Availability analysis of a two-unit cold standby system with two switching failure modes

We consider a 2-unit cold standby redundant system with two switching devices—transfer switch and connect switch. The system is analysed under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units and connect switch are exponential, whereas repair time distributions are general. At any instant after use the transfer switch fails with probability q = 1?p. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated. A few particular cases are discussed.     

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 ? q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.     

Cost-benefit analysis of single server n-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a single-server n-unit system with an imperfect switch where failures of the items (units or the switch) are not detected unless either inspected by the server or when the system is down. Initially, one unit is put into operation (the switch is working at t = 0) and n − 1 units are kept as cold standbys. A failed unit is replaced by a standby if the switch and a standby are available. The server visits the system at random to check for the failed item and the check is instantaneous. When the system is down, either because of want of the standby or failure of the switch, the server is called for, and is assumed to arrive instantaneously. The revenue as well as the cost of repair are arbitrary functions of time. The expected net gain in (0, t) is evaluated assuming that all the life-time distributions are exponential and all the repair time distributions are arbitrary.     

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.     

A computer algorithm for the analysis of maintained standby redundant systems

A computer algorithm is developed to analyse standby redundant systems with repair maintenance. The method is applicable to a generalized class of standby systems. Failure-time distributions of units need to be exponential whereas repair-times can follow general distributions. A large number of input parameters which may be of interest to system designers have been incorporated, e.g. repair efficiency, transfer switch failure, connect switch failure, preoccupied repair facility etc. The analysis procedure consists in defining a system model by writing different states and transitions between them. Once this is done, the underlying process is visualized as a semi-Markov process and various results from this theory are applied to develop a computer algorithm in FORTRAN IV for obtaining a fairly large number of system output parameters viz., mean-time-to-system failure, steady-state availability, expected number of visits to a state, expected profit rate of the system etc. Two examples are included to illustrate the usage of the procedure developed.     

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.     

A parallel redundant complex system with two types of failure under preemptive-repeat repair discipline

This paper presents the availability analysis of a complex system, which consists of two s-independent repairable subsystems A and B in series (1-out-of-2:F). Subsystem A has two identical units arranged in parallel redundancy (1-out-of-2:G), sub-system B is a single unit with two types of failure, viz., partial and catastrophic. There is only one repair facility, which is always available. The failure and repair times for both subsystems follow exponential and general distributions respectively. The model so developed is analysed under “preemptive-repeat repair discipline”. By employing supplementary variable technique Laplace transforms of various probability states are obtained along with steady-state behaviour of the system. Inversions have also been carried out so as to obtain time dependent probabilities, which determine availability of the system at any time.     

Stochastic behaviour and profit analysis of a redundant system with slow switching device

This paper studies various economic measures of a two unit cold standby system subject to slow transfer switch. Each unit of the system can be in one of the three modes—normal, partial failure and total failure. Repair time distribution of the units are general while all other transition time distributions are negative exponential. Regenerative point technique in Markov-renewal process is applied to obtain the economic measures.     

Cost-benefit analysis of one-server two-unit imperfect switch system subject to multistage repairs

This paper deals with the cost-benefit analysis of 1-server 2-unit system with imperfect switch where repairs take place in stages. The repair times of the unit and of the switch are assumed to be arbitrarily distributed while the failure rates of units and of the switch are constants. Initally, one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. The repair of the switch is given preference after completion of current repair of a unit. The analysis is carried out by regeneration point technique. Explicit expressions for the expected durations the server is busy in (0, t) with particular stages of repair of the unit and of the switch are obtained to carry out the cost-benefit analysis of the system.     

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.     

Cost-benefit analysis of a one-server two-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the server is summoned upon failure of an item (i.e. unit or switch). The amount of time the server takes to arrive is a random variable, distributed arbitrarily. The server leaves when there is no item waiting for repair. The repair times are arbitrarily distributed whereas all failure rates are constant. Initially one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. Explicit expressions for the expected uptime in (0, t) of the system, busy period of the server due to repair of a unit and that of the switch are obtained to carry out the cost-benefit analysis.     

Profit analysis of a cold standby system with two repair distributions

A single server two-identical unit cold standby system is analysed. Each unit has two operative modes—normal and quasi-normal. When a normal unit fails, it undergoes minor repair with probability p₁ and p₂ respectively. Upon minor repair unit works with reduced efficiency and is known as quasi-normal unit while upon major repair unit works as good as new (normal unit). When a quasi-normal unit fails, it undergoes minor or major repair with probability q₁ and q₂ respectively. Failure rates of normal and quasi-normal units are different. Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique in MRP the system characteristics of interest to system designers and operations managers have been obtained.     

Stochastic analysis of a multi-unit cold standby system working in orbit form

This paper considers the analysis of a single server n-similar unit system. Initially k(<n) units form an orbit which functions if one unit functions at a time and the remaining n − k units work as cold standbys. When a unit fails in the orbit it is instantaneously replaced by one of the standbys with the help of a perfect transfer switch. The system is said to fail when n − k + 1 units have failed. The distribution of time to failure and time to repair of a unit are negative exponential. Using the regenerative point technique several reliability characteristics are obtained to carry out the cost-benefit analysis.     

An (m, M) machine repair problem with spares and state dependent rates: A diffusion process approach

The diffusion approximation model for (m, M) general machine repair problems with spare part support has been developed. The inter-failure time and repair times are assumed to be generally identically and independently distributed (i.i.d.). The failure rate of operating units in a short system when fewer than M units are operating and all spares are being used, is faster than a normal system. The spare units may also fail with rates different from operating units. The repairmen switch to the faster rate to reduce a backlog of down units in the case of a busy repair facility. By using reflecting boundaries, the approximate formulae for some performance measures, namely, expected number of inoperative/operative units and probability that the system is short/down have been obtained.