BITS Faculty Publications
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Item Bayesian modeling of repairable systems with imperfect coverage and delayed detection dynamics(Wiley, 2025-02) Shekhar, ChandraIn this research article, we thoroughly examine the dynamics of a repairable system, emphasizing a two-unit configuration through a Bayesian perspective. The study integrates diverse prior distributions to model the uncertainty of unknown parameters, incorporating the coverage factor as a probabilistic measure of successful recovery from operational unit failures. The temporal characteristics of unit failure and repair are modeled using exponential distributions, ensuring analytical tractability and robustness. The repair process is bifurcated into two distinct phases: fault detection and location, followed by actual repair, with each phase governed by exponential distributions. Additionally, recovery and reboot times for failed units are also characterized by exponential distributions to maintain consistency in the probabilistic model. To address parameter uncertainty, we adopt a Bayesian methodology, enabling a comprehensive evaluation of system performance metrics. Monte Carlo simulations are employed to derive posterior distributions for critical parameters, including the mean time to system failure and steady-state availability, offering deeper insights into the system's reliability profile. To validate the efficacy of the proposed methodology, extensive numerical experiments are conducted, providing a robust confirmation of the analytical models and computational techniques.Item Reliability analysis of imperfect repair and switching failures: a bayesian inference and monte carlo simulation approach(Elsevier, 2025-06) Shekhar, ChandraReliability analysis of complex systems is essential to ensuring their dependable operation. This study examines a dual-active, single-standby storage unit system, which is integral to various industrial and technological applications. The research delves into the reliability metrics of this system, particularly addressing the challenges posed by unreliable repairs and standby switching failures. Bayesian inference, utilizing Gamma and Beta prior distributions along with Monte Carlo simulations, offers a robust methodology for estimating unknown parameters and deriving posterior distributions. The analysis assumes exponential distributions for both time-to-failure and time-to-repair, while time-to-inspection for perfect and imperfect rejuvenations also follows exponential distributions. The probability of unsuccessful standby switching, denoted as , is incorporated into the model. The results, presented through detailed tables and graphical representations, provide valuable insights into the system’s reliability and the effectiveness of the statistical methods employed.Item Modeling and Applications in Operations Research(Taylor & Francis, 2023) Shekhar, ChandraThe text envisages novel optimization methods that significantly impact real-life problems, starting from inventory control to economic decision-making. It discusses topics such as inventory control, queueing models, timetable scheduling, fuzzy optimization, and the Knapsack problem. The book’s content encompass the following key aspects: Presents a new model based on an unreliable server, wherein the convergence analysis is done using nature-inspired algorithms Discusses the optimization techniques used in transportation problems, timetable problems, and optimal/dynamic pricing in inventory control Highlights single and multi-objective optimization problems using pentagonal fuzzy numbers Illustrates profit maximization inventory model for non-instantaneous deteriorating items with imprecise costs Showcases nature-inspired algorithms such as particle swarm optimization, genetic algorithm, bat algorithm, and cuckoo search algorithm The text covers multi-disciplinary real-time problems such as fuzzy optimization of transportation problems, inventory control with dynamic pricing, timetable problem with ant colony optimization, knapsack problem, queueing modeling using the nature-inspired algorithm, and multi-objective fuzzy linear programming. It showcases a comparative analysis for studying various combinations of system design parameters and default cost elements. It will serve as an ideal reference text for graduate students and academic researchers in the fields of industrial engineering, manufacturing engineering, production engineering, mechanical engineering, and mathematics.Item Reliability analysis of standby provision multi-unit machining systems with varied failures, degradations, imperfections, and delays(Wiley, 2023-08) Shekhar, ChandraThis prospective study focuses on analyzing the reliability characteristics of multi-unit systems with standby provisioning, accounting for failures, degradation, random delays, and probabilistic imperfections. The investigation sheds light on how these unreliable attributes hinder the performance and availability of machining systems. Given the frequent occurrence of these negative attributes within machining systems, their impact on production flow, performance, and