OPTIMAL RANDOM AGE REPLACEMENT FOR AVAILABILITY

2012 ◽  
Vol 19 (05) ◽  
pp. 1250021 ◽  
Author(s):  
JOHN E. ANGUS ◽  
MENG-LAI YIN ◽  
KISHOR TRIVEDI
Keyword(s):  
Preventive Maintenance ◽  
Sufficient Conditions ◽  
Optimal Rate ◽  
Maintenance Policy ◽  
Design Decisions ◽  
System Availability ◽  
Critical Design ◽  
Long Run ◽  
Age Replacement

An age replacement maintenance policy is considered here, in which a system is restored whenever it fails, or ages without failure up to a preventive maintenance epoch (whichever comes first). The duration of the restoration activity is random, and depends on whether it was precipitated by a failure or by a preventive maintenance action. The case where the preventive maintenance epoch is deterministic has been studied previously, and shown to be optimal in a certain sense. Here, we consider the case where the preventive maintenance epoch is randomized, which is more realistic for many systems. The system availability is the long run proportion of time that the system is operational (i.e., not undergoing repair or preventive maintenance). The optimal rate of preventive maintenance to maximize availability is considered, along with sufficient conditions for such an optimum to exist. The results obtained herein are useful to systems engineers in making critical design decisions.

A cost relationship between age and block replacement policies

1988 ◽  
Vol 25 (04) ◽  
pp. 789-796 ◽  
Author(s):  
Thomas H. Savits
Keyword(s):  
Stochastic Process ◽  
Operating Cost ◽  
Cost Structure ◽  
Renewal Function ◽  
Maintenance Policy ◽  
Long Run ◽  
On Line ◽  
Age Replacement ◽  
Operating Unit

The general cost structure of a unit on line is assumed to be governed by a stochastic process , where R(t) denotes the operating cost on [0, t)and ζ denotes the time of an unscheduled (or unplanned) replacement by a new unit at a cost c 1. For an age replacement maintenance policy, scheduled (or planned) replacements occur whenever an operating unit reaches age T, whereas in the block replacement case, scheduled replacements occur every T units of time. Such scheduled replacements cost c2. The expected long-run cost per unit time can then be expressed in the form A(T)/Ε [min(ζ, T)] and B(T)/T respectively. Our main result shows that where U is the associated renewal function generated by ζ.

A hybrid preventive maintenance model for systems with partially observable degradation

2020 ◽  
Vol 31 (3) ◽  
pp. 345-365 ◽  
Author(s):  
Maxim Finkelstein ◽  
Ji Hwan Cha ◽  
Gregory Levitin
Keyword(s):  
Preventive Maintenance ◽  
Replacement Policy ◽  
Hybrid Strategy ◽  
Cost Rate ◽  
Shot Noise Process ◽  
Shock Process ◽  
Long Run ◽  
Age Replacement ◽  
Partially Observable ◽  
Maintenance Model

Abstract A new model of hybrid preventive maintenance of systems with partially observable degradation is developed. This model combines condition-based maintenance with age replacement maintenance in the proposed, specific way. A system, subject to a shock process, is replaced on failure or at some time ${T}_S$ if the number of shocks experienced by this time is greater than or equal to m or at time $T>{T}_S$ otherwise, whichever occurs first. Each shock increases the failure rate of the system at the random time of its occurrence, thus forming a corresponding shot-noise process. The real deterioration of the system is partially observed via observation of the shock process at time ${T}_S$. The corresponding optimization problem is solved and a detailed numerical example demonstrates that the long-run cost rate for the proposed optimal hybrid strategy is smaller than that for the standard optimal age replacement policy.

Preventive Maintenance of Multi-State System with Phase-Type Failure Time Distribution and Non-Zero Inspection Time

2003 ◽  
Vol 10 (03) ◽  
pp. 323-344 ◽  
Author(s):  
Dongyan Chen ◽  
Yonghuan Cao ◽  
Kishor S. Trivedi ◽  
Yiguang Hong
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Regenerative Process ◽  
Inspection Time ◽  
Maintenance Policy ◽  
System Availability ◽  
Failure Time Distribution ◽  
Set Up ◽  
Markov Regenerative Process ◽  
The Mathematical Model

Preventive maintenance is applied to improve the system availability or decrease the operational cost. This paper addresses the optimal preventive maintenance problem for multi-state deteriorating systems, where the system experiences multiple stages of performance degradation before it fails. We consider a general case where the inspection and repair time are generally distributed. The threshold type maintenance policy is employed for preventive minor maintenance and preventive major maintenance, where minor or major maintenance is carried out when the system deterioration stage is found to be larger than certain thresholds. The mathematical model of the system is set up by means of a Markov regenerative process (MRGP). With this formulation, the system steady-state probabilities under consideration are computed.

