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.     

Reliability and profit analysis of two single-unit models with three modes and different repair policies of repairmen who appear and disappear randomly

Cost-benefit analysis of a single-unit system with three possible modes of the unit—normal (N), partial failure (P) and complete failure (F)—is carried out. The paper consists of two models: in model 1, the unit goes under repair (if a repairman is available) the moment it fails partially, whereas in model 2 the unit goes under repair at complete failure. The repairman appears in, and disappears from, the system randomly. A comparison between these two models after calculating MTSF and profit has also been made.     

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 K₃, below which the expert repairman should be called immediately after the system failure and the corresponding increase in profit are calculated.     

Analysis of a two server-two unit cold standby system with correlated failures and repairs

This paper studies a two (non-identical) unit cold standby system with correlated failures and repairs. The system has two types of server—regular (not perfect) and expert. The regular repairman is always available with the system while the expert repairman is called when it is needed. The joint distributions of failure and repair times are taken to be bivariate exponential (B.V.e.). Important reliability characteristics useful to system managers are obtained.     

Optimal policies in a two-unit standby system with two types of repairmen

This paper is concerned with a two identical unit cold standby system. There is a facility of having two types of repairmen. The “regular” repairman is always kept with the system with the known fact that he might not be able to do some complex repairs within some tolerable “patience” time, while a perfect “expert” repairman is called only in need. On the completion of this tolerable time or on the system failure whichever is earlier, the expert repairman is called on to do the job. We use semi-Markov processes and numerical methods, we discuss optimum policies for calling the expert, maximizing the profit and plot the graphs.     

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.     

Stochastic analysis of a parallel system with common cause failure,preventive maintenance and two types of repair

This paper studies a two-unit (identical) parallel system with facilities of preventive maintenance and two types of repair, i.e. regular and occasional. When the regular repairman is unable to repair the unit/system, the occasional (expert) repairman is called for. The system can also fail due to common cause. The time of the failure of a unit and the system, the commencement of maintenance and to call the occasional repairman are assumed to be constant while the repair and maintenance times are arbitrarily distributed. The system is analysed by using regenerative point technique to obtain various economics related measures, such as mean time to system failure, steady state availability, probability that the repairman is busy, expected number of visits by the occasional repairman and the expected profit earned by the system.     

A two dissimilar unit multi-component system with correlated failures and repairs

This paper investigates a two non-identical unit cold standby system model. Each unit is composed of n independent components arranged in a series configuration. A single repairman is available to repair a failed unit. The priority in operation is being given to the first unit, while in repair the priority is given to the second unit. The failure and repair times of the ith and jth component for the first and second unit, respectively, are jointly distributed as bivariate exponentials (B.V.E.) with different parameters. Using a regenerative point technique, various reliability characteristics have been analysed.     

On the characteristics of a system having master and helping unit

A system having one master and one helping unit with two failure modes-partial and total-is analysed. The helping unit is used to support the master unit in operation. Whenever the helping unit fails it is either repaired or replaced with probability p(q). Failure time distributions are taken to be negative exponential whereas repair time distributions are taken to be arbitrary. Using the regeneration point technique, several system characteristics such as mean time to system failure, availability, busy period of the repairman, etc. are obtained. Finally, some graphs are drawn in order to highlight the important results in particular cases.     

A generalized multi-standby multi-failure mode system with various repair facilities

We consider a system of (m + 1) non-identical units—one functioning and m standby. Each unit of the system has the following states: normal, N types of partial failures and corresponding to them N types of total failures. There are k distinct major repair facilities and one on the spot repairman. One unit can pass from one state to another with known probability and then the time of staying in this state has a general distribution. The system starts to work at t = 0 and fails when the (m + 1)th unit after a total failure is finally rejected. Using semi-Markov techniques we obtain Laplace transforms of transition probabilities. Considering particular cases we derive known results for systems which have been defined in the past.     

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.     

Reliability and Profit Evaluation of a PLC Hot Standby System Based on a Master-Slave Concept and Two Types of Repair Facilities

Programmable Logic Controllers (PLC) are frequently used by a good number of companies like steel plants, biscuit manufacturing companies, etc. Various plants/companies use two PLC at a time: one operative, and the other as a hot standby to avoid big losses. Analysis of the reliability, and profit of a hot standby PLC system is of great importance; and hence the present paper examines such a system wherein two PLC are working in master-slave fashion. Initially, the master unit is operative, and the slave unit is in hot standby. The slave unit can also fail, but with a lower failure rate than the master unit. The master unit has the priority of operation ∓mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp; repair over the slave unit. While operating, the latest information from the master unit keeps on transferring to the slave unit. There are three types of failure: minor, major-repairable, and major-irreparable. The ordinary repairman who stays with the system repairs the minor failures. The expert repairman who is available upon demand repairs the major failures. Various measures of the system effectiveness, such as the mean time to system failure, steady-state availability, busy period of the ordinary as well as expert repairmen, expected number of replacements, etc. are obtained by using semi-Markov processes, and regenerative point Techniques. Profit incurred to the system is evaluated, and a graphical study is also made. Real data from an industrial application is used in this study.     

