Two-unit Cold Standby System Research Articles

Cost-Benefit Analysis of a Two-Unit Cold Standby System with Imperfect Repair Man and Abnormal Weather Conditions

Cost-Benefit Analysis of a Two-Unit Cold Standby System with Imperfect Repair Man and Abnormal Weather Conditions

Optimal switching and condition-based maintenance of cold standby systems subject to competitive failure and imperfect switchover

Cold standby redundant structures can improve system reliability and availability but are subjected to internal degradation and external shocks during operation. Thus, the switching process in a standby system is prone to failures. This study investigates the optimal switching and condition-based maintenance (CBM) decision of a two-unit cold standby system subject to mutually dependent competitive failure processes with an imperfect switchover. First, periodic switching and offline CBM policies under imperfect switchover are proposed; second, the reliability models of competitive failure—between soft failure caused by system degradation subject to nonfatal shock and hard failure caused by fatal shock—are established. An iterative model of the system state probability distribution is subsequently derived by analysing the characteristics of state transitions in alternate use and maintenance of the active and standby units. An analytical decision model is also established to minimise the average cost rate in a finite horizon to obtain the optimal switching period and maintenance threshold. Finally, a case study of a coal mine main ventilator system validates the proposed model.

Novel Analysis between Two-Unit Hot and Cold Standby Redundant Systems with Varied Demand

Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: Model 1 (a two-unit cold standby system) and Model 2 (a two-unit hot standby system). In Model 1, the standby unit needs to be activated before it may begin to function; in Model 2, the standby unit is always operational unless it fails. The current study demonstrates that the hot standby system is more expensive than the cold standby system under two circumstances: a decrease in demand or the hot standby unit’s failure rate exceeding a predetermined threshold. The cold standby system’s activation time is at most a certain threshold, and turning both units on at once is necessary to handle the increasing demand. In that case, the hot standby will be more expensive than the cold standby system. The authors used semi-Markov and regenerative point techniques to analyze both models. They collected actual data from a cable manufacturing plant to illustrate the findings. Plotting several graphs and obtaining cut-off points make it easier to choose the standby to employ.

Reliability of the two-unit priority standby system revisited

This paper deals with reliability assessment of the repairable two-unit cold standby system when the first, main unit has the better performance level than the second one. Therefore, after its repair, the main unit is always switched into operation. The new Laplace transform representation for the system’s lifetime is obtained for arbitrary operation and repair time distributions of the units. For some particular cases, the Laplace transform of the system is shown to be rational, which enables the use of the matrix-exponential distributions for obtaining relevant reliability indices. The discrete setup of the model is also considered through the corresponding matrix-geometric distributions, which are the discrete analogs of the matrix-exponential 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.

Effectiveness Analysis of a Two Non-Identical Unit Standby System with Switching Device and Proviso of Rest

This paper deals with two-unit cold standby system with switching device and proviso of rest. The system consists of two non-identical units which are connected in parallel redundancy. Initially, the first unit is in operative mode and second is kept in cold standby mode. There is also a proviso for rest for the first unit after a random time from its starting operation. For operation and repair, priority is always given to first unit. A switching device is used to shift the failed unit to repair mode. If the switching device is found non-operational then priority is given to it for repair provided that system is in functional mode. The effectiveness of the proposed system has been carried out by determining various reliability characteristics of the proposed model.

Profit analysis of a two-unit cold standby system model operating under different weather conditions

Generally, each machine or products are used by the human being up to its maximum capacity. If a system is performing beyond its capacity/defined conditions by the manufacturer called, the system is working under abnormal weather conditions. While, a system is performing within its capacities/stated conditions set by manufacturer called as the system working in abnormal weather conditions, for example; a car is functioning exceeding its accommodating capacity can be termed as working under abnormal weather conditions; a hydraulic machine exceeding its weight uplifting capacity of 500 tons by lifting 600 tons is termed as working under abnormal weather conditions. To overcome in such a situation, only effective maintenance strategies and suitable structure design of redundant system are the crucial factors which keep the standby system operational without failures for longer period of time. In fact, proper functioning of service mechanism and the reliability of system are strongly associated with each other. In the present paper, a water supply system simulate that is functioning of two-unit cold standby system with facilities of preventive maintenance, inspection and repair operating under different weather conditions with priority to preventive maintenance over inspection. The units are identical in nature. The single server only works under normal weather conditions capable of performing three operations inspection, repair and preventive maintenance responds to system instantly. The replacement of units is suggested if repair is impossible to perform during inspection. The operative unit undergoes for preventive maintenance after a specific time of operation. Repair of the unit is done by the server at its complete failure. All random variables are statistically independent. It is assumed that the failure rate and rate by which system undergoes for preventive maintenance are constant whereas the inspection rate, repair rate and maintenance rate follows negative exponential distribution. The expressions/graphs for several reliability measures are derived/depicted in steady state using regenerative point technique and semi-Markov process to determine the nature of the system.

