Leila Jafari

Publications

4 Optimal Production and Maintenance Policy for a Partially Observable Production System with Stochastic Demand

Authors: Viliam Makis, Leila Jafari

Abstract:

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock.

Keywords: Condition-Based Maintenance, stochastic demand, safety stock, economic manufacturing quantity

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3 Optimal Bayesian Control of the Proportion of Defectives in a Manufacturing Process

Authors: Viliam Makis, Leila Jafari, Farnoosh Naderkhani

Abstract:

In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Quality Control, semi-Markov decision process, Bayesian control chart, partially observable process

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2 Optimal Maintenance Policy for a Partially Observable Two-Unit System

Authors: Viliam Makis, Leila Jafari, Akram Khaleghei G.B.

Abstract:

In this paper, we present a maintenance model of a two-unit series system with economic dependence. Unit#1 which is considered to be more expensive and more important, is subject to condition monitoring (CM) at equidistant, discrete time epochs and unit#2, which is not subject to CM has a general lifetime distribution. The multivariate observation vectors obtained through condition monitoring carry partial information about the hidden state of unit#1, which can be in a healthy or a warning state while operating. Only the failure state is assumed to be observable for both units. The objective is to find an optimal opportunistic maintenance policy minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the partially observable semi-Markov decision process framework. An effective computational algorithm for finding the optimal policy and the minimum average cost is developed, illustrated by a numerical example.

Keywords: Condition-Based Maintenance, multivariate Bayesian control chart, two-unit system, Semi-Markov Decision Process, Partially Observable System

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1 An Optimal Bayesian Maintenance Policy for a Partially Observable System Subject to Two Failure Modes

Authors: Viliam Makis, Leila Jafari, Akram Khaleghei Ghosheh Balagh

Abstract:

In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed, illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, multivariate Bayesian control

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Abstracts

4 Optimal Production and Maintenance Policy for a Partially Observable Production System with Stochastic Demand

Authors: Viliam Makis, Leila Jafari

Abstract:

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock.

Keywords: Condition-Based Maintenance, stochastic demand, safety stock, economic manufacturing quantity

Procedia PDF Downloads 319
3 Optimal Bayesian Control of the Proportion of Defectives in a Manufacturing Process

Authors: Viliam Makis, Leila Jafari, Farnoosh Naderkhani

Abstract:

In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Quality Control, semi-Markov decision process, Bayesian control chart, partially observable process

Procedia PDF Downloads 182
2 An Optimal Bayesian Maintenance Policy for a Partially Observable System Subject to Two Failure Modes

Authors: Viliam Makis, Leila Jafari, Akram Khaleghei Ghosheh Balagh

Abstract:

In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed and illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, multivariate Bayesian control

Procedia PDF Downloads 303
1 Optimal Maintenance Policy for a Partially Observable Two-Unit System

Authors: Viliam Makis, Leila Jafari, G. B. Akram Khaleghei

Abstract:

In this paper, we present a maintenance model of a two-unit series system with economic dependence. Unit#1, which is considered to be more expensive and more important, is subject to condition monitoring (CM) at equidistant, discrete time epochs and unit#2, which is not subject to CM, has a general lifetime distribution. The multivariate observation vectors obtained through condition monitoring carry partial information about the hidden state of unit#1, which can be in a healthy or a warning state while operating. Only the failure state is assumed to be observable for both units. The objective is to find an optimal opportunistic maintenance policy minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the partially observable semi-Markov decision process framework. An effective computational algorithm for finding the optimal policy and the minimum average cost is developed and illustrated by a numerical example.

Keywords: Condition-Based Maintenance, partially observable system, semi-Markov decision process, multivariate Bayesian control chart, two-unit system

Procedia PDF Downloads 272