Single Repair Facility Research Articles

On Reliability of Repairable Hot Double Redundant System with Arbitrarily Distributed Life- and Repair Times of Its Elements

The article introduces the concept of Marked Markov processes, which are used to study a repairable hot double redundant system with a single repair facility. It is assumed that components’ life- and repair times follow arbitrary distributions. The proposed approach allows for calculating the system’s reliability function, and its mean lifetime, as well as conducting the sensitivity analysis to the shape of input distributions. The new method was validated with numerical examples by comparing it with previously obtained analytical results and showed high accuracy.

Stochastic Model on Three-Similar Units Three Phased Mission System with FCFS Repairs Pattern

The paper allocates a stochastic model on threesimilar units three-phased mission system. The developed system consists of units working in parallel, series and parallel configurations respectively. Initially, the three similar units are operational. Each component has only three states: good, degraded and failed. In this case, the single repair facility that repairs the units in first come first serve (FCFS)pattern has been thought of. Using Semi-Markov Process and regenerative point techniques, various measures of the system performance at each phase are obtained. The system has been analyzed graphically taking a particular case. Various conclusions are made regarding the reliability and cost consideration of the system at each phase as well as for the whole system(as combined Phase I, Phase II, Phase III).

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

AbstractThe reliability study of k-out-of-n systems is of interest both from theoretical and practical points of view. Applications of such models can be seen in many real-world phenomena, including telecommunication, transmission, transportation, manufacturing, and services. A probabilistic study of a real-world k-out-of-n system often helps to develop an optimal strategy for maintaining high system-level reliability. There are many investigations devoted to the reliability-centric analysis of such systems. We consider a mathematical model of a repairable k-out-of-n system that works until k of its n components have failed. During the system's life cycle, its components are repaired with the help of a single repair facility. It is supposed that the components' lifetimes have an exponential distribution and their repair times have a general distribution. The proposed model is intended to be applied to the description of operation of unmanned rotorcraft high-altitude platforms and to be validated with the help of an experimental prototype. For the considered system, we propose an algorithm for calculation of the reliability function, and for special cases, k = 2 and k = 3, its closed-form representation is given. A numerical investigation is performed for special cases. The obtained results are a first step toward the sensitivity analysis of reliability characteristics of k-out-of-n systems to the shape of the repair time distributions of their components.

Stochastic Modeling of a Single-Unit System Operating Under Different Environmental Conditions Subject to Inspection and Degradation

The main objective of the present study is to analyze a single-unit system under the concept of preventive maintenance, inspection, degradation and replacement. For this purpose, a stochastic model of single unit has been developed. The repair and preventive maintenance of the system are affected by abnormal environmental conditions, while replacement and operative original/degraded unit remain unaffected. The system does not remain as new after repair. A single repair facility is provided to the system as and when required for performing various repair activities. After, a pre-specific time ‘t’ repairman takes the unit under preventive maintenance. The system is inspected by the repairman upon failure to check the feasibility of repair and replacement. All failure and repair time distributions are arbitrarily distributed like Weibull distribution with common shape parameter and different scale parameters. Recurrence relation for various system-effective measures has been developed by using SMP and RPT. The numerical values for MTSF, availability and profit have been obtained for the interest of system designers.

Profit analysis of a computer system with preventive maintenance and priority subject to maximum operation and repair times

The aim of the present study is to carry out the profit analysis of a computer system by considering the concept of priority to preventive maintenance over different hardware and software repair activities. For this purpose, three stochastic models have been developed under different priority policies. A single repair facility is available to perform all repair activities. The hardware unit undergoes replacement after a pre-specific maximum repair time. The repairman performs the preventive maintenance of the whole system after a pre-fixed maximum operation time. All time-dependent failure rates follow exponential distribution, while the repair rates follow arbitrary distribution. Switch devices, repairs and preventive maintenance are perfect. All random variables are statistically independent. Semi-Markov process and regenerative point technique were used to derive the necessary system effectiveness measure to evaluate the profit function of all the three models. To highlight the importance of the study, graphs for profit difference between models have been depicted for a particular set of values of various parameters with respect to preventive maintenance.

Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems

ABSTRACTConsider a deteriorating repairable Markovian system with N stochastically independent identical units. The lifetime of each unit follows a discrete phase-type distribution. There is one online unit and the others are in standby status. In addition, there is a single repair facility and the repair time of a failed unit has a geometric distribution. The system is inspected at equally spaced points in time. After each inspection, either repair or a full replacement is possible. We consider state-dependent operating costs, repair costs that are dependent on the extent of the repair, and failure penalty costs. Applying dynamic programming, we show that under reasonable conditions on the system’s law of evolution and on the state-dependent costs, a generalized control-limit policy is optimal for the expected total discounted criterion for both cold standby and warm standby systems. Illustrative numerical examples are presented and insights are provided.