The establishment of the time interval between inspections for a cold standby system with component repair

Abstract The time interval between inspections of cold standby systems is a crucial decision to ensure the appropriated system reliability and the lowest costs possible. This paper presents a model developed to establish the optimal time interval between inspections for a two-unit cold standby system with component repair and subject to periodic inspection, considering reliability and costs. A Markov chain is used to define possible states, their transition probabilities and the mean time to system failure, as a function of the time interval between inspections. Given the mean time to system failure, the steady state availability is determined. Finally, the costs related to the system maintenance are established and a cost function is developed and optimized for the time interval between inspections. Numerical examples are presented and results for different system parameters are compared. Besides optimizing the time interval between inspections, the analyses also reveal the effect of repair time on system availability and mean time to system failure.

Availability and profit analysis of a two-unit cold standby system for general distribution

AbstractThis paper discussed a two-unit cold standby system by considering the concepts of degradation, inspection, preventive maintenance (PM), and priority. The unit works as a reduced capacity after its repair and is called degraded unit. There is a single repairman who visits the system immediately. The repairman inspects the failed degraded unit to see the feasibility of repair. If the repair of the degraded unit is not possible, it is replaced by new unit. PM will provide to the system when both the units are degraded and available for use. Priority for operation and repair is provided to new unit over-degraded unit. Various reliability characteristics such as mean time to system failure (MTSF), availability, busy period of the repairman, expected number of visits by the repairman, and profit of the system have been obtained using regenerative point graphical technique. For particular case, the results for MTSF, availability, and profit function are obtained considering exponential, Rayleigh, and We...

Comparative study between a single unit system and a two-unit cold standby system with varying demand.

The concerned paper illustrates the comparison of two stochastic models of a cable manufacturing plant with varying demand. Here, it shows the comparison between a single unit system (Model 1) and a two-unit cold standby system (Model 2). In Model 1, the system is either in working state on some demand or put to shut down mode on no demand. In Model 2, at initial stage, one of the units is operative while the other is kept as cold standby. At times when the operative unit stops working due to some breakdown/failure, the standby unit instantaneously becomes operative while the repairman repairs the failed unit. In this working model, only one unit remains operative at a time. However, there may be a state when both the units fail. The comparison of systems is done by means of MTSF (mean time to system failure), steady state availability and profit function using Laplace transforms and software package Code-Blocks 13.12. Different graphs have been plotted to discover which model is superior to the other model under the given conditions. The system is analysed by making use of semi-Markov processes and regenerative point technique.

Cost Analysis of a Two-Unit Cold Standby System Considering Hardware, Software Failures and Inspection with Maximum Repair Time

The present paper deals with a reliability model of a two unit cold standby system that exposed to two types of failures. In each unit there are hardware and software componentes work together and fail independently. there is a single server who visits the system immediately when required. The server inspects the unit in case of software failure and decides either to repair or replace it. The h/w components undergo for repair at their failure and are replaced by new one in case of arriving to maximum repair time. All time distributions are considered to be exponential. Various measures of reliability of the system are obtained using regenerative point technique. Finally simulation study is done to illustrate the results.

