Search results for: Viliam Makis

Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis

Abstract:

In this paper, we investigate the residual life prediction problem 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 with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example.

Keywords: Partially observable system, hidden Markov model, competing risks, residual life prediction.

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

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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Authors: Leila Jafari, Viliam Makis

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, economic manufacturing quantity, safety stock, stochastic demand.

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Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

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: Bayesian control chart, semi-Markov decision process, quality control, partially observable process.

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Authors: Leila Jafari, Viliam Makis, 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, Semi-Markov Decision Process, Multivariate Bayesian Control Chart, Partially Observable System, Two-unit System.

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Authors: Fariba Azizi, Firoozeh Haghighi, Viliam Makis

Abstract:

In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: Expectation-maximization (EM) algorithm, cause of failure, intensity, linear degradation path, masked data, reliability function.

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Authors: Nooshin Salari, Viliam Makis

Abstract:

In this paper, we propose a condition-based maintenance policy for multi-unit systems considering the existence of economic dependency among units. We consider a system composed of N identical units, where each unit deteriorates independently. Deterioration process of each unit is modeled as a three-state continuous time homogeneous Markov chain with two working states and a failure state. The average production rate of units varies in different working states and demand rate of the system is constant. Units are inspected at equidistant time epochs, and decision regarding performing maintenance is determined by the number of units in the failure state. If the total number of units in the failure state exceeds a critical level, maintenance is initiated, where units in failed state are replaced correctively and deteriorated state units are maintained preventively. Our objective is to determine the optimal number of failed units to initiate maintenance minimizing the long run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A numerical example is developed to demonstrate the proposed policy and the comparison with the corrective maintenance policy is presented.

Keywords: Reliability, production, maintenance optimization, Semi-Markov Decision Process.

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Authors: Nooshin Salari, Viliam Makis, Jane Doe

Abstract:

This paper presents a maintenance policy for a system consisting of two units. Unit 1 is gradually deteriorating and is subject to soft failure. Unit 2 has a general lifetime distribution and is subject to hard failure. Condition of unit 1 of the system is monitored periodically and it is considered as failed when its deterioration level reaches or exceeds a critical level N. At the failure time of unit 2 system is considered as failed, and unit 2 will be correctively replaced by the next inspection epoch. Unit 1 or 2 are preventively replaced when deterioration level of unit 1 or age of unit 2 exceeds the related preventive maintenance (PM) levels. At the time of corrective or preventive replacement of unit 2, there is an opportunity to replace unit 1 if its deterioration level reaches the opportunistic maintenance (OM) level. If unit 2 fails in an inspection interval, system stops operating although unit 1 has not failed. A mathematical model is derived to find the preventive and opportunistic replacement levels for unit 1 and preventive replacement age for unit 2, that minimize the long run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Numerical example is provided to illustrate the performance of the proposed model and the comparison of the proposed model with an optimal policy without opportunistic maintenance level for unit 1 is carried out.

Keywords: Condition-based maintenance, opportunistic maintenance, preventive maintenance, two-unit system.

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Authors: Seyedvahid Najafi, Viliam Makis

Abstract:

In recent years, maintenance optimization has attracted special attention due to the growth of industrial systems complexity. Maintenance costs are high for many systems, and preventive maintenance is effective when it increases operations' reliability and safety at a reduced cost. The novelty of this research is to consider general repair in the modeling of multi-unit series systems and solve the maintenance problem for such systems using the semi-Markov decision process (SMDP) framework. We propose an opportunistic maintenance policy for a series system composed of two main units. Unit 1, which is more expensive than unit 2, is subjected to condition monitoring, and its deterioration is modeled using a gamma process. Unit 1 hazard rate is estimated by the proportional hazards model (PHM), and two hazard rate control limits are considered as the thresholds of maintenance interventions for unit 1. Maintenance is performed on unit 2, considering an age control limit. The objective is to find the optimal control limits and minimize the long-run expected average cost per unit time. The proposed algorithm is applied to a numerical example to compare the effectiveness of the proposed policy (policy Ⅰ) with policy Ⅱ, which is similar to policy Ⅰ, but instead of general repair, replacement is performed. Results show that policy Ⅰ leads to lower average cost compared with policy Ⅱ. 

Keywords: Condition-based maintenance, proportional hazards model, semi-Markov decision process, two-unit series systems.

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Authors: Jaroslav Polec, Viliam Hirner, Michal Martinovič, Kvetoslava Kotuliaková

Abstract:

In this paper we present a novel error model for packet loss and subsequent error description. The proposed model simulates the error performance of wireless communication link. The model is designed as two independent Markov chains, where the first one is used for packet generation and the second one generates correctly and incorrectly transmitted bits for received packets from the first chain. The statistical analyses of real communication on the wireless link are used for determination of model-s parameters. Using the obtained parameters and the implementation of the generator, we collected generated traffic. The obtained results generated by proposed model are compared with the real data collection.

Keywords: Wireless channel, error model, Markov chain, Elliot model, Gilbert model, generator, IEEE 802.11.

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