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.     

Profit evaluation of a two unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby system subject to a single repair facility with exponential failure time and arbitrary repair time distribution. Each unit has three modes—normal (N), partial (P) and total failure (F). By using the regenerative point technique the system has been analysed to determine mean time to system failure and profit earned by the system. A numerical example is used to highlight the important results.     

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.     

Analysis of a two-unit cold standby system with three modes

This paper analyses a two-unit cold standby system under the assumption that 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. Breakdown of the system occurs when both the units are in total failure mode. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

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 system with a replaceable repair facility

This paper considers a two-dissimilar-unit cold standby system where the repair facility is subject to failure and can be replaced by a new one after it fails. By using Markov renewal theory, we obtain some reliability quantities of the system and the repair facility, respectively.     

Reliability analysis and optimization applications of a two-unit standby redundant system with spare units

Consider a two-unit standby redundant system with two main units, one repair facility, and n spare units. When the main unit has failed and the other is under repair, a spare unit takes over the operation and if it fails, it is replaced by a new one until the repair of the failed unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. In this paper, we derive expressions for 1) the distribution function of the first time to system failure, 2) the probability that the total number of failed spare units during the time interval (0,t] is n and 3) the mean of the total number of failed spare units in (0,t] and its asymptotic behaviour. Introducing costs incurred for each failed main unit and each failed spare unit, the expected cost per unit of time of the system was also derived. Finally an optinmization problem is discussed in order to compare the expected cost of the system with both main units and spare units with that of spare units only, and particular cases are considered.     

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 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.     

GERT analysis of a two-unit cold standby system with repair

This paper presents a GERT (Graphical Evaluation and Review Technique) analysis of a two-unit cold standby system. The various performance characteristics of the system have been derived analytically.     

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.     

Switch failure in a two-unit standby redundant system

In this paper we study the effect of imperfect switching on a two-unit standby redundant system, in which each unit works in three different modes (normal, partial failure and total failure) when the failure time distributions are exponential with different means and the repair times are arbitrarily distributed. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and particular cases are shown to corroborate earlier results.     

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.     

Some characteristics of a two-dissimilar-unit cold standby redundant system with three modes

This paper deals with the stochastic behaviour of a two-dissimilar-unit cold standby redundant system in which each unit works in three different modes—normal, partial failure and total failure. It is assumed that the failure and repair times are stochastically independent random variables each having an arbitrary distribution. 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. Explicit expressions for the Laplace-Stiektjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady state availability of the system are obtained. Certain important results have been derived as particular cases.     

Cost analysis of a two-unit cold standby system with two types of operation and repair

This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.     

Probabilistic analysis of a two-unit cold standby system with instructions at need

A two-unit cold standby system with an expert repairman and his assistant is examined. If the expert repairman is busy in repairing a failed unit and at that time the second unit fails, the assistant repairman repairs the latter unit. The assistant repairman needs or does not need instructions for doing repair with probability p and q, respectively. Using a regenerative point technique, various measures of system effectiveness are obtained.     

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.     

Analysis of a two-unit hot standby system with three modes

This paper discusses the stochastic behaviour of a two-unit hot standby redundant system having exponential failure and a single repair facility with general repair time distribution. Each unit of the system has three possible states—normal, partial failure and total failure. Breakdown of the system occurs when both the units are in total failure mode. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

Reliability analysis of a two-unit redundant system with a replaceable repair facility

This paper considers a two-unit redundant system where the repair facility is subject to failure and can be replaced by a new one when it fails. By using Markov renewal theory we obtain some reliability quantities of the system and the repair facility, respectively.