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One of the common approaches to improve systems reliability is using standby redundancy. Although many works are available in the literature on the applications of standby redundancy, the system components are assumed to be independent of each other. But, in reality, the system components can be dependent on one another, causing the failure of each component to affect the failure rate of the remaining active components. In this paper, a standby two-unit system is considered, assuming a dependency between the switch and its associated active component.

This paper assumes that the failures between the switch and its associated active component follow the Marshall–Olkin exponential bivariate exponential distribution. Then, the reliability analysis of the system is done using the continuous-time Markov chain method.

The derived equations application to determine the system steady-state availability, system reliability and sensitivity analysis on the mean time to failure is demonstrated using a numerical illustration.

All previous models assumed independency between the switch and the associated active unit in the standby redundancy approach. In this paper, the switch and its associated component are assumed to be dependent on each other.

The main objective of this paper is to study the optimal system for series systems with mixed standby (including cold standby, warm standby and hot standby) components.

The paper deals with the reliability and availability characteristics of four different series system configurations. The failure time of the operative, hot standby and warm standby are assumed to be exponentially distributed with parameters λ, λ, and α respectively. The repair time distribution of each server is also exponentially distributed with parameter μ.

The mean time to failure, MTTF_i, and the steady‐state availability A_i(∞) for four configurations are examined and comparisons made. For all four configurations, the configurations are ranked based on: MTTF_i, A_i(∞), and C_i/B_i where B_i is either MTTF_i or A_i(∞). Obviously, the system with height MTTF_i and A_i(∞), do not need frequent maintenance, i.e. less maintenance.

Numerical results for the cost/benefit measure have been obtained for all configurations. It is interesting to note first that the optimal configuration using the cost/MTTF_i measure is configuration 4. Next the optimal configuration using the cost/A_i(∞) measure is configuration 2.

Presents the analysis of a two‐unit cold standby system in which the standby unit takes a random amount of time for operation whenever the operative unit fails. Each unit is first repaired by the assistant repairman and is then taken up for post‐repair if necessary. The failure and repair times of each unit are assumed to be correlated and their joint density is taken as bivariate exponential. Uses regenerative point technique to obtain various reliability characteristics of interest. Studies the behaviour of steady‐state availability through graphs. Verifies earlier results.

In this paper one considers a model representing a two‐unit identical system with one unit operating online, and the other unit in warm standby. The online unit is controlled by a protective unit which protects the online unit from any damage occurring. The online and protective units may fail due either to a hardware failure or to a shock failure. The failure and repair rates for the online, standby and protective units are constant but different. Expressions for the time‐dependent availability, steady‐state availability, reliability, mean time to failure and profit function are obtained by the Laplace transform technique. Finally graphs are also drawn for the above model to illustrate the various characteristics obtained. Some applications of the model are also given.

Profit analysis of a two non‐identical unit cold standby system model with mutual changeover of the units is carried out in this paper. With mutual changeover of the unit, the operating unit, after functioning for some random amount of time, becomes standby to take rest, and the standby unit becomes operative. The failure and repair times of each unit are jointly distributed as bivariate exponential (BVE) with different parameters. Various measures of system effectiveness useful to system engineers and designers are obtained by using the regenerative point technique. Behaviour of the mean time to system failure (MTSF) and availability have also been studied graphically.

The present paper analyzed a model consisting of one unit with a warm standby unit where the main unit has three states: up, degraded and down.

The semi-Markov model under the regenerative method is used to construct the mathematical model for the system.

The effectiveness measures of the system are discussed such as availability, reliability, steady-state availability and mean time to system failure. The life and repair times of the system units are assumed to be discrete follow discrete Weibull distribution. Also, the parameters of the discrete Weibull distribution are assumed to be fuzzy with bell-shaped membership function. An application is introduced to show the results obtained for the system and the profit of the presented model.

Rarely papers in literature treated the topic of the discrete-time semi-Markov process using a regenerative point technique.

Investigates a stochastic model of a two identical unit cold standby system. Assumes that, if repair of the failed unit is not completed within a specified time, then an order is placed to replace the failed unit by the new one. The specified time is also known as the maximum repair time limit which may change from user to user of the system, so that it is assumed as a random variable. Joint distribution of failure and repair times is bivariate exponential whereas the distributions of lead time (difference between order and delivery time for a new unit) and replacement time of the new unit are negative exponential. Obtains various reliability characteristics of the system under study by using regenerative point technique. Also studied characteristics through graphs.

Presents two models. Model I deals with some characteristics of a single unit system with a sensing device and two types of repairmen. The unit is attached to a sensing device which completely monitors the operating or non‐operating status of the unit. The regular repairman is always available with the system and inspects the operation of the sensing device. If the device is not working, then an expert repairman is called to the system and the operational status of the unit is now monitored by the expert repairman. It is assumed that the failure of the unit, repair of the regular, expert and the status of the sensing device are stochastically independent random variables each having an arbitrary distribution. Several important results have been derived including profit with some applications. In model II, a two‐unit cold standby system with pre‐inspection is considered. In this model, first the regular repairman inspects every unit that fails to ascertain whether he is able to repair it or not. If he can repair it, he proceeds; otherwise an expert repairman is called. An analytical approach to find the optimum interchanging time of units by giving rest to the operative unit is obtained.

The purpose of this paper is to evaluate the performance of paper mill plant, which is a very key factor in improving its production. A number of safety challenges can be successfully fixed for a paper mill to continue to make further improvements in reliability, safety and economics. Many incidents in the paper mill plants are frequently caused by human error and equipment failure. Many of the incidents are generally based on poor managerial strategies. These types of errors could have been prevented if safety instructions had been correctly followed and supported in the maintenance system.

A paper mill plant mainly consists four sections namely the head box, wire part, press part and dryer. All these four parts are connected in series configuration. The authors have developed a mathematical model for the plant in which power supply is in standby mode. The designed system can fail in five ways, i.e. by the failure of head box failure, wire part failure, press part failure, dryer failure and power (electricity) failure. So to make proper functioning of paper machine and no interruption in power supply, the authors have considered that power supply is in standby mode.

Using the supplementary variable technique, the Laplace transformations and Markov process theory, the reliability indices of the paper mill plant model are determined.

In the present paper, the authors have developed a mathematical model based on a paper plant machine.

Studies the cost‐benefit analysis of a complex system consisting of two subsystems for example, A and B, connected in series. Subsystem A is composed of two identical units while subsystem B has only one unit. The system functions if one of the two units of subsystem A and the subsystem B are operative. Assuming a bivariate exponential density for the joint distribution of failure and repair times of the units, obtains various reliability characteristics useful to system managers. Also draws explicit results for the case when failure and repair times are independent.