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 multi-unit cold standby system with two operating modes

This paper investigates the mathematical model of a system composed of n dissimilar units—one functioning and others either failed or cold standbys. Each unit of the system has three possible modes—normal, partial failure and total failure. There is a perfect switch to operate the leading standby unit on total failure of the operative unit. The failure and repair times of each unit are assumed to follow arbitrary distributions. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are derived as particular cases.     

Reliability of a system with warm standbys and repairmen

This paper studies the reliability characteristics of a system with M operating machines, S warm standby spares and R repairmen in the repair facility. Failure times and repair times are assumed to be exponentially distributed. The k out of M+S system is analyzed where k = 1, 2, …, M, and numerical results are provided.     

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 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.     

Comparison of two unit cold standby reliability models with three types of repair facilities

This paper develops three models for cold standby redundant systems, consisting of two identical units. These models are different in the sense that different types of repairmen are employed. In model 1, the repairman is always with the system. In model 2, he comes immediately at the failure of a unit, while in model 3, he takes some random time in reaching the system.Profit is evaluated in each case. Comparison of these profits is done in two parts. Part 1 considers the comparison of different models. In part 2 comparison is done by taking different criteria for evaluating the profit for the same model. Computer programs for these comparisons are also given (in the Appendix).     

Profit analysis of the machine repair problem with cold standbys and two modes of failure

In this paper we deal with the cold-standby machine repair problem where machines have two failure modes under steady-state conditions. The two failure modes have equal probability of repair. Failure time of the machines and repair time of the repairmen are assumed to follow a negative exponential distribution. The failed machines are served by R repairment according to first-come, first served discipline. Profit model is developed in order to determine the optimal values of the number of cold standbys and the number of repairmen simultaneously, while maintaining a minimum specified level of system availability. Numerical results are presented in which several system characteristics are calculated under optimal operating conditions.     

Reliability system with two types of repair facilities

This paper deals with two identical unit cold stand-by systems. Two types of repair facilities, having a considerable difference in their costs, are used to repair the units. Repair of type 2 facility, a costlier one, is always available, while for repair of type 1 facility one has to wait for some time. If this waiting time exceeds some given maximum time, one has to call costly repair i.e. repair of type 2 facility.The system has been analysed to determine the reliability measures viz. MTSF, steady state availability, expected number of repairs etc., by using theory of semi-Markov processes and regenerative processes. Integral equations are set up for deriving these measures. These equations are solved with the help of Laplace transform technique. A cost equation is derived. The condition for maximizing the profit is also derived. Certain particular cases are analysed.     

Stochastic analysis of a repairable system with three units and two repair facilities

This paper investigates the availability characteristics and the reliability of a three-dissimilar-unit repairable system with two different repair facilities. Under some practical assumptions, we obtain the explicit expressions of the state probabilities of the system and then the explicit expressions of the following performance measures of the system: (1) the pointwise and steady-state availability; (2) the pointwise and steady-state failure frequency; (3) the pointwise and steady-state renewal frequency; and (4) the reliability and the mean time to system failure.     

Reliability analysis of a series-parallel system under different repair disciplines

In this paper we investigate a system composed of two subsystems connected in series with a single repair facility. One subsystem is K-out-of-N:G, while the other consist of several different units connected in series. The method of the supplementary variable in two models differing by the repair discipline is used to obtain the availability of the system. By making suitable transformation the reliability and the mean time to system failure (MTSF) can be deduced from the availability function.     

Reliability analysis of a system with preventive maintenance, inspection and two types of repair

This paper considers a two-unit (identical) parallel system with facilities of preventive maintenance, inspection and two types of repair, type I and type II. These two types of repair facilities have a considerable difference in their costs. Both the units of the system can fail simultaneously due to some common-cause or they can fail one by one. The time of failure of a unit and system, the commencement of maintenance and inspection are assumed to be constant while repair and maintenance times are arbitrarily distributed. Various measures of system effectiveness are evaluated using regenerative point technique.     