Optimal assignment of priorities for the machine interference problems

This paper investigates multiple machine repair problems with one repairman. Each machine is subject to two modes of failure, major and minor. The machines are identical, with times to repair and the times to failure assumed to be negative exponentially distributed. In this paper we consider the problem: when there are i and j failed machines in modes 1 and 2, respectively, which mode of failure should be selected for repair? A profit model is developed and then, to achieve the optimal profit, we derive the optimal repair policy for the single repairman. In addition, we describe a procedure to determine the optimal number of machines which should be assigned to a repairman. Numerical examples are provided in which the system characteristics are evaluated and profits are analyzed.     

Approximations of a two-unit cold standby system's reliability behaviour

In this paper we study the reliability behaviour of a two-unit cold standby system with priority. At time t = 0, the priority unit (p) begins to work and the standby unit (s) is in cold standby. The p-unit has priority whether it is working or being repaired. A single repairman is available, and the repaired unit is as good as new. We assume that the p-unit's working time X₁ has a general life distribution F(x), and its repair time Y₁ has a general distribution G(x). The s-unit's working time X₂ has an exponential distribution with mean , and its repair time has an exponential distribution with mean . Using the Markov renewal process and stochastic comparison, we give bounds of the mean time to the first failure of the system, and the system's availability.     

Markovian parallel system with the repairman's vacation

A parallel Markovian model with R repairmen and a vacation for the repairmen is considered. In this paper two models are analysed. In the first model, a repairman takes only a single vacation at a time. In the second model a repairman returning to an empty queue immediately takes another vacation. A recursive computational approach is given to solve the steady state equations of both models. Numerical results for performance measures are presented.     

Cost analysis of a two-unit warm standby reliability system with two types of repair facilities

This paper deals with a two-unit warm standby system. These units are identical, but have different failure rates and repair time distributions, when failed in operating or standby state. If the unit fails in operating state, we wait for the repairman for some maximum time or until the other unit fails, and if the unit fails in standby state we wait for the repairman until the other unit fails. On the failure of the second unit or on the completion of the maximum time, we call the repairman immediately at the higher cost.The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results pertaining to some particular cases are also added.     

Cost-benefit analysis of a two-server, two-unit, warm standby system with different types of failure

This paper deal with a two-server, two-unit redundant system in which one unit is operative and the other is a warm standby. The operative unit can fail completely, either directly from the normal state or via a partial failure, while the warm standby unit only fails due to minor faults within it. One repairman is “regular”, he always remains with the system, and the other is an “expert” who is called when needed. The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results and some graphs pertaining to a particular case are also included.     

Analysis of a system having super-priority, priority and ordinary units with arbitrary distributions

This paper deals with the analysis of a three non-identical unit cold standby system model. A single repairman is available to repair a failed unit. The priority in respect of operation and repair is being given to the units in order. All failure and repair time distributions are assumed to be general having different p.d.f.'s. Several measures of system effectiveness are obtained by using a regenerative point technique.     

A maintenance model for two-unit redundant system

In this paper, a maintenance model for two-unit redundant system with one repairman is studied. At the beginning, unit 1 is operating, unit 2 is the standby unit. The costs include the operating reward, repair cost and replacement cost, besides, a penalty cost is incurred if the system breaks down. Two kinds of replacement policy, based on the number of failures for two units and the working age, respectively are used. The long-run average cost per unit time for each kind of replacement policy is derived. Also, a particular model in which the system is deteriorative, two units are identical and the penalty cost rate is high, is thoroughly studied.     

Cost-benefit analysis of a 2-unit priority-standby system withpatience-time for repair

The cost of a one-server two-unit (one priority and the other ordinary) cold-standby system with two modes-normal and total failure-is analysed. Whenever the repair time of a failed priority unit exceeds some given maximum time, it is rejected and an order is placed for a new unit. Failure and delivery time distributions are negative exponentials, whereas repair and replacement time distributions are arbitrary. An analysis of the system is made to determine the reliability measures (MTSF (meantime to system failure), steady-state availability, busy period analysis of repairman, etc.) by using the regenerative point technique