resource utilization is significant. Moreover, these unfavorable attributes hinder the adoption of advanced technologies that rely on the continuous availability of machining systems. Thorough research on operational traits serves as a foundation for developing solutions to enhance machining system efficiency and elucidates the underlying causes of machining system failures throughout their performance lifecycle. The reliability analysis employs a state-of-the-art queue-theoretic approach. In order to model the stochastic behavior of the investigated machine repair problem in a systematic manner, we consider various statistically independent failure modes, including active/standby unit failure, degraded failure, switching failure, and common-cause failure. The unreliable characteristics of machining systems are further compounded by factors such as imperfect fault coverage, reboot delay, and imperfect repair, necessitating a comprehensive examination to strategically implement preventive, corrective, and predictive measures. The seamless operation of multi-unit machining systems is essential for the successful integration of advanced technologies such as cloud computing, industry 4.0, and IoT. Failures, delays, degradation, and imperfections within machining systems have detrimental effects on their efficiency and availability, demanding in-depth investigation. To facilitate numerical experimentation and sensitivity analysis of the reliability aspects of the proposed machining system, we develop performance indices such as system reliability, mean-time-to-failure, and failure frequency. These metrics provide valuable insights for decision-makers seeking to implement measures that ensure uninterrupted availability of the machining system.Item Transient analysis of queueing-based congestion with differentiated vacations and customer’s impatience attributes(Springer, 2023-06) Shekhar, ChandraThis research article studies the critical issue of the single-server congestion problem with prominent customer impatience attributes and server strategic differentiated vacation. Despite their apparent practical relevance, the proposed congestion problem has yet to be studied from a service/production perspective with transient analysis. The queue-theoretic approach is used for mathematical modeling. The transient queue-size distribution has been derived using a modified Bessel function and generating function technique. A time-dependent solution is advantageous for queueing systems’ dynamic behavior over a planning phase and is predominantly valuable within the real-time design process for the state-of-the-art strategic system. The time-dependent explicit expression of variance and mean for the number of waiting customers in the system is also derived for quick statistical insights. Finally, numerical results are also exhibited to study the system’s behavior in depth.Item Congestion analysis of finite tandem queueing network(IEEE, 2023) Shekhar, ChandraThis paper introduces a focused model for analyzing congestion in finite tandem networks, a crucial aspect in queueing theory with far-reaching implications for system efficiency. By examining job flow through nodes, Node-1 and Node-2, it reveals intricate relationships between latent and processing times, exploring system dynamics. Incorporating Poisson arrivals, balking, and diverse processing mechanisms, the model encompasses both direct job progression and potential balking, offering a comprehensive view. Additionally, it accounts for waiting job processing, reneging, and Node-2's breakdown vulnerabilities and recovery. The model's independence of processes amplifies its depth. This analysis enriches our understanding of finite tandem queueing networks and their congestion intricacies. The model aids in optimal resource allocation and system design, enhancing congestion and delay management in practical settings like transportation and communication networks. It forms a foundation for informed operational strategies, bolstering customer satisfaction and resource utilization in complex service systemsItem Transformation-based stationary analysis of single server feedback fluid queue: an enhanced approach(IEEE, 2023) Shekhar, ChandraThe objective of this research article is to present innovative mathematical expressions that describe the steady-state distribution of buffer content within a fluid queue influenced by an M/M/1 queue with feedback. The resulting distribution is represented using modified Bessel functions, specifically, the second-kind Bessel function modifications. These modifications offer various advantageous properties and notably simplify the mathematical complexity involved in the analysis. This novel approach proves valuable for investigating dynamic queue systems, as it enhances the efficiency of generating stationary distribution data.Item Optimal management strategies of renewable energy systems with hyperexponential service provisioning: an economic investigation(Frontiers, 2023-12) Shekhar, ChandraThe current research proposes optimal management strategies for queueing modeling-based renewable energy systems with hyper-exponentially distributed