Optimal inspection policy for a multi-unit machine

1989 ◽  
Vol 26 (03) ◽  
pp. 543-551 ◽  
Author(s):  
Dror Zuckerman
Keyword(s):  
Operating Time ◽  
Optimality Criteria ◽  
Inspection Time ◽  
Net Income ◽  
Operating Cycle ◽  
Cost Rate ◽  
Long Run ◽  
Inspection Strategy ◽  
Inspection Process ◽  
Inspection Policy

We consider a machine which generates income at rate I during its operating time. The machine is composed of N independent stochastically failing units. A failure of each one of the units causes a breakdown of the machine. The machine's status (good or failed) is observed continuously, by a controller, at zero cost. In the event of a breakdown, exactly one unit is failed, and a series of inspections is performed, in order to identify the failed unit and the reasons for its failure. At any time along the inspection process only one unit can be tested. An inspection of a given unit is characterized by its cost rate and inspection time. At the end of the inspection process, the failed unit is repaired at a known cost, and a new operating cycle is started. Our objective is to formulate an optimal inspection strategy under two optimality criteria: long-run average net income, and total expected discounted net income.

Optimal inspection policy for a multi-unit machine

1989 ◽  
Vol 26 (3) ◽  
pp. 543-551 ◽  
Author(s):  
Dror Zuckerman
Keyword(s):  
Operating Time ◽  
Optimality Criteria ◽  
Inspection Time ◽  
Net Income ◽  
Operating Cycle ◽  
Cost Rate ◽  
Long Run ◽  
Inspection Strategy ◽  
Inspection Process ◽  
Inspection Policy

We consider a machine which generates income at rate I during its operating time. The machine is composed of N independent stochastically failing units. A failure of each one of the units causes a breakdown of the machine.The machine's status (good or failed) is observed continuously, by a controller, at zero cost. In the event of a breakdown, exactly one unit is failed, and a series of inspections is performed, in order to identify the failed unit and the reasons for its failure. At any time along the inspection process only one unit can be tested.An inspection of a given unit is characterized by its cost rate and inspection time. At the end of the inspection process, the failed unit is repaired at a known cost, and a new operating cycle is started.Our objective is to formulate an optimal inspection strategy under two optimality criteria: long-run average net income, and total expected discounted net income.

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.

Comparison of sequential and continuous inspection strategies for deteriorating systems

1994 ◽  
Vol 26 (2) ◽  
pp. 423-435 ◽  
Author(s):  
C. Teresa Lam ◽  
R. H. Yeh
Keyword(s):  
Continuous Time ◽  
Iterative Algorithms ◽  
Optimal Cost ◽  
Cost Rate ◽  
State Dependent ◽  
Long Run ◽  
Inspection Strategy ◽  
Optimal Policies ◽  
Finite State ◽  
Deteriorating Systems

This paper investigates inspection strategies for a finite-state continuous-time Markovian deteriorating system. Two inspection strategies are considered: sequential inspection and continuous inspection. Unlike many previous efforts, the inspection times for the sequential inspection strategy are assumed to be non-negligible. The replacement times and costs for both strategies are non-negligible and state dependent. Our objective here is to minimize the expected long-run cost rate. Iterative algorithms are provided to derive the optimal policies for both strategies. The structures of these optimal policies and their corresponding optimal cost rates are discussed and compared.

OPTIMAL PERIODIC REPLACEMENT POLICY WITH CHECKING TIME

2005 ◽  
Vol 12 (01) ◽  
pp. 19-29 ◽  
Author(s):  
SHEY-HUEI SHEU ◽  
YAN-CHUN CHEN ◽  
LI-HSIU TENG
Keyword(s):  
Optimal Number ◽  
Replacement Policy ◽  
Inspection Time ◽  
Programming Formulation ◽  
Minimal Repair ◽  
Repair Costs ◽  
Inspection Strategy ◽  
Inspection Policy ◽  
Periodic Replacement ◽  
Replacement Time

This investigation considers a generalized inspection policy for a deteriorating production system with general random minimal repair costs. The inspection times for the inspection strategy are assumed to be non-negligible. Additionally, uncertainty probabilities associated with inspections are introduced. Using a dynamic programming formulation, the optimal inspection time for maximizing profit per unit time for a given overhaul/replacement time is determined. Next, the procedure is extended to determine the optimal periodic overhaul/replacement time, as well as the optimal number of inspections and their schedule.

