Masashi Kowada

Analysis of a system with minimal repair and its application to replacement policy

Abstract The periodic replacement with minimal repair at failures is studied by many authors, however, there is not a clear definition for minimal repair. This paper defines a minimal repair in the term of the failure rate and devices some probability quantities and reliability properties. As an application of these results, the replacement model where a system is replaced at time T or at n th failure are considered and the optimum policies are discussed.

A two-queue model with Bernoulli service schedule and switching times

In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a single server. The server serves the two queues with a Bernoulli service schedule described as follows. At the beginning of each visit to a queue, the server always serves a customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability pi, it serves the next customer; with probability 1-pi, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also determine the Laplace-Stieltjes transforms of waiting time distributions for both queues, and obtain their mean waiting times.

A two-queue and two-server model with a threshold-based control service policy

Abstract This paper investigates a queueing system consisting of two-parallel queues and two servers. The service policy is a threshold-based control one such that two thresholds v (⩾0) and N (⩾v) called control level are set up in one of the two queues, say, the second queue. At each epoch of service completion, the server decides which queue is to be served next according to the control level the number of customers in the second queue reaches. For both queues, the arrival processes are Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.

Some applications of semi-regenerative processes to two-unit warm standby system

Abstract We deal with a two-unit warm standby system with a single repair facility; a failure of an operating unit can be detected immediately but a failure of a warm standby unit can not be observed until the system is inspected. According to whether the operation of the system is stopped or not during each inspection, we consider two models. We describe the stochastic behavior of the system as a semi-regenerative process, and the pointwise availability and the steady state availability of the system are derived applying the limit theorem of semi-regenerative processes. Further, we shall discuss the optimum interinspection time maximizing the steady state availability for Model 1.

Optimal replacement under additive damage in a poisson random environment

We consider a system existing in a random environment. The randomly varying environment is described by a Poisson process called Poisson environment process(PEP). The system receives shocks at random points of time and is subject to failure. Each shock causes a random amount of damage which accumulates additively and depends on the environment state. The damage process is assumed to be a piecewise semi-Markov process (PSMP) which is constructed by the shock process and the environment process. Any of the shocks or the changes of the environment state may cause the system to fail. The optimal replacement problem of the system is examined. Sufficient conditions for the optimality of control-limit policies, the control-limit process and the corresponding bounded processes axe given

An optimal state-age dependent replacement for a network system

Abstract We consider an optimal state-age dependent replacement problem for a network system composed of a main system and a sub-system with N components. The components functioning times are exponentially distributed random variables with the same parameters, and every failed component is repaired by one repairman by taking an exponentially distributed random time. Repaired components are as good as new. The main system is subject to a sequence of randomly occurring shocks and each shock causes a random amount og damage. Shock arrivals and magnitudes depend on the accumulated damage level of the main system itself and the number of the functioning components of the sub-system. Any of the shocks or components failures might cause the main system to fail. Upon failure of the main system, it is replaced and emergency repairs for all failed components are carried out. Our aim is to determine an optimal state-age dependent replacement policy which minimizes the long-run average cost over the infinite horizon.

A queueing model of a production system with two machines, one operator and priorities

This paper studies a priority queueing model of a production system in which one operator serves two types of units with overlapping service times. The two types of units arrive in independent Poisson processes. There are two machines in the system. Units of type 1 receive two consecutive types of services at machine #1: the handwork performed by the operator and the automatic machining without the operator. Units of type 2 receive only the handwork performed by the operator at machine #2. The operator attends the two machines according to a strict-priority discipline which always gives units of type 2 higher priority than units of type 1. At each machine the handwork times have a general distribution, and at machine #1 the machining times have an exponential distribution. The Laplace-Stieltjes transform of the queue-size distributions and the waiting time distributions for a stationary process are obtained.

A semi-regenerative process of two-unit warm standby system

Abstract This paper deals with two identical units warm standby system; a failure of operating unit can be detected at any time but a failure of standby unit can not be done until a system is inspected. We are able to look upon the stochastic behavior of our model as that of semi-regenerative process. The pointwise unavailability and the steady state unavailability of the system are derived by using the limit theorem of semi-regenerativeprocess. Further, we shall discuss the optimum inspection period minimizing the steady state unavailability. A numerical example is presented.