Reliability analysis of a system with a mixture of warm and cold standby

A single-server two-unit standby system with two modes of each unit—normal and total failure—is considered. The standby units are repeatedly interconverted after a random time from warm to cold and cold to warm. Upon failure of the operative unit, the standby unit, if it is warm, starts to operate instantaneously; otherwise, the system goes down until the cold standby starts to operate. System failure occurs when both units fail totally. Identifying the system at suitable regenerative epochs, the integral equations are set up and the expressions for reliability and mean time to system failure (MTSF) are obtained. The graphical behaviour of MTSF is also studied in a particular case.     

Reliability and availability analysis of a system with warm standby and common cause failures

This paper presents reliability and availability analyses of a two unit parallel system with warm standby and common-cause failures. The standby and switching mechanisms are subject to failure. The failed system repair times are assumed to be arbitrarily distributed. Expressions for Laplace transforms of system state probabilities, steady state system availability, system reliability, and mean time to failure are developed.     

Economic analysis of the M/M/R machine repair problem with warm standbys

This paper studies the M/M/R warm-standby machine repair problem under steady-state conditions. This is a generalization of the cold standby model considered in the literature. A profit model is developed in order to determine the optimal values of the number of spares and the number of repairment simultaneously. Numerical examples are provided in which several system characteristics are computed under optimal operating conditions.     

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.     

Reliability analysis of a three-state multi-component warm standby redundant complex system with waiting for repair

Investigations have been carried out with the help of Laplace transforms and supplementary variable techniques for the evaluation of reliability analysis of a three-state multi-component warm standby redundant complex system suffering three types of failures, namely minor, major, and human due to critical human errors incorporating the concept of waiting for repair.     

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 two-unit warm standby system with partial failure mode and inspection time

A two-unit warm standby system is discussed, in which units are identical. Partial failure and complete failure of a unit can be detected by inspection from time to time. The inspection time follows an exponential distribution, whereas the repair and failure time follows an exponential and arbitrary distribution. Several reliability characteristics of interest to system designers and operation managers have been evaluated.     

Availability of a series system with warm spares

We discuss two models for the availability of a series system of components with warm spares, serviced by a single service facility. Replacement of failed components by a spare has pre-emptive priority over repair of the failed components; for the restart model, in which interrupted repairs restart from the beginning, we find the availability of the system; for the resume model, in which interrupted repairs resume from where they left off, we show how to obtain the availability of the system. Some numerical examples and the distributions of system downtime are given for both models.     

Comparison of two stochastic models for two-unit series system with cold standbys

Reliability characteristics are compared for two stochastic models of a system that has two non-identical units, arranged in series, each unit with its identical cold standby. The same set of assumptions is used for both models, except that in model 2 both of the standby units replace the failed operative unit instantaneously whereas in model 1 an operative failed unit is replaced by its corresponding standby unit (i.e. only one unit is replaced in this case). A single repair facility is available to repair the failed unit. Failure and repair time distributions are assumed to be negative exponential.     

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

A two-unit warm standby system has been modelled and analysed through GERT approach. A general concept of system utilization factor and availability curve has been introduced.     

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

A two-unit warm standby system has been modelled and analysed through GERT approach. A general concept of system utilization factor and availability curve have been introduced.     

Reliability and profit analysis of two single-unit models with three modes and different repair policies of repairmen who appear and disappear randomly

Cost-benefit analysis of a single-unit system with three possible modes of the unit—normal (N), partial failure (P) and complete failure (F)—is carried out. The paper consists of two models: in model 1, the unit goes under repair (if a repairman is available) the moment it fails partially, whereas in model 2 the unit goes under repair at complete failure. The repairman appears in, and disappears from, the system randomly. A comparison between these two models after calculating MTSF and profit has also been made.     

On the transient behaviour of a repairable system with a warm standby

In this paper, a two-unit active standby system is analysed to evaluate various measures of system performance under the assumption that the failure and repair times follow arbitrary distributions. Systems of integral equations satisfied by various state probabilities corresponding to different initial conditions have been written using the supplementary variable technique and state-space method. A particular case is analysed numerically under the assumption that the failure and repair times of both the units follow normal distributions.     

Reliability of a standby system with beta-distributed componentlives

The exact distribution of the sum of 2 independent beta variables is presented. It is applied to a standby system with beta-distributed component lives and permits the calculation of its exact reliability when the exact parameters-values are known. It appreciably improves the current approximate method     

Repairable consecutive-k-out-of-n: G systems with r repairmen

In this paper, we study repairable consecutive-k-out-of-n: G systems with r repairmen. The systems are either circular or linear. It is assumed that the working time, and the repair time of each component in the system are both exponentially distributed; and every component after repair is 'as good as new'. Each component is classified as either a key component, or an ordinary one according to its priority role to the system's repair. By using the definition of generalized transition probability, the state transition probabilities of the system are derived. Some important indices related to repairmen are obtained, and some reliability indices are derived by using the Laplace transform technique. Numerical examples are then studied in detail to demonstrate the theoretical results developed in the paper. The proposed method, and its numerical illustrations for the examples verify the validity & generality of the studied system.     

Stochastic analysis of a two-unit warm standby system with slow switching device

This paper studies a two-unit warm standby system subject to slow switch. Failure rates and switchover time of a unit from standby to operative are constant while repair times are arbitrarily distributed. Using the theory of regenerative and Markov-renewal processes several important measures of reliability are obtained.     

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.     

Repair system where the repairmen change depending on the failed machines

In this study, the repair system of the machines having multi-input sources is analyzed in the steady state by assuming that the repairmen change is dependent on the failed machines. In the cases of two and three repairmen, it is assumed that the service abilities of each repairman differ. The mean number of failed machines and the mean waiting failed machines are derived as the characteristic values of the system.     

Reliability of a stand-by system with common-cause failures and scheduled maintenance

The paper investigates the reliability of a stand-by system incorporating the concepts of repair and scheduled maintenance. Further, the system experiences dual mode of failures—first, failure due to change in operating characteristics and second, failure due to common-cause. Certain important results have been derived as particular cases. In the end, a numerical example has also been discussed.