers in the system at the time of failure, as well as the customers that arrive between the failure and the completion of corrective maintenance. However, it is possible to avoid the failure and subsequent corrective maintenance by performing preventive maintenance at observation time. It is true that customers in the system at the start of preventive maintenance and those that arrive prior to its completion are lost. Since the queueing system should serve as many customers as possible, our objective is to minimize the number of lost customers. We then formulate this problem as a semi-Markov decision process and prove the switch curve structure of the optimal policy.

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.

Maintenance Decision Model for a Two-Machine Production Line With Multistage Degradation Machines

2018 ◽  
Author(s):  
Yunyi Kang ◽  
Feng Ju
Keyword(s):  
Decision Model ◽  
Production Systems ◽  
Maintenance Policy ◽  
Multi Stage ◽  
Markov Decision ◽  
Optimal Maintenance ◽  
Markov Decision Model ◽  
Maintenance Decision ◽  
Maintenance Policies ◽  
Optimal Maintenance Policy

In this work, we develop preventative maintenance policies on two-machine-and-one-buffer production systems with machines subject to multi-stage degradation. Condition-based maintenance policies are generated for both machines, with consideration on both the machine degradation stages and the buffer level. Moreover, the policies are flexible, allowing a machine to be recovered to any better operating state, while merely recovering to the best operating state is possible in many previous work. A Markov decision model is formulated to find the optimal maintenance policy and computational experiments show that the policies improve the performance of a system in finite production runs.

Control Improvement of the Reactor Protection System

2011 ◽  
Vol 71-78 ◽  
pp. 4199-4202
Author(s):  
Bo Ya Zhao ◽  
Song Yang ◽  
Zhe Zhang ◽  
Ri Sheng Sun
Keyword(s):  
Preventive Maintenance ◽  
Protection System ◽  
Maintenance Policy ◽  
Block System ◽  
Replacement Model ◽  
Optimal Maintenance ◽  
Age Replacement ◽  
Reactor Protection System ◽  
Optimal Maintenance Policy ◽  
Random Failures

In this paper an optimal maintenance policy for a Reactor Protection System (RPS) for a nuclear plant was developed. RPS consists of continuously operating sub-systems that were subject to random failures. A block system diagram for RPS had been proposed that facilitates analyzing of individual sub-systems separately. The proposed maintenance policy is the Age Replacement model, which incorporated both corrective and preventive maintenances. A Markov model was used to optimize the preventive maintenance interval of those sub-systems whose failure and repair rates were exponentially distributed. Finally, a sensitivity analysis had been performed and recommendations for maintaining the required RPS availability have been suggested.

A Generalized Age-Replacement Model

1992 ◽  
Vol 6 (4) ◽  
pp. 525-541 ◽  
Author(s):  
Stephan G. Vanneste
Keyword(s):  
Optimization Procedure ◽  
Control Limit ◽  
Maintenance Policy ◽  
Unimodal Function ◽  
Replacement Model ◽  
Markov Decision ◽  
Optimal Maintenance ◽  
Age Replacement ◽  
Replacement Problem ◽  
Optimal Maintenance Policy

Four practically important extensions of the classical age-replacement problem are analyzed using Markov decision theory: (1) opportunity maintenance, (2) imperfect repair, (3) non-zero repair times, and (4) Markov degradation of the working unit. For this general model, we show that the optimal maintenance policy is of the control limit type and that the average costs are a unimodal function of the control limit. An efficient optimization procedure is provided to find the optimal policy and its average costs. The analysis extends and unifies existing results.

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