Unit Cold Standby Research Articles

A two Identical Unit Cold Standby System with two Repairmen and Correlated Failure and Repair Times

The paper deals with the stochastic analysis of a two identical unit cold standby system model. As soon as a unit fails it is attended first by assistant repairman, who completes its repair to make it as good as new with fixed known probability p. Otherwise, with probability q( =1-p), the unit repaired by assistant repairman goes to expert repairman so as to make it as good as new. Both the repairmen are always available with the system and they work their jobs simultaneously. The failure time and repair time by assistant repairman are correlated random variables having their joint distribution as Bivariate exponential. Various measures of system effectiveness useful to system designers and operation managers are obtained by using regenerative point technique. The MTSF and steady state profit have also been studied through graphs in respect of parameter alpha for three different values of repair rate by expert repairman and two different values of correlation coefficient between failure and repair times and important conclusions are drawn.. KEYWORDS :Bivariate exponential distribution, Mean time to system failure (MTSF), Regenerative point, Laplace transform.

Exploring the synergistic effects of warm and cold standby units in availability modelling and assessment of complex series-parallel systems

Exploring the synergistic effects of warm and cold standby units in availability modelling and assessment of complex series-parallel systems

Bayesian Study of a Continuous Parametric Markov Chain Model of a Three Identical Unit Cold Standby System with Random Shocks

Bayesian Study of a Continuous Parametric Markov Chain Model of a Three Identical Unit Cold Standby System with Random Shocks

Mean residual lifetime assessment approach for a multi-state standby system

In this paper, a new MRL assessment approach for a multi-state standby system is considered. The three-state system is backed up with a binary cold standby unit. Given that the system is at a specific state at time t, obtaining the MRL is worth considering in conducting the maintenance and repair plans of the system. For different degradation rates and time points, MRL results are examined. An HCTMP is considered for the degradation. Therefore, when the system is observed to be at its perfect state, the MRL decrease with an increase in all the failure rates of the system. However, when the system is observed to be at its partial state, the MRL is not affected by the increase in the failure rate pertained to the perfect state. The MRL when the system has known to be failed before time t and backed up with the standby unit increases with the time increase whereas the MRL when the system is at its perfect(or partial) state is constant when time increases. Moreover, cost evaluation of the system is analyzed. The results are supported with numerical examples and graphical representations.

Exploring the Synergistic Effects of Warm and Cold Standby Units in Availability Modeling and Assessment of Complex Series-Parallel Systems

Exploring the Synergistic Effects of Warm and Cold Standby Units in Availability Modeling and Assessment of Complex Series-Parallel Systems

Comparative analysis between serial systems with cold standby units

Comparative analysis between serial systems with cold standby units

Classical and Bayesian inference procedures of a three unit cold standby system with dependent structure

Two unit cold standby systems have been exhaustively dealt with in the past. Nevertheless, the study of standby systems with three or more units, though relevant in the current situation has not received much attention because of mathematical nuances involved in analyzing them. Further, such systems have been studied under the assumption that (i) the lifetime or repair time of the units to be exponential or (ii) the lifetime and repair time of the units are independent. The present contribution is an improvement in the state-of-the-art in the sense that three unit cold standby system with dependent structure is shown to be capable of exhaustive analysis, both from classical and Bayesian inference perspectives.

Some inferences on reliability measures of two-non-identical units cold standby system waiting for repair

Some inferences on reliability measures of two-non-identical units cold standby system waiting for repair

Reliability Analysis of Cold Standby Parallel System Possessing Failure and Repair Rate Under Geometric Distribution

Background and Aim: With an increase in demands about the reliability of industrial machines following continuous or discrete distribution, the important thing to be noticed is that in all previous research works where systems had more than one failure, no iteration technique was studied to separate the failed unit on the basis of its failure. Therefore, the aim of our paper is to analyze the real industrial problems following cold standby units arranged in parallel manner with the new concept of inspection procedure for failed units to detect the exact failure and being the communicator to the repairman for repairing the exact failed part of the unit for saving time and maintenance cost. Methods: The geometric distribution and regenerative techniques were applied for calculating different reliability measures like mean time to system failure, availability of a system, inspection, repair and the time of unit failure. Results: Graphical and analytical analyses were also conducted to analyze the increasing/decreasing behavior of profit function w.r.t repair and failure rate. The system responded properly in fulfilling the basic needs. Conclusion: The calculated value of all reliability parameters proved helpful for studying any other models following the same concept under different environmental conditions. Thus, it can be concluded that, reliability increases with an increase in the repair and decreases with an increase in the failure rate. Also, the results evaluated in this paper provide the better reliability testing strategies that help develop new techniques which lead to increase the effectiveness of the system.

A Fast and Accurate Reliability Approximation Method for Heterogeneous Cold Standby Sparing Systems

Cold standby sparing is a widely-used fault-tolerant technique where spare units are unpowered and non-operational before being activated to replace a malfunctioned on-line unit. The dynamic failure rate behavior of cold standby units poses unique challenges to the reliability analysis of cold standby systems (CSSs). The existing reliability analysis methods developed for CSSs have various limitations, such as being applicable to only the exponential component time-to-failure distribution, CSSs with identical components, and small-scale systems due to high computational complexity. In this paper, we advance the state of the art by proposing a fast and accurate reliability approximation method based on the Lyapunov central limit theorem for heterogeneous 1-out-of-n cold standby systems with non-identical components. The Lyapunov's conditions are proved for CSSs with exponential, Weibull, normal, and mixed component time-to-failure distributions. The accuracy and efficiency of the proposed method are verified and compared with the existing methods through comprehensive case studies on CSSs with different sizes and different types of distributions. The results show that the proposed method can estimate the reliability of large-scale CSSs efficiently and accurately.