Profit Analysis of a Two-Unit Cold Standby System with Delayed Repair of Partially Failed Unit and Better Utilization of Units

paper presents the profit analysis of a two unit cold standby system with delayed repair of partially failed unit and better utilization of units. It is assumed that the system stops functioning only when both the units fail. The failure time distributions and delayed time distribution of each unit are assumed to be negative exponential with different parameters whereas the repair time distributions are taken to general. Formulas for various reliability indices of the system including availability, busy period analysis of the repairman, and profit function analysis by using the regenerative point technique are derived. General Terms Redundancy; Standby system; Stochastic; Failure and Repair times; Correlation.

Stochastic Analysis of a Two-Unit Cold Standby System with Arbitrary Distributions for Life, Repair and Waiting Times

Stochastic Analysis of a Two-Unit Cold Standby System with Arbitrary Distributions for Life, Repair and Waiting Times

Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

The present paper analyzes a two-unit cold standby system wherein both units may become operative depending upon the demand. Initially, one of the units is operative while the other is kept as cold standby. If the operative unit fails or the demand increases to the extent that one operative unit is not capable of meeting the demand, the standby unit becomes operative instantaneously. Thus, both units may become operative simultaneously to meet the increased demand. Availability in three types of upstates is as follows: (i) when the demand is less than or equal to production manufactured by one unit; (ii) when the demand is greater than whatever produced by one unit but less than or equal to production made by two units; and (iii) when the demand is greater than the produces by two units. Other measures of the system effectiveness have also been obtained in general case as well as for a particular case. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of the system effectiveness.

English

Present paper investigates a two-unit cold standby system with three accidental effects. On the failure of a unit, a repairman comes to repair it. During its repair, an accident may take place which may or may not affect the repairman. If it affects, it may be minor or major. Two models have been discussed. In Model 1, it is assumed that when the repairman gets minor injury with an accident, he goes for treatment/rest for some time. After recovery, he comes back and resumes the repair. If major injury takes place, another repairman is called to complete the repair. In Model 2, it is assumed that whenever minor or major accident takes place, another repairman is called. In both the models, it is assumed that after accident the rest of the repair is done with more attention so that no further accident takes place. Various measures of the system effectiveness are obtained by making use of semi-Markov processes and regenerative point technique. Study through graphs is also made.

RELIABILITY MEASURES OF A COLD STANDBY SYSTEM WITH PREVENTIVE MAINTENANCE AND REPAIR

The purpose of the present study is to determine reliability measures of a two-unit cold standby system with preventive maintenance and repair. The units are identical in nature subject to constant failure from normal mode. Preventive maintenance of the operative unit is carried out after a pre-specific time "t" up to which no failure occurs. However, repair of the unit is done at its failure. The unit works as new after repair and preventive maintenance. The switch devices are perfect. The distributions of failure time and the time by which unit undergoes for preventive maintenance are taken as negative exponential while that of preventive maintenance and repair times are assumed as arbitrary with different probability density functions. The random variables associated with failure, preventive maintenance and repair times are statistically independent. The semi-Markov process and regenerative point technique are adopted to derive the expressions for system performance measures in steady state. The graphical behavior of MTSF, availability and profit function have been observed with respect to preventive maintenance rate for particular values of other parameters and costs.

Stochastic analysis of a two-unit cold standby system with two-stage repair and waiting time

In this study we investigated the cost-benefit analysis of a two-unit cold standby system with two-stage repair of a failed unit. We discuss the concept of waiting time with two-stage repair for a two-unit cold standby system. The repair process is divided into two stages. In the first stage, the repairing process of the unit is started but it does not get completed; instead the process is completed in the second stage. The elapsed time between two stages is called the waiting time. Techniques of regenerative point processes have been used to measure the effectiveness. The time dependent availability, steady state availability, reliability, (MTTF) and profit function were obtained numercially and graphically. The MTTF, the steady-state availability and the profit function decreased with respect to the increase of failure rate and waiting rate.

On a two-unit cold standby system considering hardware, human error failures and preventive maintenance

This paper deals with the study of the stochastic analysis of a two-unit cold standby system considering hardware failure, human error failure and preventive maintenance (PM). All time distributions are considered to be arbitrary. Various measures of reliability of the system are obtained using the regenerative point technique. All these measures are also derived based on time t 0 . (Practically PM can be performed after time t 0 from the beginning of the system operation.) Finally a simulation study is carried out to illustrate the result.

Asymptotics for solutions of a defective renewal equation with applications

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.