Stochastic behaviour of a two-unit cold standby redundant system with administrative delay and two types of repairs

In this paper we consider a two-unit cold standby redundant system in which each unit works in three modes—normal, partial failure and total failure with two types of repairs (major and minor) after partial failure mode, with administrative delay to locate expert repair man for major repair. The administrative time distribution is assumed to be exponential, whereas the repair and failure time distributions are exponential and arbitrary. The technique of regenerative processes is applied to obtain various reliability characteristics of interest to system designers.     

Cost-benefit analysis of a single server three-unit redundant system with inspection, delayed replacement and two types of repair

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. The type of the failure of operative or warm standby unit is detected by inspection only. The service facility plays the triple role of replacement, inspection and repair of a unit. Failure time distributions of operative and warm standby units are negative exponential whereas the distributions of replacement time, inspection time and repair times are arbitrary. The system has been studied by using regenerative points.     

Analysis of a repairable redundant system with delayed replacement

The paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. Failure time distributions of operative and standby units are exponential whereas all repair times follow arbitrary distributions. The system has been studied in detail by applying the results from the theory of semi-Markov process and mean-time-to-system-failure, steady-state availability, expected number of visits to a state, second moment of time in an up-state and expected profit of the system have been obtained.     

Cost analysis of a 3-state 2-unit reparable system

This paper presents the cost analysis of a 2-unit system with 3 states: good, degraded and failed. The units suffer from two types of failure: partial and catastrophic. The partial failure brings a unit to degraded state, whereas the catastrophic failure breaks down a unit completely. There is one repair facility, which is availed only when the system is either degraded or failed. The failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of various probability states have been obtained along with steady-state behaviour of the system. Inversions have also been computed so as to obtain time dependent probabilities, which determine expected profit as well as availability of the system at any time.     

Busy period analysis of a two-unit warm standby system with imperfect switch

Busy period analysis of a two-unit warm standby system with two modes (normal and total failure) and imperfect switching device has been studied by considering the availability of a single repair facility. Failure time distributions of the units are negative exponential whereas repair time distributions of units and switch are arbitrary. Using the regeneration point technique several reliability characteristics have been obtained. Moreover, the present model employs switch failure in non-regenerative states, for the first time.     

Profit evaluation of a two unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby system subject to a single repair facility with exponential failure time and arbitrary repair time distribution. Each unit has three modes—normal (N), partial (P) and total failure (F). By using the regenerative point technique the system has been analysed to determine mean time to system failure and profit earned by the system. A numerical example is used to highlight the important results.     

Cost analysis of a three-state repairable redundant complex system under various modes of failures

In this paper investigations have been carried out for the availability and mean time to failure analysis of a three unit repairable electronic equipment having three states; viz; good, degraded and failed under critical human errors. The three states three units repairable electronic equipment suffers two types of failures; viz; unit failure and failure due to critical human errors. Entire system can fail due to critical human errors. The failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of the probabilities of the complex system being in various states are obtained along with steady state behaviour of the equipment. A numerical example has also been appended to highlight the important results. Three graphs have also been given in the end. There is only one repair facility, which is availed only when the system is in either degraded or failed state due to unit failure.     

Analysis of a two-unit cold standby system with three modes

This paper analyses a two-unit cold standby system under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units are exponential, whereas repair time distributions are arbitrary. Breakdown of the system occurs when both the units are in total failure mode. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

Reliability analysis of multi-unit cold standby system with two operating modes

This paper investigates the mathematical model of a system composed of n dissimilar units—one functioning and others either failed or cold standbys. Each unit of the system has three possible modes—normal, partial failure and total failure. There is a perfect switch to operate the leading standby unit on total failure of the operative unit. The failure and repair times of each unit are assumed to follow arbitrary distributions. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are derived as particular cases.     

