Stochastic behavior of a two-unit cold standby redundant system subject to random failure

The present paper deals with a stochastic model of a two-unit cold standby redundant system subject to random failure. The random failure occurs at random times which follow an exponential distribution. Using a regenerative point technique in the Markov-renewal process, several reliability characteristics are obtained. The mean time to system failure function is studied graphically.     

Stochastic analysis of a two-unit redundant system with two types of failure

The present paper investigates a stochostic model of a two-unit warm standby system with a single repair facility. Before repair, the failed unit is sent for fault detection to decide whether it failed due to machine defect or critical human error. The probability of having machine defect and C.H.E. has been fixed. Using the regenerative point technique in the Markov renewal process various measures of system effectiveness are obtained.     

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.     

Analysis of two-unit redundant system under partial failure and two types of repairs

In this paper we consider a redundant system with two identical units, providing for partial failure mode and two types of repairs for a failed unit. Failure and repair time are assumed to follow general distribution. Applying the regenerative theory in Markov-renewal process, several reliability characteristics of interest to system designers are obtained.     

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.     

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.     

Stochastic analysis of a redundant system with two types of failure

This paper deals with the analysis of a system model consisting of two units, in which one is operative and the other is on cold standby. The failure of an operative unit may be caused by a machine as well as by random shocks which occur after a certain interval of time.Using the regenerative point technique in Markov renewal processes, several effective measures of reliability are obtained.     

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.     

Two-unit cold-standby redundant system subject to random checking, corrective maintenance and system replacement with repairable and non-repairable types of failure

We consider a system comprising two identical units. Initially one unit operates and the other remains as a cold standby. At random intervals, checking is done to ascertain the need of Corrective Maintenance (CM). In case CM has to be carried out, the standby unit starts operating. While the unit is operative, it may fail. Failures are of two types, repairable and non-repairable. When the system fails with non-repairable failure of both the units, it is replaced. Several reliability characteristics of interest to system designers as well as to operations managers have been evaluated.     

Analysis of a two-unit warm standby system subject to degradation

This paper deals with the reliability analysis and the mean time to system recovery of a single server, two-unit (priority and ordinary) warm standby subject to degradation. Initially the priority unit is operative and the ordinary unit is kept as a warm standby. The priority unit passes through three different operative stages (excellent, good and satisfactory) before it fails. The priority unit enters into the total failure mode only from the satisfactory stage, and after repair it enters into the normal mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with different probabilities. The failure, repair and degradation time distributions are assumed to be general and arbitrary. The system is observed at suitable regenerative epochs in order to carry out the expected first passage time analysis. Moreover, three special cases have been considered. The results of Gupta [Int. J. Systems Sci.22 (11) 2329–2338 (1991)] are derived from the present results as a special case. A computer program for calculating the mean time to system failure and the mean time to system recovery is made.     

Stochastic behaviour of a two-unit paralleled system

This paper deals with a two-unit paralleled system with a single repair facility. Most papers on this subject assumed that at least one of the life time and repair time distribution is exponential. However the above assumption is violated by this paper. Then the various state probabilities (densities) have derived by employing the method of supplementary variables. We obtain the stochastic behaviour from these probabilities; (1) the long-run availability, (2) the idleness probability for the repair crew, and (3) the expected number (per unit time in long run) of system failures. Also comparison between the constant failure rate and non-constant failure rate is shown by numerical example.