Reliability of systems with two failure modes by using structure functions

This paper deals a three-state (normal, short-mode and open-mode failures) device network that is required to control the quantity of s-t flow. If the control policy is to pass the flow or to shut off the flow, i.e. the amount of s-t flow equals one, this network system is a conventional three-state system. In order to obtain the reliability of the network system, we propose a new structure function. Some examples are presented to show that using the structure function simplifies the reliability calculation.     

On a two-dissimilar-unit standby system with three modes and administrative delay in repair

This paper considers a two-dissimilar-unit cold standby redundant system with three modes of each unit under the assumption that there is an administrative delay in getting the repair man at the system location. The system is analyzed by the semi-Markov process technique, assuming that the failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Further, special cases of the results of this paper coincide with earlier results obtained by Pandey and by Gupta.     

Stochastic analysis of a deteriorating standby system with three modes and inspection

A two-unit (identical) deteriorating standby system is analysed. Each unit can be in one of the three modes—normal, partial failure and total failure. A unit can fail totally but not partially during its standby state. Standby is inspected at random epochs. Using regenerative point technique in Markovrenewal process theory, several reliability characteristics of interest to system designers and operation managers are obtained.     

A two unit priority redundant system with three modes and correlated failures and repairs

This paper considers a two dissimilar units priority redundant system with three modes. One of the units has a priority operative mode and the other has a priority repair mode. Assuming that the joint distribution of failure and repair times is exponentially bivariate, some reliability characteristics useful to system managers have been obtained. Results for a system with two similar units are obtained as a particular case.     

Cost analysis of a two unit, three state standby redundant complex system with two types of repair facilities under waiting

This paper deals with the cost analysis of a two unit, three state standby redundant complex system, incorporating the concept of two types of repair facilities, viz. minor and major repair. The concept of waiting time for the major repair of the failed system has also been introduced. The system can suffer from two types of failures, namely catastrophic and partial. Failure and waiting times of units follow exponential time distribution, whereas repair of units follows general time distribution. Using the supplementary variable technique, Laplace transforms of probabilities of the complex system being in various states have been computed. In addition, using Abel's lemma, steady state behaviour has also been examined. Some important graphs have been sketched at the end to highlight the important results.     

Performance analysis of cellular networks with mobile relays under different modes

With the popularity of smart phones and tablets, people make intensive use of these devices on public transport. The deployment of mobile relays on public transport may increase the quality of mobile services.The objective of this paper is to study the performance of cellular networks when mobile relays are deployed in public transport vehicles. We consider two modes: in the FDD mobile relay mode, the same spectrum is reused for all links while in the TDD/FDD hybrid mode, a small part of the spectrum is dedicated to the access link between the terminals inside a transport vehicle and the mobile relay. We provide a general analytical model for the two mobile relay modes by using the stochastic geometry approach. Key metrics like the CDF of the SINR and the CDF of the end-to-end rate are computed. Furthermore, the cell total average rate and the energy efficiency in different modes are evaluated. It has been found that penetration loss is a factor that determines how much gain mobile relay can bring. Numerical results show that when the ratio of vehicular UEs in the cell is 0.4 and the penetration loss is 20 dB, the FDD mobile relay mode and the TDD/FDD hybrid mobile relay mode can achieve \(+16.3, +29.1\%\) cell rate gain respectively compared with the direct mode.     

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.     

Availability analysis of systems with two types of repair facilities

This paper presents two mathematical models of repairable systems. Failed systems repair times are arbitrarily distributed. Two types of repair facilities are needed to repair a failed system. Laplace transforms of the state probability equations are developed.     

不同驱动方式下网络控制系统的建模与分析

控制回路通过实时网络闭环而成的反馈控制系统称为网络控制系统.文中介绍了时间驱动和事件驱动的异同,建立了节点在不同驱动方式下网络控制系统的数学模型.由分析可知在设计网络控制系统时要对传感器、控制器、执行器选择合适的触发方式.