Department of Mathematics

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End date: 2019Subject: search.filters.subject.Machine repair

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Now showing 1 - 8 of 8
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    Reliability Analysis of Redundant Repairable System with Degraded Failure
    (MERC, 2004) Kulshrestha, Rakhee
    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.
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    Bilevel control of degraded machining system with warm standbys, setup and vacation
    (Elsevier, 2004-12) Kulshrestha, Rakhee
    In this paper, we study (N, L) switch-over policy for machine repair model with warm standbys and two repairmen. The repairman (R1) turns on for repair only when N-failed units are accumulated and starts repair after a set up time which is assumed to be exponentially distributed. As soon as the system becomes empty, the repairman (R1) leaves for a vacation and returns back when he finds the number of failed units in the system greater than or equal to a threshold value N. Second repairman (R2) turns on when there are L(>N) failed units in the system and goes for a vacation if there are less than L failed units. The life time and repair time of failed units are assumed to be exponentially distributed. The steady state queue size distribution is obtained by using recursive method. Expressions for the average number of failed units in the queue and the average waiting time are established.
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    Queueing analysis of two unreliable servers machining system with switching and common cause failure
    (Inder Science, 2013) Shekhar, Chandra
    In this paper, we analyse the performance of primary and secondary unreliable servers in a multi-component machining system. For the smooth functioning of the system, there is a provision of warm spares that may not be perfect in switching the failed operating unit. Primary server is prone to complete or partial breakdown whereas secondary server faces only complete breakdown independently or simultaneously due to common cause. The life time and repair time of the operating units, breakdown and the repair time of the servers are exponentially distributed. Various performance indices are formulated to study the behaviour of the queueing model of concerned machining system developed more significantly. By taking an illustration, the sensitivity analysis is carried out. The numerical results are summarised in tabular form and also depicted via graphs.
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    Markov model for switching failure of warm spares in machine repair system
    (River Publication, 2014) Shekhar, Chandra
    In this investigation, we study the performance characteristics of (m,M) machining systems having warm spares and two heterogeneous servers. The first server is permanent and available full time in the system, whereas the second server takes vacation according to the specific threshold policy. In some real time systems, spares may or may not replace/switch in the system whenever an operating unit failure occurs, as such switching failure has been incorporated. In this paper, we consider a two dimensional continuous time finite state space Markov chain. The steady state queue size distribution for the Markovian machine repair problem, considering switching failure, is obtained computationally using matrix method based on successiveover relaxation. We derive various system characteristics namely, expected number of failed machines in the system, throughput of the system, probability that the server is on vacation, etc. In order to gain maximum net profit, a cost function is constructed in terms of different cost elements to determine the optimal threshold level for the server vacation. For illustration purpose, numerical results are provided. In order to examine the effects of system parameters, the sensitivity analysis has also been facilitated
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    Vacation queuing model for a machining system with two unreliable repairmen
    (Inder Science, 2014-07) Shekhar, Chandra
    This investigation is concerned with multi-component machining system having two types of warm standby units and two unreliable heterogeneous repairmen. The life time and repair time of the failed units are exponentially distributed. The first repairman is working according to N (N ≥ 1) policy whereas the second repairman has the privilege of going for a vacation of random length. Both repairmen may also fail while rendering the repair to the failed units either individually or simultaneously. Runge-Kutta method is used to obtain the transient-state probabilities of the system states for which Chapman-Kolmogrov differential equations governing the model are constructed. We have established some indices for the system performance in terms of transient probabilities. The sensitivity analysis is carried out to examine the system efficiency and profitability as per requirements. The numerical results are provided in order to explore the sensitivity of the system descriptors on the performance measures more precisely.
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    A time-shared machine repair problem with mixed spares under N-policy
    (Springer, 2016-02) Shekhar, Chandra
    The present investigation deals with a machine repair problem consisting of cold and warm standby machines. The machines are subject to breakdown and are repaired by the permanent repairman operating under N-policy. There is provision of one additional removable repairman who is called upon when the work load of failed machines crosses a certain threshold level and is removed as soon as the work load again ceases to that level. Both repairmen recover the failed machines by following the time sharing concept which means that the repairmen share their repair job simultaneously among all the failed machines that have joined the system for repair. Markovian model has been developed by considering the queue dependent rates and solved analytically using the recursive technique. Various performance indices are derived which are further used to obtain the cost function. By taking illustration, numerical simulation and sensitivity analysis have been provided.
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    Queueing Analysis of Machine Repair Problem with Controlled Rates and Working Vacation Under F-Policy
    (Springer, 2015-12) Shekhar, Chandra
    This paper deals with the queueing characterization of a machine repair problem with single working vacation and controlled arrival of failed machines under F-policy. The server allows the failed machines to enter the system till full capacity K and thereafter the arrival of the failed machines is prohibited which continues till the queue length is reduced to the threshold value F. The server takes some time to start the repair of the failed machines. The life time of the machines, startup time and repair time of the server are exponentially distributed. When the system is empty, the server goes for a single vacation but it keeps on serving the failed units even during vacation at a different pace, and is said to be on working vacation. The matrix method has been used to obtain the steady state probabilities of the system states. Various performance characteristics have been derived. The numerical results have been obtained and shown in tables and graphs.
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    Transient analysis of machining system with spare provisioning and geometric reneging
    (Inder Science, 2017) Shekhar, Chandra
    In this investigation, we deal with the transient analysis of repairable machining system having multi identical online and warm standby machines. There is facility of repair of failed machines rendered by an unreliable server who is prone to failure and follows the threshold policy in rendering the service and being repaired. The failed machines waiting in the queue may renege and opt sequentially whether to leave the queue or remain in the queue in geometric fashion at the epochs of availability of secondary server. By constructing the transient differential difference equations, the probabilities associated with the system states are determined using the numerical method based on Runge-Kutta method. Various queueing and reliability indices viz. expected number of failed machines in the system, throughput, reliability, mean time to failure, failure frequency, etc., are established and numerically computed by taking illustration. The sensitivity analysis and numerical simulation are performed for exploring the effects of parameters on some performance measures.