Two-unit Cold Standby Redundant System Research Articles

Cost Analysis of a System Involving Common-Cause Failures and Preventive Maintenance

Problem statement: Many authors have studied the cost analysis of a two-unit cold standby redundant system with two types of unit failure, but no attention was paid to the reliability of a system involving common-cause failures and preventive maintenance. Question was raised whether the preventive maintenance would be effective on the reliability and performance of the system. Determine the efficacy of preventive maintenance on the reliability and performance of the system. Approach: In this study, the Mean Time to System Failure (MTSF), steady state availability and the profit function of a two-unit cold standby repairable redundant system involving common-cause failures and preventive maintenance were discussed. We analyzed the system by using Kolmogorov's forward equations method. Some particular cases have also been discussed graphically. Results: The results indicated that the system with preventive maintenance is better than the system without preventive maintenance. Conclusion: These results indicated that the better maintenance of parts of the system originated better reliability and performance of the system.

Stochastic behaviour of a two-unit standby system with two types of repairmen and patience time

Stochastic behaviour of a two-unit cold standby redundant system, with two types of repairmen is analysed. The first repairman (usually called “regular” repairman) will always remain with the repair facility, with the known fact that he might not be able to do some complex repair within some tolerable (patience) time. An expert repairman is called to the system if and only if the regular repairman is unable to do the job, within some fixed time or on system failure, whichever occurs first. Techniques of regenerative point processes have been used to obtain various measures of system effectiveness and thereby profit incurred. The time-dependent availability, steady-state availability, reliability, Mean Time To Failure (MTTF), and profit function are obtained numerically and graphs are also drawn.

Probabilistic analysis of a two-unit cold standby redundant system subject to failure of controlled weather device

This paper studies stochastic analysis of a two-unit cold standby system taking into account failure of a weather condition device. All failure times and time to repair the weather condition device have a negative exponential distribution, whereas repair rates of the operating unit are general. The regenerative points technique in Markov renewal processes (MRP) is applied to obtain several reliability characteristics of interest to system designers.

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.

Reliability study of a two-unit cold standby redundant system with repair of two phases

Cost analysis of a two-unit cold standby redundant system with repair of two phases, preventive maintenance (PM) and imperfect switch is studied, considering the availability of a single serverman, all time distributions are arbitrary and two possible policies for the unit which is under PM, when the operating unit fails. We consider two models, model I for no-recalling state and model II for recalling state. Several reliability characteristics have been obtained. Moreover numerical results are given to illustrate the theoritical results.

A two-unit cold standby system with imperfect repair and excessive availability period

A two-unit cold standby redundant system supported by a single repair facility is considered. The units after repair do not behave like new ones and a unit can be repaired, at most, k( k < ∞) times. The failure time distribution of either unit is different after each repair. Further, the system performance is maintained for a random time even after breakdown. The reliability characteristics are provided for the model.

Reliability of a reparable system with preventive maintenance and imperfect switch

A two-unit cold standby redundant system with repair, post-repair, preventive maintenance (PM) and imperfect switchover is considered using three types of PM [types (a), (b) and (c)]. The Laplace transform (LT) of the survivor function (sf) of time to the first system failure (TFSF) and the mean TFSF are derived. A theorem about the effect of PM [type (a)] is proved. Finally numerical calculations are presented to illustrate the results.

Stochastic behaviour of a two-unit system with two types of repairman and subject to random inspection

Stochastic behaviour of a two-unit cold standby redundant system, with two types of repairman and subject to random inspection is studied. One repairman is “regular”; he always remains with the system and plays the dual role of inspection and repair. An expert repairman is called if the regular repairman is unable to do the job within some fixed time, or on system failure, whichever is earlier. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of system effectiveness and profit incurred. Optimal policies for calling the expert repairman and maximum profit have been analysed, and some graphs are given.

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.

Reliability study of a two-unit cold standby redundant system with two types of failure and preventive maintenance

This paper deals with a 2-unit cold standby redundant system with two types of failure and preventive maintenance (PM), from the point of view of cost-benefit analysis. The system has been studied using regenerative points.

On a two-unit cold standby redundant system with random switching time

This paper, which contains two sections, deals with a two-unit cold standby redundant system with random switching time and imperfect switchover. In Section I, we use the survival functions to find the mean TFSF and the L.S.T. of the distribution to the first system failure. Finally, we find the limiting distribution to the first system failure. In Section II, we find the mean TFSF considering two types of preventive maintenance (PM), type (a) and type (b). Finally we prove that the mean TFSF with type (b) PM is greater than or equal to the mean TFSF with type (a) PM.

