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.

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.

Optimal State-Dependent Replacement Policy for Deteriorating Systems

1997 ◽  
Vol 04 (04) ◽  
pp. 349-356 ◽  
Author(s):  
Ruey Huei Yeh
Keyword(s):  
Optimal Policy ◽  
Operating Cost ◽  
Sufficient Conditions ◽  
Optimization Criterion ◽  
Replacement Policy ◽  
Cost Rate ◽  
Optimal State ◽  
State Dependent ◽  
Long Run ◽  
Deteriorating Systems

This paper investigates the optimal state-dependent replacement policy for semi-Markovian deteriorating systems. It is assumed that the replacement time, replacement cost, operating cost rate and sojourn time distributions are all state-dependent. The optimization criterion is to minimize the expected long-run cost per unit time. Under some sufficient conditions on the cost and time parameters, we show that the optimal policy is of control limit type and has monotonic properties which facilitate the derivation of the optimal policy. Finally, a numerical example is given to illustrate the structure of the optimal policy.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489 ◽  
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

scholarly journals A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (2) ◽  
pp. 473-489 ◽  
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

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.

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.

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.

scholarly journals Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1589
Author(s):  
Jaume Masoliver ◽  
Miquel Montero ◽  
Josep Perelló
Keyword(s):  
Diffusion Process ◽  
Discount Rate ◽  
Continuous Time ◽  
Environmental Planning ◽  
Dynamical Evolution ◽  
Jump Diffusion ◽  
Economic Evolution ◽  
Discount Function ◽  
Long Run ◽  
Future Discounting

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution, specially when extreme situations occur (pandemics, global wars, etc.). When, between jumps, the dynamical evolution is governed by an Ornstein–Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continuous time random walk.

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