Useful Inequalities for Upper and Lower Bounds for the Repairable Aging Cold Standby System

In this paper, we study a cold standby repairable system consisting of two non-identical components and a single repair facility with one repairman. It is assumed that, one of the two components is operating while the other is in cold standby and also two components follow a geometric process. Under these assumptions, at first we present Laplace-Stieltjes transform of the system lifetime and then we give some useful inequalities about the mean lifetime of the system.

Performance Measures for a three-unit compact circuit

This paper analyses a three component system with single repair facility. Denoting the failure times of the components as T1 and T2 and the repair time as R, the joint survival function of (T1, T2, R) is assumed to be that of trivariate distribution of Marshall and Olkin. Here, R is an exponential variable with parameter α and T1 and T2 are independent of each other. In this paper use of Laplace-Transform is taken for finding Mean Time Between Failure, Availability and Mean Down Time and table for Reliability measure is shown in the end.

Stochastic Analysis of Dis-Similar Standby System with Discrete Failure, Inspection and Replacement Policy

AbstractThe device named autoclave used in pharma industries has been studied in this paper. This study provides the discussion how to obtain the reliability testing strategy of two dis-similar parallel units. The system is considered to be in operative condition if at least one out of two is in operative state. A single repair facility is available for repairing both kinds of failed units. In addition to repair mechanism, inspection policy has also been introduced for failed automatic unit. But the manual one does not require any such supervision facilty. Various essential measures of system effectiveness such as mean time to system failure (MTSF), steady state availability, busy period of supervisor and repairman are examined probabilistically by using geometric distribution and regenerative point techniques. A graph has been plotted to represent the behaviour of profit function and MTSF with respect to different failure and repair rate.

Analysis of a Single-Unit System with Weibull Failure and Repair densities Subject to Server Failure

The main concentration in the present paper is to analyze a single- unit system using the concepts of inspection, degradation, preventive maintenance, and server failure. A single repair facility inspect the original and degraded unit upon failure to check the feasibility of repair. The repair facility may fail during maintenance, repair and inspection and undergoes for treatment with Weibull probability density function. The unit after repair becomes degraded. Switch devices are perfect. All random variables like repair time, failure time, inspection time and treatment rate are independent and statistically independent. For the analysis of the system various measures of system effectiveness are obtained by using semi-Markov processes and regenerative point technique. With the help of numerical and graphical results for MTSF, availability and profit functions it is concluded that present system is more reliable, available and profitable, when random variables have less vale of shape parameters. Keywords: System, Availability, Inspection, Degradation and Preventive Maintenance

Analysis of a redundant system with priority and Weibull distribution for failure and repair

The main objective of the present study is to analyse a redundant system under the concept of priority and Weibull distribution for all random variables with different scale parameter and common shape parameter. For this purpose, by using semi-Markovian approach and regenerative point technique a reliability model is developed for a two non-identical unit system. A single repair facility is provided to the system to perform all repair activities. After a pre-specified time to enhance the performance and efficiency of the system the unit goes for preventive maintenance (PM). Priority to the repair of original unit is given over the PM of duplicate unit. Numerical results for the mean time of system failure, availability and profit function have been derived for a particular case to highlight the importance of the study.

MTSF (mean time to system failure) and profit analysis of a single-unit system with inspection for feasibility of repair beyond warranty

This paper discussed the MTSF and profit analysis of a single-unit system with inspection for feasibility of repair beyond warranty subject to a single repair facility. Any failure during warranty is rectified by the manufacturer free of cost to the users provided failures are not due to the negligence of users. Beyond warranty, unit goes under inspection after failure for feasibility of its repair or replacement. The failure time of the system follows negative exponential distribution while repair and inspection time distributions are taken as arbitrary. The expressions for reliability, MTSF, availability of the system and profit function have been determined by using supplementary variable technique. Using Abel’s lemma steady state behavior of the system has been derived. The numerical results for reliability and profit function are also obtained by taking particular values of various parameters and repair cost.

Performance Analysis of a Computer System with Imperfect Fault Detection of Hardware

The purpose of the present work is to evaluate the functioning of a computer system using the concepts of imperfect fault detection of hardware parts and up-gradation of software upon their failure. A stochastic model for a data processor system consisting of two identical units- one is operative and the other kept as a standby is developed. A single repair facility is supplied to the system which plays the double function of the sensor as well as a maintenance man. Upon failure of the detector to detect the fracture of the hardware component unit immediately replaced by the maintenance man. Nonetheless, only up-gradation of the software is made upon failure. All time distribution except failures follows an arbitrary distribution while failures are exponentially dispersed. The expressions for several reliability measures are derived by making use of semi-Markov processes and regenerative point of technique. Numerical results are drawn from a particular case to highlight the importance of the study.

