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.     

Availability analysis of two-unit warm standby system with inspection time

This paper deals with two identical units warm standby system when a failure of unit is detected by actual inspection but a system down can be detected at any time without inspection. Where the lifetime distribution of unit is the bivariate exponential distribution and other distributions are arbitrary. The Laplace transform of the point-wise availability of the system and the steady state availability of the system are derived by using the supplementary variable method. Further, we discuss the optimum inspection period maximizing the steady state availability. 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.     

Cost analysis of a two-unit standby system under the influence of earthquakes

This paper deals with two models. In model 1, which is cold standby, when an earthquake comes the operation of the unit is stopped. In model 2, which is warm standby, a medium intensity earthquake will cause a short circuit failure mode. The repair is available immediately upon calling. In model 1, the failure rate is taken to be constant whereas the repair time distribution is arbitrary. In model 2, the failure and repair time distributions are considered to be arbitrarily distributed. Applying the regenerative theory in Markov renewal processes, various reliability characteristics of interest have been explicitly obtained.     

Benefit analysis of a two-unit standby system subject to jerks with installation time

This paper deals with the stochastic behaviour of a two-unit warm standby system subject to instantaneous jerks which cause failure and dislocation of the units from their proper place and position. A single installation-cum-repair facility is available, which first installs the unit to its proper place and position and then starts repairing the failed unit immediately after installation. The failure and dislocation rate is taken to be constant whereas the installation and the repair time distributions are taken to be arbitrary. Various reliablity parameters of interest have been derived by using regenerative theory in Markov-renewal processes. A special case has also been discussed.     

Cost analysis of a two-unit standby system with delayed replacement and better utilization of units

This paper develops the model for a system, having two identical units—one operative and the other cold standby. Each unit of the system has three modes—normal, partial failure and total failure. The replacement time of a failed unit by a standby unit is not negligible but is a random variable. System fails when both the units fail totally. Failure time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers and operations managers have been evaluated using the theory of regeneration point technique.     

Cost analysis of a two-unit cold standby system with two types of operation and repair

This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.     

On a two-unit cold standby redundant system with random switching time

This paper, which contains two sections, deals with a two-unit cold standby redundant system with random switching time and imperfect switchover. In Section I, we use the survival functions to find the mean TFSF and the L.S.T. of the distribution to the first system failure. Finally, we find the limiting distribution to the first system failure. In Section II, we find the mean TFSF considering two types of preventive maintenance (PM), type (a) and type (b). Finally we prove that the mean TFSF with type (b) PM is greater than or equal to the mean TFSF with type (a) PM.     

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 analysis of a two-unit chargeable standby system with interchangeable units and two types of failure

This paper studies the analysis of a stochastic model related to a two-unit chargeable standby system with interchangeable units (identical), i.e. the operative and standby units are interchanged at random epochs. The system can fail either due to power fluctuations or due to the operator's inefficiency. Failure time distributions are negative exponential while the distributions of repair times and time to interchange (of units) are arbitrary. Using a regenerative point technique, we have obtained various reliability characteristics to carry out the cost-benefit analysis.     

GERT analysis of a two-unit warm standby system with repair

A two-unit warm standby system has been modelled and analysed through GERT approach. A general concept of system utilization factor and availability curve have been introduced.     

GERT analysis of a two-unit cold standby system with repair

This paper presents a GERT (Graphical Evaluation and Review Technique) analysis of a two-unit cold standby system. The various performance characteristics of the system have been derived analytically.     

GERT analysis of a two-unit warm standby system with repair

A two-unit warm standby system has been modelled and analysed through GERT approach. A general concept of system utilization factor and availability curve has been introduced.     

Reliability analysis of two-unit warm standby system with partial failure mode and inspection time

A two-unit warm standby system is discussed, in which units are identical. Partial failure and complete failure of a unit can be detected by inspection from time to time. The inspection time follows an exponential distribution, whereas the repair and failure time follows an exponential and arbitrary distribution. Several reliability characteristics of interest to system designers and operation managers have been evaluated.     

Stochastic analysis of a two-unit cold standby system subject to maximum operation and repair time

A two-unit standby system is considered under excess time stochastic behaviour, i.e. the failure and repair time of the on line (off line) unit is exceeding some prespecified value. Whenever an operating unit crosses a prespecified operation time, it is sent to preventive maintenance and when repair of a failed unit crosses a prespecified time, the unit is rejected and replaced by a new unit. Using the regeneration point technique, certain characteristics of the system are derived and the cost of the system is calculated. Particular cases of the system are also considered.     

A two-unit system with allowed down time and random check of standby

This paper deals with the cost-benefit analysis of a two-unit (priority and ordinary) cold standby system under two very practicable assumptions: (i) the ordinary unit goes for a check at random epochs; (ii) the system remains down for a random time if, during the repair of ordinary unit, the priority unit also fails. The important measures of system effectiveness are obtained by using the regenerative point technique (R.P.T).     

Reliability analysis of a two-unit cold standby system with a replaceable repair facility

This paper considers a two-dissimilar-unit cold standby system where the repair facility is subject to failure and can be replaced by a new one after it fails. By using Markov renewal theory, we obtain some reliability quantities of the system and the repair facility, respectively.     

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.     

Stochastic analysis of a two-unit warm standby system with slow switching device

This paper studies a two-unit warm standby system subject to slow switch. Failure rates and switchover time of a unit from standby to operative are constant while repair times are arbitrarily distributed. Using the theory of regenerative and Markov-renewal processes several important measures of reliability are obtained.