Stochastic behaviour of a two-unit standby system with better utilization of units

This paper obtains various measures of reliability of a two-unit redundant system with three modes. Upon partial failure of an operative unit the cold standby starts operation only when it becomes active. A single service facility is available (1) for repairing a partially or totally failed unit and (2) to activate the cold standby unit whenever required. Failure time distributions are negative exponential while repair and activating time distributions are general.     

A reliability physics model for dissimilar two-unit standby system with single repair facility

In this paper, the reliability and availability analysis of a repairable dissimilar two-unit standby system is carried out using stress-strength failure model. Single repair facility with the time taken to repair a unit being either deterministic or random has been considered. The analysis is carried out for arbitrary stress, strength and repair time distributions.     

Performance-related reliability measures for a repairable two-unit gracefully degrading system

The system analysed is a two-unit gracefully degrading system with repair. After each repair, the unit is tested to see if the repair meets certain predefined specifications. If it does, the unit is put to operation, otherwise it goes to post-repair. The failure-time and testing-time distributions are exponential whereas all other distributions are arbitrary. The technique of embedded SMP is employed to obtain several system performance parameters, namely, MTFF (mean time to first failure), availability, computational availability, expected number of visits to a certain state etc.     

Operational behaviour of a three state standby redundant electronic equipment under critical human errors

This paper deals with the operational behaviour of a cold-standby redundant system incorporating the concept of three states, with four types of failures, namely major unit failure, minor unit failure, partial failure due to critical human errors and complete failure due to critical human errors, under only one repair facility. Failure and repair times for the complex system follow exponential and general distributions, respectively. Repair is undertaken only when the system is either in degraded state or in failed state. Laplace transforms of the probabilities of being in various states as well as in up and down states are computed, along with the steady state behaviour of the system. A particular case of such a system has also been appended to highlight the important results.     

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.     

Comparison of two stochastic models for two-unit series system with cold standbys

Reliability characteristics are compared for two stochastic models of a system that has two non-identical units, arranged in series, each unit with its identical cold standby. The same set of assumptions is used for both models, except that in model 2 both of the standby units replace the failed operative unit instantaneously whereas in model 1 an operative failed unit is replaced by its corresponding standby unit (i.e. only one unit is replaced in this case). A single repair facility is available to repair the failed unit. Failure and repair time distributions are assumed to be negative exponential.     

An approximation analysis for the availability of a parallel redundant system with general distributions

This paper presents an approximation method for deriving the availability of a parallel redundant system with general distributions. The system discussed is composed of two identical units. A single service facility is available for the performance of preventive maintenance(PM) and repair. The failure times, repair times and PM times are assumed to be arbitrarily distributed. The presented method formulates the problem of the availability analysis of a parallel redundant system as a semi-Markov process which represents the state transitions of one specified unit in the system. This method derives the availability easily and accurately. Further, when all the distributions are exponential, the availability obtained by this method is exact.     

A two-unit cold standby system with allowed down-time and correlated failures and repairs

This paper considers the stochastic behaviour of a two-unit cold standby system with allowed down-time and a single repair facility to repair the failed unit. It is assumed that the repair and failure times of a unit are associated with each other in some way or other and their joint distribution is bivariate exponential.     

MTTF and availability evaluation of a two-unit, two-state, parallel redundant complex system with constant human failure

This paper deals with MTTF and availability analysis of a two-state complex general repairable system consisting of two units arranged in parallel. Single service facility is available for the service of unit failure. The failure and repair times for the system follow exponential and general distributions respectively. Laplace-transforms of the various state probabilities have been derived and steady state behaviour of the system has also been examined. Availability at any time is obtained by the inversion process. To make the system more compatible with the physical situation, MTTF for the system has also been evaluated and various graphs have been plotted to highlight the utility of the model.     

Cost analysis of a two-dissimilar unit cold standby redundant system with administrative delay and no priority in repair

This paper deals with the cost analysis of a two-dissimilar unit cold standby redundant system with three modes for each unit under the assumption that there is administrative delay and no priority in repair. The failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers have been obtained. Moreover some previous results are derived from the present results as special cases.