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

2015 ◽  
Vol 52 (02) ◽  
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 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.

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 Optimal Condition-Based Maintenance Strategy for Multi-Component Systems under Degradation Failures

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4346
Author(s):  
Kui Wang ◽  
Chao Deng ◽  
Lili Ding
Keyword(s):  
Critical Level ◽  
Condition Based Maintenance ◽  
Maintenance Strategy ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Optimal Monitoring ◽  
Long Run ◽  
Component Systems ◽  
Maintenance Decision ◽  
The Impact

This paper proposes a condition-based maintenance strategy for multi-component systems under degradation failures. The maintenance decision is based on the minimum long-run average cost rate (LACR) and the maximum residual useful lifetime (RUL), respectively. The aim of this paper is to determine the optimal monitoring interval and critical level for multi-component systems under different optimization objectives. A preventive maintenance (PM) is triggered when the degradation of component exceeds the corresponding critical level. Afterwards, the paper discusses the relationship between the critical level and the monitoring interval with regards to the LACR and RUL. Methods are also proposed to determine the optimal monitoring interval and the critical level under two decision models. Finally, the impact of maintenance decision variables on the LACR and RUL is discussed through a case study. A comparison with conventional maintenance policy shows an outstanding performance of the new model.

Modeling a sequentially inspected system prone to degradation and shocks

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Himani Pant ◽  
S.B. Singh
Keyword(s):  
Single Unit ◽  
Pipeline System ◽  
System Productivity ◽  
Content Type ◽  
Cost Rate ◽  
Oil Pipeline ◽  
Unit System ◽  
Long Run ◽  
Degradation Failure ◽  
Average Cost Rate

PurposeIn certain environments, the system may not fail completely, but undergoes degradation, and the system productivity might decrease. Meanwhile, at the same time, the system may be vulnerable to shocks. A single-unit system prone to degradation and shocks is proposed in this study, and emphasis is placed upon determining its availability and cost rate.Design/methodology/approachThe considered single-unit system is expected to have three states, namely, normal, degraded and failed. As the system enters the degraded state, it is said to be partially failed. The degraded state incurs higher degradation than the normal state and is more prone to shocks. Inspections are used to determine the state and failure type of the system. Inspections are predetermined to be carried out sequentially at time I, I+aI, I+aI+a2I,… where 0 < a ≤ 1, until the detection of degradation/failure. Perfect repairs are conducted instantly on spotting the partial/complete failure. Two cases have been considered of repair taking constant times and random times.FindingsExplicit results on the reliability, availability (both point and limiting availability) and long-run average cost rate (LRACR) of a sequentially inspected single-unit system prone to degradation and shocks under constant and random repair times are given. Numerical example of an oil pipeline system is taken to clarify the acquired results.Originality/valueA sequentially inspected single-unit system prone to degradation and shock is studied unlike done previously.

Availability analysis and maintenance optimization for multiple failure mode systems considering imperfect repair

2021 ◽  
pp. 1748006X2110127
Author(s):  
Qingan Qiu ◽  
Baoliang Liu ◽  
Cong Lin ◽  
Jingjing Wang
Keyword(s):  
Failure Modes ◽  
Maintenance Cost ◽  
Imperfect Maintenance ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Availability Analysis ◽  
Long Run ◽  
Optimal Maintenance ◽  
Maintenance Policies ◽  
Periodic Inspections

This paper studies the availability and optimal maintenance policies for systems subject to competing failure modes under continuous and periodic inspections. The repair time distribution and maintenance cost are both dependent on the failure modes. We investigate the instantaneous availability and the steady state availability of the system maintained through several imperfect repairs before a replacement is allowed. Analytical expressions for system availability under continuous and periodic inspections are derived respectively. The availability models are then utilized to obtain the optimal inspection and imperfect maintenance policy that minimizes the average long-run cost rate. A numerical example for Remote Power Feeding System is presented to demonstrate the application of the developed approach.

