Evaluation of some reliability characteristics of a system under three types of failure with repair -replacement at failure (original) (raw)
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American Journal of Operational Research, 2013
In this paper, we studied a series system consisting of single unit. The system is subjected to three types of failures. Type I failure is minor in which the system is imperfect ly repaired. Type II failure is majo r in which the entire system is replaced. Type III failure is called a partial failure in wh ich the system works in reduced capacity and is perfectly repaired. Failure and repair t ime are assumed exponential. We developed the explicit exp ressions for mean time to system failure (MTSF), steady-state availability, busy period and profit function using Kolmogorov forward equations method. Special cases are studied to determine the impact of various system parameters on MTSF, busy period, steady-state availability and profit function.
Open Journal of Applied Sciences, 2013
In this paper, we study the reliability and availability characteristics of a repairable system consisting of two subsystems A and B in series. Subsystem A consists of two units A 1 and A 2 operating in active parallel while subsystem B is a single unit. Failure and repair times are assumed exponential. The explicit expressions of reliability and availability characteristics like mean time to system failure (MTSF), system availability, busy period and profit function are derived using Kolmogorov forward equations method. Various cases are analyzed graphically to investigate the impacts of system parameters on MTSF, availability, busy period and profit function.
In this paper, we studied a system consisting of two subsystems A and B. Subsystem A has two units A 1 and A 2 in warm standby, subsystem B is a single unit. Failure and repair time are assumed exponential. We developed the explicit expressions for mean time to system failure (MTSF), steady-state availability, busy period and profit function using Kolmogorov's forward equations method. Special cases are studied to determine the impact of various system parameters on MTSF, steady-state availability and profit function.
American Journal of Computational and Applied Mathematics, 2012
This paper deal with the stochastic modeling of system comprising two subsystems A and B in series. Subsystem A consists three active parallel units. Failure time and repair time are assumed exponential. We developed explicit exp ressions for mean time to system failure (MTSF), system availability, busy period and profit function using kolmogorov's forward equations method and perform graphical analysis to see the behavior of failure rates and repair rates on measures of system effect iveness such MTSF, system availability and profit function.
Journal of Mathematics and Statistics, 2005
Many authors have studied the effectiveness of a redundant system under two or three types of failure under the assumption that such failures are repairable. Little attention is paid on whether such repair act ion can restore the system operating condition to as good as new (perfect repair) and the effect of such perfect repair on the system performance. In this study, various measures of system effect iveness such as mean time to system failu re (MTSF), steady state availability, busy period and profit function of a 2-out-of-3 repairable system with perfect repair are analy zed using Kolmogorov's forward equation method. Some particular cases have been discussed graphically. The results have indicated that perfect repair action plays a v ital ro le on system performance. Simu lations results show that perfect repair is important part icularly in increasing mean time to system failure, availability and system performance as a whole.
Applied Mathematics, 2013
In this paper, we study the reliability and availability characteristics of a repairable 2-out-of-3 system. Failure and repair times are assumed exponential. The explicit expressions of reliability and availability characteristics such as mean time to system failure (MTSF), steady-state availability, busy period and profit function are derived using Kolmogorov's forward equations method. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF, availability, busy period and profit function.
Estimation of Reliability Parameters of a Complex Repairable System
In this paper estimation of reliability parameters of a complex repairable system is considered and semi-markov process is used in analyzing various reliability parameters such as Transition Probabilities, Mean sojourn times, MTSF, Availability and Busy period of repairman in repairing the failed units. In the past, Arora et-al[2] has done reliability analysis of two unit standby redundant system with constrained repair time. Gupta et-al [6] has worked on a compound redundant system involving human failure. Rander et-al [2] has evaluated the cost analysis of two dissimilar cold standby systems with preventive maintenance and replacement of standby units. A pioneer work in this field was done by Gopalan [1] and Osaki [3] by performing analysis of warm standby system and parallel system with bivariate exponential life respectively. Earlier, Pathak et al [7&8] studied reliability parameters of a main unit with its supporting units and also compared the results with two different distributions. In this paper, Chapman-Kolmogorov equations are used to develop recursive relations. Also the involvement of preventive maintenance in the model increases the reliability of the functioning units. In the end a particular case is also taken for discussion. System Description about the model: The system consists of three units namely one main unit A and two associate units B & C. Here the associate unit B and C dependents upon main units A and the system is operable when the main unit and at least one associate unit is in operable. Main unit are employed to rotate B and C. As soon as a job arrives, all the units work with load. It is assumed that only one job is taken for processing at a time. There is a single repairman who repairs the failed units on first come first served basis. Using regenerative point technique several system characteristics such as transition probabilities, mean sojourn times, availability and busy period of the repairman are evaluated. In the end the expected profit is also calculated. Assumptions used in the model: a. The system consists of one main unit and two associate units. b. The associate unit A and B works with the help of main units. c. There is a single repairman which repairs the failed units on priority basis. d. After random period of time the whole system goes to preventive maintenance. e. All units work as new after repair. f. The failure rates of all the units are taken to be exponential whereas the repair time distributions are arbitrary. g. Switching devices are perfect and instantaneous.
International Journal of Trend in Scientific Research and Development
This paper proposes the study of modelling and analysis of a two unit parallel system. A constant failure rate is considered for the units which are identical in nature. All repair activities like repair, replacement, preventive maintenance are mended immediately by a single server. The repair of the unit is done after its failure and if the fault is not rectified by the server within a given repair time, called maximum repair time, the unit replaced by new one. And, if there is no fault occurs up to a pre operation time, called maximum operation time, the unit undergoes for the preventive maintenance. The unit works as new after all repair activities done by the server. Priority to repair of one unit is given over the replacement of the other one. All random variables are statistically independent. The distribution for the failure, preventive maintenance and replacement rates are negative exponential whereas the distribution for all repair activities are taken as arbitrary with different probability density functions. Semi-Markov and regenerative point techniques are used to derive some reliability measures in steady state. The variation of MTSF, availability and profit function has been observed graphically for various parameters and costs.
Reliability Analysis of Redundant Repairable System with Degraded Failure
International Journal of Engineering- …, 2004
This investigation deals with the transient analysis of the machine repair system consisting of M-operating units operating under the care of single repairman. To improve the system reliability/availability, Y warm standby and S cold standby units are provided to replace the failed units. In case when all spares are being used, the failure of units occurs in degraded fashion. In such situation there is a facility of one additional repairman to speed up the repair. The lifetime and repair time of units are exponentially distributed. We use matrix method to solve the governing Chapman-Kolmogorov equations. Expressions for the system reliability, availability, mean time to system failure, etc. are established in terms of transient probability. Computational scheme is discussed to facilitate the numerical results. Sensitivity analysis is also carried out to depict the effect of various parameters on the system reliability.
2004): Reliability Analysis of redundant repairable system with degraded failure
2016
This investigation deals with the transient analysis of the machine repair system consisting of M-operating units operating under the care of single repairman. To improve the system reliability/availability, Y warm standby and S cold standby units are provided to replace the failed units. In case when all spares are being used, the failure of units occurs in degraded fashion. In such situation there is a facility of one additional repairman to speed up the repair. The lifetime and repair time of units are exponentially distributed. We use matrix method to solve the governing Chapman-Kolmogorov equations. Expressions for the system reliability, availability, mean time to system failure, etc. are established in terms of transient probability. Computational scheme is discussed to facilitate the numerical results. Sensitivity analysis is also carried out to depict the effect of various parameters on the system reliability.