AN OPPORTUNITY-BASED AGE REPLACEMENT POLICY CONSIDERING WARRANTY

1999 ◽  
Vol 06 (03) ◽  
pp. 229-236 ◽  
Author(s):  
BERMAWI P. ISKANDAR ◽  
HIROAKI SANDOH
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Failure Time Distribution ◽  
Warranty Period ◽  
Preventive Replacement ◽  
Long Run ◽  
Age Replacement

This study discusses an opportunity-based age replacement policy for a system which has a warranty period (0, S]. When the system fails at its age x≤S, a minimal repair is performed. If an opportunity occurs to the system at its age x for S<x<T, we take the opportunity with probability p to preventively replace the system, while we conduct a corrective replacement when it fails on (S, T). Finally if its age reaches T, we execute a preventive replacement. Under this replacement policy, the design variable is T. For the case where opportunities occur according to a Poisson process, a long-run average cost of this policy is formulated under a general failure time distribution. It is, then, shown that one of the sufficient conditions where a unique finite optimal T* exists is that the failure time distribution is IFR (Increasing Failure Rate). Numerical examples are also presented for the Weibull failure time distribution.

Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

2003 ◽  
Vol 40 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Sophie Mercier ◽  
Michel Roussignol
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Sufficient Conditions ◽  
Maintenance Policy ◽  
System A ◽  
Up States ◽  
Finite State ◽  
Degradation Degree ◽  
Preventive Maintenance Policy ◽  
Finite State Space

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

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.

Stochastic Models in Preventive Maintenance Policies

2014 ◽  
Vol 1016 ◽  
pp. 802-806
Author(s):  
Onur Gölbaşı ◽  
Nuray Demirel
Keyword(s):  
Poisson Process ◽  
Stochastic Models ◽  
Preventive Maintenance ◽  
Operating Cost ◽  
Replacement Policy ◽  
Market Demand ◽  
Imperfect Maintenance ◽  
Maintenance Policy ◽  
Maintenance Policies ◽  
Age Replacement

In recent decades, philosophy behind maintenance has varied consistently due to the changes in complexity of designs, advances in automation and mechanization, adaptation to the fast growing market demand, commercial computation in the sectors, and environmental issues. In mid-forties, simplicity of designs, limited maintenance opportunities, and immaturity of trade culture made enough to performonly fix it when it brokeapproach, i.e. corrective maintenance, after failures. Last quarter of the 21thcentury made essential to constitute more conservative and preventive maintenance policies in order to ensure safety, reliability, and availability of systems with longer lifetime and cost effectiveness. Preventive maintenance can provide an economic saving more than 18% of operating cost of systems. In this basis, various stochastic models were proposed as a tool to constitute a maintenance policy to measure system availability and to obtain optimal maintenance periods. This paper presents a general perspective on common stochastic models in maintenance planning such as Homogenous Poisson Process, Non-Homogenous Poisson Process, and Imperfect Maintenance. The paper also introduces two common maintenance policies, block and age replacement policy, using these stochastic models.

Condition-Based Maintenance Policy under Imperfect Inspection Using Monte-Carlo Simulation

2012 ◽  
Vol 201-202 ◽  
pp. 955-958
Author(s):  
En Shun Ge ◽  
Qing Min Li ◽  
Guang Yu Zhang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Preventive Maintenance ◽  
Condition Based Maintenance ◽  
Gamma Process ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Numerical Example ◽  
Long Run

Condition-based Maintenance (CBM), which can efficiently improve the performance of the deteriorating system, would be influenced by imperfect inspection in practice. Aiming at this problem, a new CBM model under imperfect inspection is presented for deteriorating system, which described by Gamma process. The system is inspected periodically, and a preventive maintenance is performed if the degradation level exceeds a threhold. The inspection is imperfect, that means the measurements contain errors, and the CBM model should take these measure errors into account. The algorithm is shown to estimate the long run cost rate using Monte-Carlo method. Through numerical example, the influence of mesurement error over long run cost is analyzed. Therefore, the correctness and rationality of the model are proved.

Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

2003 ◽  
Vol 40 (01) ◽  
pp. 1-19 ◽  
Author(s):  
Sophie Mercier ◽  
Michel Roussignol
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Sufficient Conditions ◽  
Maintenance Policy ◽  
System A ◽  
Up States ◽  
Finite State ◽  
Degradation Degree ◽  
Preventive Maintenance Policy ◽  
Finite State Space

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

Sign in / Sign up

Export Citation Format

Share Document