Patience Time Research Articles

Stochastic behaviour of a two-unit standby system with two types of repairmen and patience time

Stochastic behaviour of a two-unit cold standby redundant system, with two types of repairmen is analysed. The first repairman (usually called “regular” repairman) will always remain with the repair facility, with the known fact that he might not be able to do some complex repair within some tolerable (patience) time. An expert repairman is called to the system if and only if the regular repairman is unable to do the job, within some fixed time or on system failure, whichever occurs first. Techniques of regenerative point processes have been used to obtain various measures of system effectiveness and thereby profit incurred. The time-dependent availability, steady-state availability, reliability, Mean Time To Failure (MTTF), and profit function are obtained numerically and graphs are also drawn.

Comparative study of the profit of a two server system including patience time and instruction time

The paper is concerned with two unit cold standby systems having one regular repairman and one expert repairman. The expert is called only if the regular repairman is not able to complete the repair within some toletable (patience) time. In model 1, it is assumed that an expert, on his arrival, gives instructions to the regular repairman for completing the repair, in model 2, it is assumed that the expert himselg takes over the system and the regular repairman leaves the repair in the presence of the expert. In model 3, there is no provision of calling the expert. Techniques of the semi-Markov processes and regenerative processes are used to obtain various measures of system effectiveness and profit incurred. A pairwise comparison of model 1 is made with model 2 and model 3 through graphs.

Optimum preventive maintenance for a 2-unit priority-standby system with patience–time for repair

This paper deals with the effect of preventive maintenance (PM) on the reliability measurcs for a 2-unit priority standby system with patience-time for repair. Four types of PM (type (a),(b), (c), and(d)) are considcrcd. Failurc, repair, PM, and replacement time disiributiotls are general whereas delivery time distribution is negative exponential. Regenerative technique in Markov renewal is applied to obtain several reliability characteristics of interest to designers. Finally numerical calculations are given to illustrate the theoretical results

On queues with impatience

The purpose of this note is to provide a bibliographical update on the subject of impatience in general queueing systems, and to outline some of the similarities and differences in the results from the existing papers on the subject. All of the papers mentioned are concerned with GI/G/1 queues in which a customer drops out of the queue if his waiting time exceeds his patience time, which is a random variable

Cost analysis in two-unit warm standby models with a regular repairman and patience time

The present paper deals with two-unit warm standby models having one regular and one expert repairman. It is assumed that the expert is called only if the regular repairman is not able to complete the repairs within some tolerable (patience) time. In model 1, it is assumed that the regular repairman can always do the repairs of the unit, failed from standby state. In model 2, the regular repairman sometimes may not be able to do the repairs of the above nature within some patience time and the expert is called for in case of standby failure also. The various measures of system effectiveness are calculated using semi-Markov and regenerative processes. Based on these measures a rule is developed when the services of the expert man should be utilized profitably.

Cost analysis in a two-unit standby system with a regular repairman and patience time : Vibha Goyal and K. Murari. Microelectron. Reliab.24, 453 (1984)

Cost analysis in a two-unit standby system with a regular repairman and patience time : Vibha Goyal and K. Murari. Microelectron. Reliab.24, 453 (1984)

Single-server queues with impatient customers

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

Single-server queues with impatient customers

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of aGI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classicalGI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

Cost analysis in a two-unit standby system with a regular repairman and patience time

This paper develops a model for standby redundant system consisting of two identical units and a regular repairman. In an effort to increase the working time of the system, we put some “patience time” as the upper limit to repair time of the regular repairman. If the regular repairman is not able to do the repair within this patience time, we call an “expert” repairman for doing the repairs. Then the various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the services of the expert repairman should be utilized profitably or not. Further using numerical methods, we discuss the optimum patience time for various costs, maximizing the profit.

Cost analysis of a two-unit standby system with two types of repairmen

This paper is concerned with a two-unit cold standby system with two types of repairmen. One “regular” repairman is kept for repairing the units as soon as they fail. It is assumed that sometimes he might not be able to do the repairs within some tolerable time (patience time). Another “expert” repairman, assumed to be perfect, is called on to do the repairs on the completion of this patience time or on the failure of the system, whichever is later. Various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the expert repairman should be called after the system failure. Further numerical results for a case, in which repair time and patience time both have non-Markovian property, are also investigated. Then the upper bound of the cost K 3, below which the expert repairman should be called immediately after the system failure and the corresponding increase in profit are calculated.