Stochastic behaviour of a two-unit cold standby redundant electronic equipment under human failure

This paper presents a mathematical model to evaluate availability and M.T.T.F. of a two-unit cold standby system with three possible states of each unit; viz. good, partially failed and failed, incorporating the concept of human failure. The model has been developed for exponential failures and general repairs. Single service facility is available in each state during the operational stage of the electronic equipment. Laplace transforms of the various state probabilities have been obtained. Steady-state probabilities, steady-state availability and mean time to failure have been derived.     

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.     

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.     

Two models for two-dissimilar-unit cold standby redundant system with partial failure and two types of repairs

This paper deals with the availability function and the mean time to the first failure for two models of a cold standby redundant system with two different types of repair. Each model consists of two dissimilar units. In the first model, the operative unit has two modes of operation, normal mode and partial failure mode. The standby unit has one mode of operation, normal mode. In the second model, each unit has three modes of operation, normal mode, failure mode and total failure mode. Both models are analyzed by the semi-Markov process technique, assuming that the failure time and repair time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Moreover, we give computer programs for calculating the MTSF for each model (see Appendix).     

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.     

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.     

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.     

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.     

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-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.     

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.     

Stochastic behaviour of a two-unit standby system with better utilization of units

This paper obtains various measures of reliability of a two-unit redundant system with three modes. Upon partial failure of an operative unit the cold standby starts operation only when it becomes active. A single service facility is available (1) for repairing a partially or totally failed unit and (2) to activate the cold standby unit whenever required. Failure time distributions are negative exponential while repair and activating time distributions are general.     

A two-unit cold standby system with three modes and correlated failures and repairs

The economic parameters are studied for a two-unit cold standby system with three modes and failure and repair times having bivariate exponential density as their joint distribution. The system is studied at suitable regenerative epochs to obtain these economic parameters. Explicit results have also been obtained for the case when failure and repair times are independent. Two important parameters of the system, i.e. MTSF and availability, have been studied graphically to observe the effect on them of correlation.     

A two-unit cold standby system with allowed down-time and correlated failures and repairs

This paper considers the stochastic behaviour of a two-unit cold standby system with allowed down-time and a single repair facility to repair the failed unit. It is assumed that the repair and failure times of a unit are associated with each other in some way or other and their joint distribution is bivariate exponential.     

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.     

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

This paper deals with the cost analysis of a two-dissimilar unit cold standby redundant system with three modes for each unit under the assumption that there is administrative delay and no priority in repair. The failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers have been obtained. Moreover some previous results are derived from the present results as special cases.     

Approximations of a two-unit cold standby system's reliability behaviour

In this paper we study the reliability behaviour of a two-unit cold standby system with priority. At time t = 0, the priority unit (p) begins to work and the standby unit (s) is in cold standby. The p-unit has priority whether it is working or being repaired. A single repairman is available, and the repaired unit is as good as new. We assume that the p-unit's working time X₁ has a general life distribution F(x), and its repair time Y₁ has a general distribution G(x). The s-unit's working time X₂ has an exponential distribution with mean , and its repair time has an exponential distribution with mean . Using the Markov renewal process and stochastic comparison, we give bounds of the mean time to the first failure of the system, and the system's availability.     

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.     

Optimal policies in a two-unit standby system with two types of repairmen

This paper is concerned with a two identical unit cold standby system. There is a facility of having two types of repairmen. The “regular” repairman is always kept with the system with the known fact that he might not be able to do some complex repairs within some tolerable “patience” time, while a perfect “expert” repairman is called only in need. On the completion of this tolerable time or on the system failure whichever is earlier, the expert repairman is called on to do the job. We use semi-Markov processes and numerical methods, we discuss optimum policies for calling the expert, maximizing the profit and plot the graphs.