Cost analysis of a multi-component parallel redundant complex system with overloading effect and waiting under critical human error

The cost analysis of a multi-component parallel redundant complex system is considered, incorporating the concept of overloading effect and waiting time for repair under critical human error. Failure and waiting times follow an exponential time distribution, whereas repair time follows a general distribution. Using the supplementary variable technique, Laplace transforms of the probabilities of the complex system being in various states have been computed. Some graphs have been plotted to highlight the main results.     

Inspection policy for two-unit parallel redundant system

This paper deals with a single-server two-unit parallel redundant system with non-negligible inspection time. We shall assume that a failure of a unit or the system failure is detected by inspection only. We consider two inspection policies and under each inspection policy the stationary availability is derived by applying Piecewise Markov Process. Optimum inspection schedule is discussed to maximize the stationary availability of the system. A numerical example is presented.     

A two-unit parallel redundant system with bivariate exponential lifetimes

In this paper we discuss a two-unit parallel redundant system with a single repair facility in which the lifetimes of two units obey a bivariate exponential distribution and the repair time of the failed unit obeys an arbitrary distribution. Applying an extended Markov renewal process, we obtain the quantities of interest thoroughly in reliability theory.     

Cost analysis of a three-state parallel redundant complex system

This paper deals with the cost analysis of a three state system consisting of two independent units in parallel redundancy. The failure and repair times for the system follow exponential and general distributions respectively. The Laplace-transforms of various state probabilities have been derived and steady state behaviour of the system has also been examined. A few particular cases have also been discussed at the end to highlight the utility of the model.     

Light maintenance for a two-unit parallel redundant system with bivariate exponential lifetimes

Maintenance is of great interest in reliability theory. A two-unit parallel redundant system is a typical redundant repairable system and is applied in many practical fields such as computer systems. Many contributions to such systems have been proposed and analyzed extensively. The earlier models have mainly assumed that the lifetimes of two units are independently distributed. However, some papers considered a two-unit parallel redundant system in which the lifetimes of two units are dependent and distributed by a Bivariate Exponential (BVE) distribution. In this paper we discuss a two-unit parallel redundant system with single repair facility in which the lifetimes of two units obey a BVE distribution. Consider the maintenance policy for the operative unit. The time of the beginning of the lightly maintenance measured from the instant that the unit begins to be operative, is assumed to obey a BVE distribution. We derive the limiting availability for the system by applying a unique modification of regeneration point techniques in Markov renewal processes. This paper also gives a numerical example of the limiting availability for the system.     

Analysis of a two-unit parallel redundant system with phase type failure and general repair

Explicit expressions for the Laplace transform of the reliability and availability of a general two-unit parallel redundant system are obtained. The mean time to system failure and steady state availability are deduced as special cases. Some particular cases of our result are also obtained.     

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.     

A two-unit parallel redundant system with three modes and bivariate exponential lifetimes

A two-unit parallel redundant system is applicable in many practical fields, such as computer systems. Whereas the earlier models for such a system have assumed that the failures of the two units are independent, these are taken here to be dependent and have a joint bivariate exponential (BVE) distribution. Each unit has three modes and when the system fails completely, it is repaired (or replaced) with arbitrary rate. Using Sugasaw and Kaji's (Microelectronics and Reliability, 21 (5), 661–670) modification of the regenerative point technique as applied to Markov-renewal process theory, several reliability characteristics of interest to system designers are obtained.     

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.     

Cost analysis of a 2-unit standby redundant electronic system with critical human errors

In this paper, investigations have been carried out for the evaluation of availability and expected profit during the operable stage of a standby redundant, electronic system, incorporating the concept of human failure. The system can be in any of the three states: good, degraded and failed. One repair facility is available for the repair of a unit in failed or degraded state. The system cannot be repaired when it fails due to critical human errors. The repair of the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and the operational availability of the system at any time.     

Reliability analysis of a two-unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby redundant system subject to a single repair facility with exponential failure and general repair time distribution. Each unit can work in three different modes — normal, partial failure and total failure. There is a perfect switch to operate the standby unit on total failure of the operative unit. The system has been analysed to determine the reliability parameters e.g. mean time to system failure (MTSF), steady state availability, mean recurrence to a state and expected number of visits to a state, first two moments of time in transient state, by using the theory of Semi-Markov Process. Howard's reward structure has been super-imposed on the Semi-Markov Process to obtained expected profit of the system. A number of results obtained earlier are derived as particular cases.     

Cost analysis of a three-state standby redundant electronic equipment

In this paper, the investigations have been carried out for the cost function analysis of a standby redundant system having three states. The two-unit standby redundant system suffers two types of failures: viz. minor and major, which bring the system to degraded or a complete failure stage. There is only one server and is always available. Failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of the probabilities of the complex system being in various states have been derived, which have been inverted further so as to obtain time dependent probabilities. To highlight the important results, two graphs have also been given in the end.     

Interval reliability of a two-unit stand-by redundant system

This brief note obtains expressions for Interval Reliability of a 2-unit stand-by repairable system by using the regenerative point technique of the Markov Renewal Process.     

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.     

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.     

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.     

MTTF and availability evaluation of a two-unit, two-state, parallel redundant complex system with constant human failure

This paper deals with MTTF and availability analysis of a two-state complex general repairable system consisting of two units arranged in parallel. Single service facility is available for the service of unit failure. The failure and repair times for the system follow exponential and general distributions respectively. Laplace-transforms of the various state probabilities have been derived and steady state behaviour of the system has also been examined. Availability at any time is obtained by the inversion process. To make the system more compatible with the physical situation, MTTF for the system has also been evaluated and various graphs have been plotted to highlight the utility of the model.     

Cost analysis of a two-unit standby system with two types of repairmen

This paper is concerned with a two-unit cold standby system with two types of repairmen. One “regular” repairman is kept for repairing the units as soon as they fail. It is assumed that sometimes he might not be able to do the repairs within some tolerable time (patience time). Another “expert” repairman, assumed to be perfect, is called on to do the repairs on the completion of this patience time or on the failure of the system, whichever is later.Various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the expert repairman should be called after the system failure. Further numerical results for a case, in which repair time and patience time both have non-Markovian property, are also investigated. Then the upper bound of the cost K₃, below which the expert repairman should be called immediately after the system failure and the corresponding increase in profit are calculated.     

Reliability analysis of a two-unit parallel system with dissimilar units and general distributions

We study the reliability characteristics of a parallel system attended by a single repair facility and general failure and repair time probability distribution functions (pdf). The basic mathematical problem is the solution of a pair of simultaneous Wiener-Hopf integral equations.A formal solution procedure of the equations has been discussed in the case of unspecified characteristic functions (cf).Fairly explicit solutions are performed if at least one of the failure time pdf's has a rational cf.We compare some of the results presented in previous literature.