Magdi S. Moustafa

Optimal major and minimal maintenance policies for deteriorating systems

Abstract We present a maintenance model for a multi-state semi-Markovian deteriorating system. Our model allows one of three maintenance decisions (do-nothing, minimal maintenance or replacement) to be taken at each state of the system. We use control limit policy and the policy-iteration algorithm to find the optimal maintenance policies that minimizes the expected long-run cost rate of the system. Numerical examples are given to illustrate the proposed policies.

Reliability analysis of K-out-of-N: G systems with dependent failures and imperfect coverage

Abstract This paper presents a Markov model for reliability analysis of K -out-of- N : G systems subject to dependent failures with imperfect coverage. Closed form solutions of the probabilities are used to obtain the reliability and the mean time to failure (MTTF). A numerical example is provided to illustrate the results.

Transient analysis of reliability with and without repair for K-out-of-N:G systems with two failure modes

This paper presents Markov models for transient analysis of reliability with and without repair for K-out-of-N:G systems subject to two failure modes. The reliability of repairable systems can be calculated as a result of the numerical solution of a simultaneous set of linear differential equations. Closed form solutions of the transient probabilities are used to obtain the reliability for nonrepairable systems.

Availability of K-out-of-N:G systems with M failure modes

Markov models for analyzing the availability of K-out-of-N systems subject to M failure modes are presented. Closed form solutions of the steady-state probabilities of the systems and hence the availability are calculated.

Optimal minimal maintenance of deteriorating system subject to exponential failures with maintenance and repair of general distributions

The article presents a model of multistage degraded system subject to minimal maintenance, random failures and partial repairs. Constant state dependent transition rates for the degradation failure processes are considered while the minimal maintenance and the partial repairs follow general distributions with square of coefficient of variation less than or equal to one and state dependent which are more realistic and can be modelled by hypoexponential or Erlang distributions to use the Markovian property. The objective of the article is to calculate the steady state availability of the system, and the optimal mean time to minimal maintenance maximising the availability in case of state independent Erlang and deterministic distributions. This article extends previous results that can be considered as particular cases of this one. Numerical examples are provided to illustrate applicability of the expressions that are obtained throughout the article.

Optimum Machine Performance in Fault-Tolerant Networked Control Systems

This paper investigates the effect of failures on the productivity of fault-tolerant networked control systems under varying loads. Higher speeds of operation are sometimes used to increase production and compensate for down time due to component failures. Improved Markov models are developed and used to calculate system probabilities. When these probabilities are combined with the maximum speed of operation in each system state, the average speed of operation is obtained. If machines cannot be run at maximum speed all the time, the Markov models are used again to find the best speed mix that would yield maximum output capacity

Reliability model of series-parallel systems

Abstract Markov models are used to obtain closed form solutions of the reliability of a series-parallel system. The system consists of two identical equipment in series. Each equipment has one component. To improve equipment reliability, extra component is connected in parallel with the original one. Therefore; each equipment is considered as 2-component fault-tolerant one. The component has a Poisson failure, and a repair of contant rate. The system fails if at least one equipment is out of order.

On the performability of on-board train networks with fault-tolerant controllers

This paper studies a mixed load of control and entertainment on top of Gigabit Ethernet on-board a train wagon. The control load is comprised of sensors and actuators of different sampling periods. There is a dedicated server for control and a dedicated server for entertainment. It is proven that the system can tolerate the failure of one controller, shifting both entertainment and control loads to the remaining controller while guaranteeing correct performance. The maximum acceptable entertainment load is found. Enhancements to the network are introduced in order to minimize degradation of entertainment service due to a controller failure. OPNET simulations are used to study packet transmission/reception and end-to-end delay. Finally, a performability model is developed; this model will help system designers determine the cost- effectiveness of architectural features aiming at increasing performance.

A semi-Markov decision algorithm for the optimal maintenance of a multistage deteriorating two-unit standby system

The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs for a multi-state deteriorating system subject to aging and fatal shocks. In this paper, we propose a model for a two-unit standby system where a cold standby unit is attached to an operating (active) one. For this model, the active unit goes through a finite number of states of successive degradation preceding the failure, while the other one is in cold standby state. At each deterioration state of the active unit, two types of maintenance are considered, minimal and major, depending on the degrading level. The minimal maintenance aims to improve the degradation of the unit by recovering it to the previous degradation stage. The maximum allowable number of minimal maintenances for all states of the active unit must not exceed a certain limit. On the other hand, the major maintenance is necessary when the active unit fails. Once this maintenance is completed, the unit is restored to as good as new. To make the system operate more time without any interruption, the standby unit can be switched online until the active unit finishes its minimal or major maintenance. The switch between the two units is perfect and switchover is instantaneous. After using the standby unit, it is serviced or overhauled to maintain it in as good as new state. We use an iterative numerical approach, based on the policy iteration method, to drive the optimal state-dependent maintenance policy that minimizes the long-run expected cost rate of the system. Finally, numerical examples are given to illustrate and evaluate the performance of the proposed policy.

Scheduling in a multi-class series of queues with deterministic service times

We consider a problem of scheduling in a multi-class network of single-server queues in series, in which service times at the nodes are constant and equal. Such a model has potential application to automated manufacturing systems or packet-switched communication networks, where a message is divided into packets (or cells) of fixed lengths. The network is a series-type assembly or transfer line, with the exception that there is an additional class of jobs that requires processing only at the first node (class 0). There is a holding cost per unit time that is proportional to the total number of customers in the system. The objective is to minimize the (expected) total discounted holding cost over a finite or an infinite horizon. We show that an optimal policy gives priority to class-0 jobs at node 1 when at least one of a set ofm−1 inequalities on partial sums of the components of the state vector is satisfied. We solve the problem by two methods. The first involves formulating the problem as a (discrete-time) Markov decision process and using induction on the horizon length. The second is a sample-path approach using an interchange argument to establish optimality.