Reliability and availability analysis of warm standby systems in the presence of chance with multiple critical errors

This paper presents a reliability and availability analysis of k active, N warm standby units in the presence of chance with M multiple critical errors. The system is in a failed state when (N + 1) units have failed (active and/or warm standby units have failed) or one of the multiple critical errors has occurred. Failed units are not repaired but a failed system will be repaired with repair times arbitrarily distributed. The expressions for reliability, availability and steady-state availability are derived.     

Availability and frequency of warm standby systems in the presence of chance with multiple critical errors

This paper presents the availability and frequency of encountering different state of k active, N warm standby units in the presence of chance with M multiple critical errors. The system is in a failed state when one of any multiple critical errors has occurred or when (N+1) units have failed. Failed units are not repaired. However, failed system will be repaired with constant repair rates. The expressions for steady-state availability and frequencies of down- and up-states are derived.     

Reliability and availability analysis of a k-out-of-N:G redundant system with repair in the presence of chance of multiple critical errors

The paper presents a reliability and availability analysis of a k-out-of-N:G redundant system with repair facilities in the presence of chance of multiple critical errors. The system is in a failed state when N−k+1 units have failed or any one of the multiple critical errors has occurred. Failed units and failed system will be repaired with constant repair rate to state with N−k+1 failed units. Laplace transforms of the state probabilities, the reliability and the availability of the system are derived. The system steady-state availability is also given.     

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 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.     

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.     

Reliability analysis of a k-out-of-N:G redundant system in the presence of chance with multiple critical errors

A reliability analysis of a k-out-of-N: G redundant system with multiple critical errors and r repair facilities in the presence of chance, is dealt with in this paper. The system is in a failed state when k units have failed or one of any multiple critical errors has occurred. Failed system repair times are arbitrarily distributed. The formulae for reliability function in terms of a Laplace transform, steady-state availability and mean time to failure are derived.     

Cost analysis of a 2-unit standby redundant electronic system with critical human errors

In this paper, investigations have been carried out for the evaluation of availability and expected profit during the operable stage of a standby redundant, electronic system, incorporating the concept of human failure. The system can be in any of the three states: good, degraded and failed. One repair facility is available for the repair of a unit in failed or degraded state. The system cannot be repaired when it fails due to critical human errors. The repair of the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and the operational availability of the system at any time.     

Stochastic analysis of k-out-of-N:G redundant systems with repair and multiple critical and non-critical errors

Probabilistic analysis of k-out-of-N:G redundant systems with repair facilities and multiple critical and non-critical errors is presented. Failed unit (active and/or by any one of the multiple non-critical errors) will be repaired with the same constant repair rate. The system is in a failed state when any one of the multiple critical errors has occurred or (N − k + 1) units have failed. Failed system will be repaired with repair times arbitrarily distributed. The formulas for reliability and steady-state availability are given.     

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.     

Reliability analysis of a three-state multi-component warm standby redundant complex system with waiting for repair

Investigations have been carried out with the help of Laplace transforms and supplementary variable techniques for the evaluation of reliability analysis of a three-state multi-component warm standby redundant complex system suffering three types of failures, namely minor, major, and human due to critical human errors incorporating the concept of waiting for repair.     

Stochastic behavior of a two-dissimilar-unit standby redundant system with repair maintenance

A standby redundant system of two dissimilar units is considered under the assumptions that both the failure and the repair time distributions are arbitrary. The system states are defined corresponding to the failure of the specified units. The first passage time distributions, the expected numbers of visits to a certain state, the transition probabilities, and the limiting probabilities are obtained using the unique modifications of the regeneration point techniques in Markov renewal processes. Two particular cases are finally presented.     

Stochastic analysis of a two unit cold standby system with preparation time for repair

This paper deals with the cost-benefit analysis of a two unit cold standby system in which the cold standby unit replaces the failed operative unit after a random amount of time. Inspection is required to decide whether it needs type I or type II repair. Failure, repair, replacement and inspection time distributions are arbitrarily distributed. A repair man is not always available with the system, but is called for repair whenever the operative unit fails.     

Stochastic analysis of a general standby system with constant human error and arbitrary system repair rates

This paper presents a mathematical model for performing reliability and availability analyses of a general standby system with constant human error and common-cause failure rates. In addition, system repair times are assumed arbitrarily distributed. Markov and supplementary variable techniques were used to develop equations for the model. The method of linear ordinary differential equation is developed to obtain the general expressions of the steady state availability. The Laplace transform technique was used to obtain the system time-dependent availability, reliability and mean time to failure expressions.     

Stochastic analysis of a two-unit warm standby system with slow switch subject to hardware and human error failures

In this paper several important measures of reliability for a two-unit warm standby system with slow switch subject to hardware and human error failures are obtained using regenerative points technique in Markov renewal processes. All times distributions are exponential except the repair times distributions are general.     

Stochastic analysis of standby system with duplex units

This paper investigates a mathematical model of a system composed of two units, one operative and the other cold standby. Each unit of the system is made of two non-identical parallel components and each component is made of n-elements. Henceforth we call each unit of the system a duplex unit. Failure and repair time distributions of each element of a component are negative exponential and vary from element to element, whereas the repair time distribution of a unit is arbitrary. Upon the failure of the operative unit the standby unit does not operate instantaneously. This type of situation may be found in many electronic networks. Several reliability characteristics of interest have been obtained.     

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.     

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.     

Reliability analysis of a system with a mixture of warm and cold standby

A single-server two-unit standby system with two modes of each unit—normal and total failure—is considered. The standby units are repeatedly interconverted after a random time from warm to cold and cold to warm. Upon failure of the operative unit, the standby unit, if it is warm, starts to operate instantaneously; otherwise, the system goes down until the cold standby starts to operate. System failure occurs when both units fail totally. Identifying the system at suitable regenerative epochs, the integral equations are set up and the expressions for reliability and mean time to system failure (MTSF) are obtained. The graphical behaviour of MTSF is also studied in a particular case.