Department of Mathematics

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    Fuzzy analysis of machine repair problem with switching failure and reboot
    (River Publication, 2014) Shekhar, Chandra
    Multi-component machining systems are being used in every sphere of engineering sector such as job shops, flow lines, communication system, computer system, etc. This paper presents fuzzy analysis of availability characteristics of machining system comprising of multi- active units and multi-standby units. The Markov machine repair model has been developed by incorporating the concepts of switching failure and reboot. The life times of identical active units and identical standby units follow the fuzzified exponential distribution. The time-to-repair of failed unit is also governed by the fuzzified exponential distribution. The automatic switching of standby unit to replace the failed units may not be perfect in many realistic scenarios as we assume the switching failure probability. The system may reboot itself automatically if the active unit fails and available standby unit is not able to replace the failed unit perfectly. We employ the parametric non-linear program with -cut approach to establish the membership function of availability of the system and availability of both standbys. A numerical example is also provided to validate the suggested approach which facilitates more useful information for the designers and practitioners to examine general repairable system more accurately
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    N-policy for a multi-component machining system with imperfect coverage, reboot and unreliable server
    (Taylor & Francis, 2014-06) Shekhar, Chandra
    This investigation aims at predicting the transient performance measures of a machining system comprising of M operating units and multi types of warm standbys under the care of a single unreliable server. To deal with more realistic situations, the concepts of imperfect recovery and reboot delay are also incorporated. The queue size distribution is obtained by using the matrix method. The explicit expressions for various performance measures such as reliability, throughput, expected number of failed units in the system, failure frequency of the server, etc. are obtained. A numerical illustration is presented to demonstrate the practical application of the proposed model in the flexible manufacturing systems.
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    Transient analysis of computing system with reboot and recovery delay
    (Emerald, 2020-04) Shekhar, Chandra
    The purpose of this paper is to present a sensitivity analysis of fault-tolerant redundant repairable computing systems with imperfect coverage, reboot, and recovery process.
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    Fault-tolerant redundant repairable system with different failures and delays
    (Emerald, 2020-04) Shekhar, Chandra
    The internet of things and just-in-time are the embryonic model of innovation for the state-of-the-art design of the service system. This paper aims to develop a fault-tolerant machining system with active and standby redundancy. The availability of the fault-tolerant redundant repairable system is a key concern in the successful deployment of the service system.
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    Load sharing redundant repairable systems with switching and reboot delay
    (Elsevier, 2020-01) Shekhar, Chandra
    Industry 4.0 depicts the fourth industrial revolution which prompts an insightful, associated and decentralized manufacturing. The prime viewpoint is an uninterrupted linkage between decision-makers, machines, and products during the manufacturing process empowered by the digital framework. The prime objective is to analyze the optimal design of fault-tolerant machining system with various types of machining hindrance. In this article, we investigate fault-tolerant redundant repairable machining system which is an indispensable part of computer and communication systems, manufacturing and production systems, security systems, etc. Besides the random failure of operating units and standby units, probabilistic common cause failure of the machining system, an automatic switch of the available standby unit in place of a failed operating unit with a significant switching lag is a key concern in the present study with unpredictable switching failure and reboot delay. The workload is shared in general with M operating units but continues in short mode as overload until there are at least units in the system with the degradable failure rate. Numerical simulation, comparative analyses and optimal analyses of queue characteristics are also performed significantly and the conclusion is drawn for system designers and decision-makers to develop state-of-the-art maintenance and repair policies.
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    M/G/1 fault-tolerant machining system with imperfection
    (JIMO, 2021) Shekhar, Chandra
    The internet of things (IoT) is an emerging archetype of technology for the guaranteed quality of services (QoS). The availability of the uninterrupted power supply (UPS) is one of the most challenging criteria in the successful implementation of the service system of IoT. In this paper, we consider a fault-tolerant power generation system of finite operating machines along with warm standby machine provisioning. The time-to-failure for each of the operating and standby machines are assumed to be exponentially distributed. The time-to-repair by the single service facility for the failed machine follows the arbitrary distribution. For modeling purpose, we have also incorporated realistic machining behaviors like imperfect coverage of the failure of machines, switching failure of standby machine, reboot delay, switch over delay, etc. For the evaluation of the explicit expression for steady-state probabilities of the system, the only required input is the Laplace-Stieltjes transform (LST) of the repair time distribution. The step-wise recursive procedure, illustrative examples, and numerical results have been presented for the following different type of repair time distribution: exponential (), -stage Erlang (), deterministic (), uniform (), -stage generalized Erlang () and hyperexponential (). Concluding remarks and future scopes have also been included.