Stochastic analysis of a 2-unit standby system with two failure modes and slow switch

This paper considers the cost-benefit analysis of a one-server two unit system subject to two different failure modes and slow switch. The failure rates of the units are constant. The repair times and the switchover time are assumed to be arbitrarily distributed. The server repairs the units and puts the standby unit into operation. Detailed analysis of the system is done by using regenerating point technique and results are obtained for mean time to system failure, steady state availability, busy period of a repair man, expected number of visits by the repair man and expected profit earned by the system.     

A redundant system with non-instantaneous switchover and “preparation time” for the repair facility

This paper discusses two models of two-unit standby redundant systems in which the switchover time is a random variable and the repair facility is not available for a random time immediately after each repair completion. In model I the probability distributions of the life time of the online unit and switchover time are general while all the other distributions are exponential. Model II is a cold standby system in which the probability distributions of the “preparation time” of the repair facility is exponential and all the other distributions are general. Using the regeneration point technique the availability functions of the two systems are determined. Several special cases are also discussed.     

CHE failure in a two-unit standby system with slow switch, repair and post repair

A mathematical model of a two-unit cold standby system with critical human errors (CHE) and slow switch is investigated. The CHE leads to complete system failure, and repair and post-repair are needed before the system can be put back into operation. Slow switch means that on failure of the operative unit the switch puts the standby unit into operation after a random time. Failure time and switchover time distributions are negative exponential whereas all the repair and post repair time distributions are general. Using a regenerative point technique, we obtain various reliability characteristics which can be used to carry out the cost-benefit analysis. In a particular case, the behaviour of the cost function is also studied graphically.     

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.     

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.     

Laplace Transforms for the Two-Unit Cold-Standby Redundant System

A conditional transform approach is applied to the two-unit standby redundant system with instantaneous switchover, and with failure and repair times that follow general well-behaved distributions for each unit. Transforms of distributions are obtained for T, the time to system failure, the number of repairs completed during T, the time spent on repair during T, and the idle time of the repairman during T. Applicable numerical methods are also discussed.     

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.     

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.     

Two unit repairable redundant standby system

The Laplace-Stieltjes (LS) transform for the distribution of time to first system failure (TFSF), transition probability, availability and mean time to system failure have been derived for two unit repairable redundant standby system with perfect as well as imperfect switchover condition. General expressions for computing various reliability performance indices have been obtained by using Markov Renewal techniques considering general distributions for time to failure and time to repair for the units.     

The effect of preventive maintenance on a system with imperfect switchover

A two-unit standby redundant system with repair, preventive maintenance and imperfect switchover is considered. The Laplace-Stieltjes transform (LST) of the survivor function (sf) of the time to the first system failure (TFSF) and the mean are derived. Finally a theorem about the effect of preventive maintenance is proved.     

Stochastic analysis of a complex two-unit system with non-instantaneous switchover and imperfect repair

Expressions for the availability and reliability for a two-unit standby redundant system with non-instantaneous switchover and imperfect repair are obtained.     

A Standby Redundant Model with Noninstantaneous Switchover

This paper considers the case of a standby redundant system where the switchover is not instantaneous. The duration of time between the instant at which action is initiated on the standby subsystem in order to bring it to the active state and the instant at which it becomes operating standby is called switchover time, and is considered to be a random variable. A policy specifying the instant at which action is initiated on the standby subsystem in order to bring it to the operating standby state is proposed and under this proposed policy, the Laplace transform of the probability density function of time to system failure and the expression for expected time to system failure are derived.     

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.     

On a two-dissimilar-unit standby system with three modes and administrative delay in repair

This paper considers a two-dissimilar-unit cold standby redundant system with three modes of each unit under the assumption that there is an administrative delay in getting the repair man at the system location. The system is analyzed by the semi-Markov process technique, assuming that the failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Further, special cases of the results of this paper coincide with earlier results obtained by Pandey and by Gupta.     

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.