maintenance/repair under the assumption of an admission control policy. Using the concept and steps of the matrix-analytical method, the steady-state probability distribution associated with energy systems is explicitly presented. A relatively straightforward computation that can help with modeling wind energy generation, investigating wind farm performance, optimizing energy based on system storage, reliability inspection, service maintenance planning, and numerous other purposes can be employed to mathematically derive several system performance indicators. The investigation findings are validated via quantitative outcomes, illustrative possesses, and a step-by-step recursive methodology for efficient management of the renewable energy system. Additionally, considering multiple governing parameter values, the nature-inspired optimization technique, Cuckoo Search (CS), is employed to demonstrate the optimum anticipated cost of renewable energy system. A comparison with other metaheuristics and semi-classical approaches is also presented to establish the best convergence results. In order to help system designers, policymakers, engineers, and researchers, several numerical examples are also provided to construct more practical strategies based on the production of energy, storage, and system management. The economic, parametric, and performance investigation findings are highlighted, and the opportunities and recommendations for further research are provided. In a nutshell, the outcomes of the present analysis can be adopted to formulate the most effective economic strategies and regulate decision-making processes in the energy sectorsItem Cost analysis of a finite capacity queue with server failures, balking, and threshold-driven recovery policy(IJMEMS, 2024-07) Shekhar, ChandraThe study is on the cost dynamics which is concerned with finite queues in particular to susceptibility to server outages, threshold-driven recovery and Catastrophic events, but main focus is on balking behaviour of the customers. A thorough investigation of the financial implications of interruptions and efficacy to recovery strategies is done and to alleviate the impact of breakdowns, disasters and customer refusals the queue system designs through empirical research is conducted. Various recovery policies have been compared with the existing thresholds, and the study further endeavors to categorize the cost-effective approach to mitigate the economic concerns of server failures and catastrophic incidents. The study brings discernments on the expected development in the management of the queuing system along with the assistance in complete decision-making in cost efficiency and enhancement of the complete system performance.Item Comparative and performance analyses of unreliable server queues(CRC Press, 2024) Shekhar, ChandraQueue-based scenarios with server breakdowns have become an exciting topic for queueing theorists, researchers, and practitioners in past decades. These queueing systems are generally used in many realistic waiting line models in our day-to-day life, such as computer and communication systems, production systems, transportation systems, flexible manufacturing systems, etc. Several scholars and researchers have worked on queueing systems with server breakdowns and provided significant results during the last few decades. Gaver [1] and Shogan [2] investigated queueing systems with server breakdowns and provided explicit expressions of several queuing-based system performance indicators. Jayaraman et al. [3] studied a bulk queueing system with state-dependent arrival rate and server breakdown. In 2004, Ke [4] discussed a bi-level control policy for the batch arrival queue with an early start-up and unreliable server. Later, Jain and Agrawal [5] considered an https://www.w3.org/1998/Math/MathML" display="inline"> M X / M /1 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003481263/3627ff2f-b685-486a-bdfb-379751e6ddcc/content/inline-math8_1.tif"/> queueing system with multiple breakdown states of the unreliable server under https://www.w3.org/1998/Math/MathML" display="inline"> N https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003481263/3627ff2f-b685-486a-bdfb-379751e6ddcc/content/inline-math8_2.tif"/> -policy. In the same year, Wang and Yang [6] investigated a controllable queueing system with an unreliable server. They illustrated many interesting numerical experiments for the optimal analysis using the semi-classical optimizer, the Quasi-Newton method. For more in-depth analysis, one can refer to the research findings in (cf. [7–15]) and references therein. Recently, Ke et al. [16] studied a feedback retrial queue with balking behavior of the customer and unreliable server and developed a cost optimization problem determining the optimal parameter setting under the stability condition using Probability Global Search Lausanne (PGSL) approach. A retrial queueing system with a finite number of sources and customers collision is discussed by Nazarov et al. [17]. They proved that the limiting probability distribution of the number of customers in the queueing system follows a Gaussian distribution.