Reliability analysis of a two-unit cold standby system with inspection, replacement, proviso of rest, two types of repair and preparation time

This paper deals with a two-unit standby system-one operative and the other in cold standby. Single repair facility which acts the inspection, replacement, preparation and repair. We wait the serverman for some maximum time or until the other unit fails. The analysis is carried out on the supposition that all time distributions are general except failure, delivery, replacement and inspection time distributions are exponentials. Stochastic behavior of the system has been studied by the regeneration point technique and several parameters of interest are obtained. Numerical results pertaining to some special 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.     

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.     

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

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.     

Probabilistic analysis of a two-unit cold standby system with instructions at need

A two-unit cold standby system with an expert repairman and his assistant is examined. If the expert repairman is busy in repairing a failed unit and at that time the second unit fails, the assistant repairman repairs the latter unit. The assistant repairman needs or does not need instructions for doing repair with probability p and q, respectively. Using a regenerative point technique, various measures of system effectiveness 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.     

Stochastic behaviour of a two-unit redundant system with switchover time

There is a two-unit standby redundant system. Standby is kept in cold state. Whenever one unit is operating and the other is in the waiting standby state, switching is initiated on the latter after a random time. If the operative unit fails before the time to initiate switching action on the waiting standby unit, the system fails and the failed unit immediately undergoes repair type 2 along with the switching. However, if the operative unit fails when the other unit is as standby (after switchover), the failed unit undergoes repair type 1 and the unit as standby takes over the operation. All the distributions are arbitrary except failure-time, which is exponential.The system is defined with the help of states which generate a pseudo semi-Markov process. Abundant use of results from the theory of SMP has been made to obtain a large number of parameters which measure reliability characteristics of the system viz. MTSF, steady-state availability, expected number of visits to a state, conditional transition probabilities, first passage time distributions, expected profit rate, etc. Numerical examples are included to illustrate the results.     

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

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.     

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.     

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.     

Cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair

This paper deals with the cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair where each unit of the system has two modes, normal and failed. It is assumed that the failure, repair, replacement and inspection times are stochastically independent random variables each having an arbitrary distribution. The cold standby unit replaces the failed operative unit after a random amount of time. An inspection is required to decide whether it needs type I (minor repair) or type 2 (major repair). In this system the repairman is not always available with the system, but is called whenever the operative unit fails. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Pointwise availability, steady-state availability, busy period by a server and the expected cost per unit time of the system are obtained. Certain important results have been derived as 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 Analysis of a Two-Unit Standby-Redundant System with Preventive Maintenance

We consider a standby-redundant model of two units, where we assume that one unit is operative and the other unit is in standby at time t = 0. If the operative unit fails, a unit in standby is put into preventive maintenance policy of the operative unit to maintain our the preventive maintenance policy of the operative unit to maintain our system with high reliability. Our concern for the system is the time to the first system-down. The Laplace-Stieltjes transform of the time distribution to the first system-down and the mean time to the first system-down are derived by applying the relationship between Markov renewal processes and signal flow graph. Further, the behavior after the system-down is investigated by using the results of Markov renewal processes. Finally, numerical examples are presented for the k-Erlang failure time distributions. The optimal preventive maintenance time is discussed.     

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.     

Cost analysis of a two unit cold standby system under different weather conditions

This paper deals with the cost analysis of a two unit cold standby system under two different weather conditions—normal and abnormal. Failure rates of units and rates of change of weather conditions are constant, whereas repair rates are general. The system is analysed in detail using regenerative point technique and results are obtained for mean time to system failure, steady state availability, busy period analysis, expected number of visits by repairman and expected profit earned by the system.     

Cost-benefit analysis of a one-server two-unit cold standby system with repair and preventive maintenance

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the type where the operating unit is taken up for PM whenever the other unit is available for operation. Initially, one unit is placed in operation and the other unit is kept as a cold standby. When the operating unit fails while the other unit is under service (repair or PM), the system breaks down. The busy period of the server in a time interval (O, t] is divided into time spent for repair and time spent for PM. By identifying regenerative epochs, suitable expressions for the expected values of these times are obtained. The pointwise availability is also derived. With the assumptions that a revenue is earned linearly with up-time, and repair and PM costs are incurred linearly with repair and PM times, respectively, the net expected revenue for a period (O, t] is derived. A particular case where the time to failure of the operating unit is 2-Erlang and the times for repair and PM are exponential has been analysed.     

On a two dissimilar unit cold standby system with switchover time and proper initialization of connect switching

This paper investigates the stochastic behaviour of a two dissimilar unit cold standby system with connect switching. The connect switch keeps this system in good connection with other systems. The standby unit takes random switchover time to assume the operative state when the operative unit fails. The failure times of the units and connect switch and the repair times of the units are assumed to have different arbitrary distributions. The mean waiting times in the states of the system and expression for the steady state availability of the system are obtained. The results obtained by Kumar and Lal and Laprie [1, 2] are derived from the present results as special cases.     

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.