Reliability Measures of a Two-Unit Cold Standby Repairable System with Priority to Operation over Preventive Maintenance

main objective of present work is to carry out various important reliability measures of a twounit cold s tandby repairable system with priority to operation over preventive maintenance by using regenerative points technique and semiMarkov process. A single repair facility is pr ovided to conduct repair and maintenance of the system as and when required. All times distributions are exponential except the repair and preventive maintenance time distributions which are considered as general.

A Stochastic System with Possible Maintenance of Standby Unit and Replacement of the Failed Unit Subject to Inspection

this paper, a stochastic system of two identical units has been investigated by conducting possible maintenance of the cold standby unit before getting it into operation. A single repair facility is provided immediately to rectify the faults which occur during system operation. The inspection of the failed unit is done to see the feasibility of its repair. If repair of the unit is not feasible to the system, it is replaced immediately by new one. The random variables are statistically independent. The time to failure of the unit follows negative exponential distribution while the distributions for maintenance, inspection and repair times are taken as arbitrary with different probability density functions. The maintenance and repair of the unit are perfect. The semi- Markov process and regeneration point technique are used to derive the expressions for some reliability measures of vital significance. The graphical behavior of MTSF, Availability and profit function have been observed for particular values of different parameters and costs.

English

In this paper a two unit standby system with single repair facility has been considered. When a working unit fails, it is immediately taken over by standby unit and repair on the failed unit is started immediately. Taking two types of distribution, namely, Weibull and Erlangian, various system effectiveness measures such as MTSF, Availability and Busy Periods are compared and results are interpreted numerically. Regenerative Point Technique and Semi-Markov process have been employed in this paper to find the results. Results are supported with numerical data also. Failure time distributions are taken to be exponential whereas the repair times are particular. The result obtained from this can be applied to study complex system where small change in the value of one variable affects the system measures to a great extent.   Key words: MTSF, availability, busy period, regenerative point technique, Semi-Markov process.

Reliability Analysis of a Single-Unit System with Inspection Subject to Different Weather Conditions

The purpose of this paper is to develop and analyze a reliability model of a single-unit system considering two weather conditions-normal and abnormal. The unit may fail completely either directly from normal mode or via partial failure. A single repair facility is available who plays the dual role of inspection and repair. The server first inspects the totally failed unit to see the feasibility of its repair. If repair of the unit is not feasible, it is replaced by new one. Server conducts the repair only on totally failed unit. The operation, inspection and repair of the unit are stopped in abnormal weather as a precautionary measure to avoid excessive damage to the system. Failure rates and rate of change of weather conditions are constant whereas the inspection and repair rates are general. By using semi-Markov process and regenerative point technique some reliability measures of system effectiveness are obtained. Graphs of MTSF, availability and profit for a particular case are drawn to highlight the importance of the study.

Availability analysis of repairable redundant system with three types of failures subject to common cause failure

This paper deals with the availability analysis of a redundant system consisting of N-non-identical components and S warm standby components under the care of single repair facility. The system may fail due to three reasons: 1) human error such as wrong adjustments in the design or development phase of the system or system may undergo damage during maintenance; 2) hardware failure; and 3) software failure. The incorporation of common cause failure gives the major impact on the system performance since it may cause dependant failures of some or all components of the system. An irreducible Markov process is used to construct the system of governing differential equations associated with three types of failure subject to common cause failure. The system availability for different configurations under transient condition is examined by using a numerical approach based on Runge-Kutta method of fourth order. Further, the sensitivity analysis is facilitated to demonstrate the validity of analytical results by taking a numerical illustration. The effect of different parameters on system performance indices are demonstrated graphically.

Reliability Modeling and Cost-Analysis of a System with Replacement of the server and Unit subject to Inspection

In this paper, a single-unit system is probed stochastically in detail considering the ideas of replacement of the server and unit subject to inspection. The unit may fail completely either directly from normal mode or via partial failure. A single repair facility (called server) is provided immediately to the system for conducting inspection and repair of the unit at different failure modes. If inspection reveals that repair of the unit at its partial and complete failure is not feasible, it is replaced by new one. The server is also subjected to failure while performing jobs. An expert person (may be a medical Doctor) is called to give treatment to the failed server. If server is not curable by treatment, he is replaced by another server to resume the remaining jobs. The failure time of the unit and server are distributed exponentially while the distributions of inspection and repair times of the unit as well as inspection and treatment time of the server are taken as arbitrary with different probability density functions. To carry out cost analysis, the expressions for some reliability and economic measures are derived using semi-Markov process and regenerative point technique. The numerical results for a particular case are also obtained to depict the graphical behavior of MTSF, availability and profit function with respect to treatment rate.

Availability of a k-out-of-N:F System with Generally Distributed Repair Time and Preventive Maintenance

This paper investigates the behaviour of a system composed of N independent unit subject to failure. A single repair facility is available to attend to the failed unit. At a random time interval the system is overhauled and put back in operation as a new. The method of the supplementary variable is used to set the equations describing the reliability. Induction is further used to obtain a closed solution.