Comparison of sequential and continuous inspection strategies for deteriorating systems

1994 ◽  
Vol 26 (02) ◽  
pp. 423-435 ◽  
Author(s):  
C. Teresa Lam ◽  
R. H. Yeh
Keyword(s):  
Continuous Time ◽  
Iterative Algorithms ◽  
Optimal Cost ◽  
Cost Rate ◽  
State Dependent ◽  
Long Run ◽  
Inspection Strategy ◽  
Optimal Policies ◽  
Finite State ◽  
Deteriorating Systems

This paper investigates inspection strategies for a finite-state continuous-time Markovian deteriorating system. Two inspection strategies are considered: sequential inspection and continuous inspection. Unlike many previous efforts, the inspection times for the sequential inspection strategy are assumed to be non-negligible. The replacement times and costs for both strategies are non-negligible and state dependent. Our objective here is to minimize the expected long-run cost rate. Iterative algorithms are provided to derive the optimal policies for both strategies. The structures of these optimal policies and their corresponding optimal cost rates are discussed and compared.

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.

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.

Road Inspection Scheduling Model Using Constraint Programming

2013 ◽  
Vol 357-360 ◽  
pp. 2720-2725
Author(s):  
Hsi Sung Wang ◽  
Shu Shun Liu
Keyword(s):  
Constraint Programming ◽  
Route Planning ◽  
Inspection Time ◽  
Time Consumption ◽  
The Road ◽  
Scheduling Model ◽  
Inspection Process ◽  
Road Inspection ◽  
Solution Mechanism ◽  
Inspection Scheduling

The research objective is to support the maintenance unit with route planning prior to performing road inspection, the model is based on VRP problem settings, and with the addition of compulsory road sections and allowing shortcuts through small pathways during the inspection to reduce time consumption. By employing Constraint Programming (CP) technology and optimization solution mechanism to construct inspection scheduling model, and the objective is to minimize time consumption of the road inspection. The province and county roads in Douliou city are chosen as examples for analysis, plans out best routes for inspection process, and also displays all the road sections passed by inspection vehicle. Thus this model can be used as reference to support the authorities to efficiently allocate resources for the inspection process, and achieve the objective as shorten the inspection time consumption.

Optimal repair/replacement policy for a general repair model

2001 ◽  
Vol 33 (1) ◽  
pp. 206-222 ◽  
Author(s):  
Xiaoyue Jiang ◽  
Viliam Makis ◽  
Andrew K. S. Jardine
Keyword(s):  
Average Cost ◽  
Failure Time ◽  
Operating Time ◽  
Replacement Policy ◽  
Repair Cost ◽  
Virtual Age ◽  
Preventive Replacement ◽  
Long Run ◽  
Special Cases ◽  
Cost Limit

In this paper, we study a maintenance model with general repair and two types of replacement: failure and preventive replacement. When the system fails a decision is made whether to replace or repair it. The repair degree that affects the virtual age of the system is assumed to be a random function of the repair-cost and the virtual age at failure time. The system can be preventively replaced at any time before failure. The objective is to find the repair/replacement policy minimizing the long-run expected average cost per unit time. It is shown that a generalized repair-cost-limit policy is optimal and the preventive replacement time depends on the virtual age of the system and on the length of the operating time since the last repair. Computational procedures for finding the optimal repair-cost limit and the optimal average cost are developed. This model includes many well-known models as special cases and the approach provides a unified treatment of a wide class of maintenance models.

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