Optimization of Leased Equipment Maintenance Policy Based on History Failure Data

2021 ◽  
pp. 2150030
Author(s):  
Ke Dong ◽  
Kehong Chen
Keyword(s):  
Power Law ◽  
Cost Model ◽  
Maintenance Strategy ◽  
Maintenance Policy ◽  
Power Law Process ◽  
Total Cost ◽  
Cost Rate ◽  
Failure Data ◽  
Expected Total Cost ◽  
The Cost

We propose a maintenance policy for new equipment on a repair-refund maintenance strategy in this paper and derive the optimal lease period from the lessor’s perspective based on independent and identical distribution of historical failure data which obey power law process. The cost model of a full refund and a proportional refund is studied, and the corresponding optimal leasing period is determined by reducing the expected total cost rate to the largest extent. We use a numerical example to illustrate the proposed cost model and analyze the sensitivity of related parameters. Furthermore, we show that the proportional refund policy is preferable than a full refund to the lessor. Finally, according to the simulation outcome, the proposed methods are effective and instructions for lessor in regard to equipment lease are provided.

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.

Reliability and maintenance modeling for competing failures with intermission considered

2019 ◽  
Vol 233 (5) ◽  
pp. 898-907
Author(s):  
Jingyi Liu ◽  
Yugang Zhang ◽  
Bifeng Song
Keyword(s):  
System Reliability ◽  
Rest Period ◽  
Maintenance Cost ◽  
Reliability Model ◽  
Maintenance Policy ◽  
General Applicability ◽  
Industrial Systems ◽  
Soft Failure ◽  
Long Run ◽  
Degradation Failure

There are many industrial systems experiencing multiple dependent competing failure processes, in detail degradation failure (soft failure) and catastrophic failure (hard failure). Earlier research studied failure behaviors and system reliability during operational period, but did not consider the intermission period. Some industrial systems are not always operating continuously while with intermissions or rest period. The degradation and random shock processes are different between operating period and intermissions, which caused it more challenging and complicated to establish reliability model. In this article, a new reliability model for multiple dependent competing failure processes is developed with intermission considered. The system reliability can be analyzed based on the proposed model more practically. Besides, a preventive replacement maintenance policy is studied by minimizing the average long-run maintenance cost with intermission periods considered. Finally, the availability and general applicability of presented model are demonstrated by a case in different parameter settings.

Geometric process repair model for an unreliable production system with an intermediate buffer

2016 ◽  
Vol 231 (4) ◽  
pp. 747-759 ◽  
Author(s):  
Guoqing Cheng ◽  
Binghai Zhou ◽  
Ling Li
Keyword(s):  
Production System ◽  
Buffer Stock ◽  
Sensitivity Analyses ◽  
Cost Rate ◽  
Long Run ◽  
Proposed Model ◽  
Joint Policy ◽  
Traditional Assumption ◽  
Average Cost Rate ◽  
Continuous Demand

In this paper, we consider an unreliable production system consisting of two machines (M1 and M2) in which M1 produces a single product type to satisfy a constant and continuous demand of M2 and it is subjected to random failures. In order to palliate perturbations caused by failures, a buffer stock is built up to satisfy the demand during the production unavailability of M1. A traditional assumption made in the previous research is that repairs can restore the failed machines to as good as new state. To develop a more realistic mathematical model of the system, we relax this assumption by assuming that the working times of M1 after repairs are geometrically decreasing, which means M1 cannot be repaired as good as new. Undergoing a specified number of repairs, M1 will be replaced by an identical new one. A bivariate policy [Formula: see text] is considered, where S is the buffer stock level and N is the number of failures at which M1 is replaced. We derive the long-run average cost rate [Formula: see text] used as the basis for optimal determination of the bivariate policy. The optimal policies [Formula: see text] and [Formula: see text] are derived, respectively. Then, an algorithm is presented to find the optimal joint policy [Formula: see text]. Finally, an illustrative example is given to validate the proposed model. Sensitivity analyses are also carried out to illustrate the effectiveness and robustness of the proposed methodology.

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