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

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system in which each unit works in three different modes—normal, partial failure and total failure, with administrative delay and no priority in repair. The administrative time distribution is assumed to be exponential and the repair and failure time distributions are exponential and arbitrary. Various reliability parameters for system designers have been evaluated.

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.

Analysis of two-unit-standby redundant system with administrative delay in repair

A two-unit cold standby redundant system is analysed under the assumption that administrative time is spent in locating the repairman and getting him available at the system location. The administrative time distribution is assumed to be exponential and whereas the repair and failure time distribution are exponential and arbitrary. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.

A parallel redundant complex system with two types of failure under preemptive-repeat repair discipline : P. P. Gupta and S. C. Agarwal. Microelectron. Reliab.24, 395 (1984)

This paper deals with the cost—benefit analysis of a single-server two-unit cold standby redundant repairable system subject to inspection. An inspection policy model is considered in which the failure of a unit is detected by inspection only but system failure is detected instantaneously without inspection. The failure time of a unit is assumed to be exponentially distributed with parameter λ. Initially, a unit is switched on and the other one is kept as cold standby. The system breaks down if a unit fails while the other is still under repair. In this paper, the system is characterised by the probabilities of its being in the up or the down state. Integral equations are set up for these probabilities by identifying suitable regenerative epochs. Laplace transform technique is employed to solve these equations. System characteristics, namely:1.pointwise availability of the system during (0, t2.s-expected up-time of the system in (0, t3.s-expected busy-period of the service facility in (0, t4.steady-state availability of the system;are obtained to carry out the cost—benefit analysis. Numerical results pertaining to three particular cases are also presented.

Stochastic behaviour of a standby redundant system with three modes

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system in which 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. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure and steady state availability of the system are obtained. A few particular cases are discussed.

A multicomponent two-unit cold standby system with three modes

This paper investigates a mathematical model of a two-unit cold standby redundant system with three possible states of each unit—normal, partially failed and failed. Each unit has n components, each having a constant failure rate and a repair rate, an arbitrary function of the time spent. These vary from component to component. Steady-state probabilities, steady-state pointwise availability, mean time to system failure and Laplace transforms of various transient probabilities have been obtained. Several earlier results are verified as special cases.

Stochastic behaviour of a two-unit cold standby system with three modes and allowed down time

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system under two very general sets of conditions: (i) each unit of the system having three different modes of working—normal, partial failure and total failure; (ii) breakdown of the system occurring when with both the units in total failure mode, the system is not regarded as failed (the system fails only when the breakdown does not terminate within the allowed down time). Failure-time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.

Busy-period analysis of a one-server two-unit system subject to non-negligible inspection time

This paper deals with the busy-period analysis of a single-server two-unit cold standby redundant repairable system subject to inspection. Inspection policy models deal with stochastically failing systems in which failure is detected by inspection only. Previous authors assume that the time required for inspection is zero, while the current study deals with preparedness models when duration of inspection is non-negligible. A preparedness model is considered in which the failure of a unit is detected by actual inspection but a system break-down can be detected instantaneously without inspection. The failure time of a unit is assumed to be exponentially distributed with parameter γ. Initially, a unit is switched on and the other one is kept as a cold standby. The system breaks down if a unit fails while the other is still under repair. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes and employs the Laplace-transform technique to solve these equations. Measures of system effectiveness, namely: 1. 1. Point-wise availability of the system in (0, t], 2. 2. s-expected up-time of the system in (0, t], 3. 3. s-expected busy-period of the service facility in (0, t], 4. 4. Steady-state availability of the system, have been derived to obtain the s-expected net gain per unit time. Finally, numerical results pertaining to four particular cases are presented.

Analysis of a two-unit cold standby redundant system with allowed down-time

This paper analyses a two-unit cold standby system under two very general sets of conditions : ( i) each unit of the system having three different modes of working, normal, partial failure and total failure ; and ( ii) breakdown of the system occurring when both the units are down and failure occurs when breakdown is not repaired within the allowed down-time. We obtain a Laplace-Stieltjes transform of the distribution of time to system failure, it's mean time and steady state probabilities of the system being in up, down or failed states.