Stochastic Analysis of a Three-Unit Non-Identical Repairable System with Simultaneous Working of Cold Standby Units

Here, stochastic analysis of a repairable system of three units has been carried out by taking one unit in operation (called main unit) and two identical units (called duplicate units) in cold standby. The switch device is used to convert the standby units into operative mode. A single server is hired to handle repair activities of the units who visits the system instantly whenever needed. The repair done by the server is perfect and thus the repaired unit follows the same lifetime distribution as the original. The constant failure rates are considered for both main and the duplicate units while their repair time distributions are taken as arbitrary. Some important reliability measures including mean sojourn times (MST), transition probabilities (TP), mean time to system failure (MTSF), availability, expected number of repairs for both kinds of units separately, expected number of visits by the server and busy period analysis of the server due to repair are determined using semi-Markov process (SMP) and regenerative point technique (RPT). The arbitrary values of the parameters are considered to examine the behaviour of some significant reliability measures through graphs. The possible application of the system model can be visualized in a power supply system of a house where a set of solar panels are kept in spare for their simultaneously working when main power supply is discontinued.

Analysis of Two Non-Identical Unit Cold Standby System in Presence of Prior Information

Characteristics of a two non-identical unit system with a cold standby facility are studied from Bayesian point of view with different type of priors assumed for unknown parameters. Time to failure and time to repair of the operating units are assumed to follow Lindley distribution. Several measures of system effectiveness, such as reliability, MTSF, steady state availability, expected profit etc. are obtained by using regenerative point technique. At the end, a numerical illustration is also carried out, for validation of the proposed system model.

Reliability properties of [formula omitted]-out-of-[formula omitted] systems with one cold standby unit

In this paper, we study reliability properties of a k-out-of-n system with a single cold standby unit. We mainly focus on the case when the system operates in discrete time. In order to describe its aging behavior we consider three different mean residual life functions. By using some properties of order statistics we present several monotonicity results associated with these reliability characteristics. Since the calculation of the described quantities requires finding sums of infinite series, we provide a procedure to approximate them with an error not greater than a desired value. As an illustration we consider three special cases when the component lifetimes have geometric, negative binomial and discrete Weibull distributions.

Reliability modeling of two-unit cold standby systems: A periodic switching approach

In the present paper, we use the concept of virtual age to propose a periodic switching policy for assessing the reliability of a two-unit cold standby system. This approach is suitable for units that recover with discontinuous activity and get younger. To restore the units and bring back the state of the system to a desirable condition, the active unit and cold standby unit are periodically replaced with each other at some given time interval. The survival function of the system under the periodic switching policy is derived in terms of the baseline time-to-failure distribution. The results indicate that, when the units have an increasing failure rate, the new switching policy improves the performance of the units which, in turn, increases the reliability of the system. Since the switching is not always failure-free, we derive also the survival function of the system in the case of imperfect switching. By considering the cost of switching and the system profit, we investigate the optimal length of the time interval for switching the active unit with the standby unit such that the mean profit of the system is maximized. To examine the theoretical results, we present some illustrative examples. Finally, we use a Monte-Carlo simulation to evaluate the system reliability.

Reliability analysis of a two-unit cold standby system with arbitrary distributions and change in units

The objective of this paper is to improve systems’ reliability by the change between units of the industrial systems at random times. In this paper, we deal with the study of the industry system consisting of two dissimilar units; one of them is the active unit while the other unit is a cold standby unit. After a random amount of time $$ \tau_{0} $$ from the starting of the system operation, the cold standby unit replaces the active unit and the active unit is converted to a cold standby. All-time distributions are considered to be arbitrary. Various measures of the reliability of the system are obtained using the regenerative point technique. All these measures are also derived based on time $$ \tau_{0} $$ . Finally, a simulation study is obtained to explain the result.

Comparative Analysis between Serial Systems with Cold Standby Units

Comparative Analysis between Serial Systems with Cold Standby Units

ReliabilityMeasures of a Two Unit Model in Cold Standby Mode with Expert Repairman

In this paper,the profit of a two unit cold standby system have been analysed.We have taken a two unit cold standby system having an expert repairman and his assistance.When a unit failed then standby unit becomes operating unit and his assistance repairman can repair the failed unit after getting the instruction from the expert. When the expert is busy in repairing the failed unit and also at that time standby unit failed then he leave the repair in the suspension and give instruction to his assistance.The profit rate is calculated where the failure follow exponential distributions. Graphs are plotted with the help of data given in terms of reliability parameters such as availability,MTSF,busyperiod,expected no. of repairman visits using regenerative point of graphical technique.

Stochastic behavior of dissimilar units cold standby system waiting for repair

Investigation of the time behavior of repairable systems spans a very large class of stochastic processes. The repetition of the same events connects the theory of reliability with Markov and semi-Markov processes. Exploiting this theory, the present study deals with two repairable dissimilar units’ cold standby system waiting for repair facility after failure of system units. Also, the regenerative point technique has been employed to obtain various reliability measures for the assumed system. Next, a particular case with exponential failures, arbitrary waiting and arbitrary repair rate is simulated followed by conclusions in the last section.

Effectiveness Analysis of Two Unit Cold Standby System with Fault Detection, Inspection and Priority

Effectiveness Analysis of Two Unit Cold Standby System with Fault Detection, Inspection and Priority

English

English