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.

A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy

2019 ◽  
Vol 234 (1) ◽  
pp. 138-150
Author(s):  
Yi Jiang
Keyword(s):  
Operating Time ◽  
Replacement Policy ◽  
Sensitivity Analyses ◽  
Optimal Order ◽  
Shock Model ◽  
Cost Rate ◽  
Long Run ◽  
Average Operating ◽  
Average Operating Time ◽  
Average Cost Rate

In this article, a generalized δ-shock model with multi-failure thresholds is studied. For the new model, the system fails depending on the interval times between two consecutive shocks which arrive according to a Poisson process. The shorter interval times may cause more serious failures and thus result in longer down times and more costs for repair. Assuming that the repair is imperfect, an order-replacement policy N is adopted. Explicitly, the spare system for replacement is ordered at the end of ( N – 1)th repair and the aging system is replaced at the Nth failure or at an unrepairable failure, whichever occurs first. In addition, the system must meet the requirement of availability, that is, the long-run average operating time per unit time should not be lower than a certain level. The average cost rate C( N) and the stationary availability A( N) are derived analytically. Some convergence properties of A( N) and C( N) are also investigated. The optimal order-replacement policy N* can be obtained numerically with the constraint of availability. Finally, an illustrative example is given and some sensitivity analyses are conducted to demonstrate the proposed shock model.

Collaborative Optimization of Replacement and Spare Ordering of a Deteriorating System with Two Failure Types

2012 ◽  
Vol 220-223 ◽  
pp. 210-214 ◽  
Author(s):  
Guo Qing Cheng ◽  
Ling Li
Keyword(s):  
Average Cost ◽  
Life Time ◽  
Collaborative Optimization ◽  
Replacement Policy ◽  
Cost Rate ◽  
Ordering Policy ◽  
Long Run ◽  
Proposed Model ◽  
Average Cost Rate ◽  
Optimal Ordering

This paper proposes a model to find optimal ordering and replacement policies for a deteriorating system. Assume that the life time of system has a normal distribution, and it has two failures types, typeⅠfailure is repairable, whereas typeⅡfailure is catastrophic which leads to replacement. A replacement policy N is adopted by which the system will be replaced by an identical new one if available at the time following the Nth typeⅠfailure or the 1st typeⅡfailure whichever occurs first. Furthermore, it considers an ordering policy M in which a spare unit is ordered at the time of the Mth typeⅠfailure or 1st typeⅡfailure, whichever occurs first. The objective is to derive the long-run average cost rate and then find the optimal policy (N,M) such that the average cost rate is minimized. Finally, a numerical example is provided to illustrate the proposed model.

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.

Modelling and Optimization of Integrated Planning of Production and Maintenance with Subcontract Constraint

2018 ◽  
Vol 40 ◽  
pp. 184-203 ◽  
Author(s):  
Nouhayla Hafidi ◽  
Abdellah El Barkany ◽  
Morad Mahmoudi
Keyword(s):  
Production System ◽  
Unit Cost ◽  
Production Capacity ◽  
Threshold Level ◽  
Research Direction ◽  
Optimal Choice ◽  
Proposed Model ◽  
Joint Policy ◽  
Two Parameters ◽  
New Research

This article addresses the problem of the joint policy of production and maintenance under constraint of outsourcing. The production system considered brings together two companies; the principal represented by a machine Md, while the subcontractor represented by a machine Ms. Our production system aims to satisfy a constant and continuous demand for a single product type. Indeed, outsourcing is justified by the lack of production capacity. However, the main objective is to determine simultaneously for each period, the age of preventive maintenance, the optimal stock threshold level, the maximum capacity of subcontractor and its unit cost of production, to better satisfy the customer's need. The last two parameters encourage an optimal choice of subcontractor, while minimizing the total cost generated by the contractor, including the costs of maintenance, production, storage and shortage. The results show that the proposed model performs quite well and opens new research direction for future improvements.

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.

scholarly journals A Single-Stage Manufacturing Model with Imperfect Items, Inspections, Rework, and Planned Backorders

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 446 ◽  
Author(s):  
Chang Wook Kang ◽  
Misbah Ullah ◽  
Mitali Sarkar ◽  
Muhammad Omair ◽  
Biswajit Sarkar
Keyword(s):  
Production System ◽  
Single Stage ◽  
Order Quantity ◽  
Lot Size ◽  
Defective Items ◽  
Long Run ◽  
Proposed Model ◽  
Imperfect Items ◽  
Inspection Process ◽  
Inspection Station

Each industry prefers to sell perfect products in order to maintain its brand image. However, due to a long-run single-stage production system, the industry generally obtains obstacles. To solve this issue, a single-stage manufacturing model is formulated to make a perfect production system without defective items. For this, the industry decides to stop selling any products until whole products are ready to fulfill the order quantity. Furthermore, manufacturing managers prefer product qualification from the inspection station especially when processes are imperfect. The purpose of the proposed manufacturing model considers that the customer demands are not fulfilled during the production phase due to imperfection in the process, however customers are satisfied either at the end of the inspection process or after reworking the imperfect products. Rework operation, inspection process, and planned backordering are incorporated in the proposed model. An analytical approach is utilized to optimize the lot size and planned backorder quantities based on the minimum average cost. Numerical examples are used to illustrate and compare the proposed model with previously developed models. The proposed model is considered more beneficial in comparison with the existing models as it incorporates imperfection, rework, inspection rate, and planned backorders.

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.

Availability and cost assessment of systems with dormant failure undergoing sequential inspections

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Himani Pant ◽  
S.B. Singh
Keyword(s):  
Average Cost ◽  
Inspection Time ◽  
Failed State ◽  
Content Type ◽  
Cost Rate ◽  
Long Run ◽  
Inspection Policy ◽  
Average Cost Rate ◽  
The Cost ◽  
Random Times

PurposeThe system encountering dormant failure subject to sequential inspections is modeled and the emphasis is made on determining the availability and long-run average cost rate for the model. The derived results are then utilized to obtain the optimal inspection period minimizing the cost.Design/methodology/approachExplicitly, a system with a functional and a failed state is taken into account. Inspections are performed to reveal the dormant failures and are assumed to be carried out at time T, T + aT, T + aT+a2 T, … where 0 < a = 1 in each cycle. Perfect repairs taking random times are performed if the system is found in a failed state during any inspection.FindingsSome theorems on the point availability, limiting availability and long-run average cost rate are obtained in the study. An illustration is shown to explain the results obtained in the proposed work. The effect of inspection time on the availability and cost rate is also analyzed graphically.Originality/valueThe availability and cost rate for a system with dormant failure under a sequential inspection policy are figured out unlike previous research.

A bivariate replacement policy for an imperfect repair system based on geometric processes

2018 ◽  
Vol 233 (4) ◽  
pp. 670-681
Author(s):  
Qinglai Dong ◽  
Lirong Cui ◽  
Hongda Gao
Keyword(s):  
Optimal Solution ◽  
Working Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Repair System ◽  
Cost Rate ◽  
Delayed Repair ◽  
Long Run ◽  
Average Cost Rate ◽  
Geometric Processes

A repair replacement model for a deteriorating system with delayed repair is studied, in which the successive working times after repair and the consecutive repair times of the system are described by geometric processes. The instantaneous availability is studied in the case of general distributions for the working time, repair time and delayed repair time. A bivariate replacement policy is considered, that is, the system is replaced whenever the working age of the system reaches T or at the first hitting time of the working time after repair with respect to the working time threshold τ, whichever occurs first. The explicit expression of the long-run average cost rate under the replacement policies is derived. The corresponding optimal replacement policy can be determined numerically, and numerical examples are presented to demonstrate the application of the developed model and approach. It is shown that the optimal solution and optimal value are sensitive to the tiny change in the ratios of the Geometric processes and the expectation of the delayed repair time.

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