Journal Vol – 19 No -1, January 2024  Journal &gt; Journal &gt; Journal Vol – 19 No -1, January 2024 RELIABILITY OPTIMIZATION OF A DEGRADED SYSTEM UNDER PREVENTIVE MAINTENANCE USING GENETIC ALGORITHM Authors: Shakuntla Singla, Diksha Mangla, Poonam Panwar, S Z Taj DOI NO: https://doi.org/10.26782/jmcms.2024.01.00001  admin January 20, 2024 Abstract:  The reliability parameters of a Mathematical model are analyzed for a system with three identical units and a standby. In this study, the primary unit is considered more important due to its high cost and working in two types of degraded conditions before a complete malfunction. Under the concept of preventive maintenance, the states of deterioration are reversed. The working of the system under two different efficiencies is discussed. The reliability of the Mathematical model, depending on the availability and working time, has been optimized using the Mathematical tool “Genetic Algorithm”. The optimum values of all parameters based on the exponential distribution are considered to optimize the reliability, and thus provide maximum benefits to the industry. Sensitivity analysis of the availability and the working time is carried out to understand the effects of changing parameters. Graphical and tabular analyses are presented to discuss the results and to draw conclusions about the system’s behavior. Keywords: deteriorated state,genetic algorithm,malfunction rate,preventive maintenance,regenerative point graphical technique,sensitivity analysis, Refference:  I. Bhunia, A.K. and Sahoo, L. (2011). Genetic algorithm based reliability optimization in interval environment. In: Nedjah, N., dos Santos Coelho, L., Mariani, V.C., de Macedo Mourelle, L. (eds) Innovative Computing Methods and Their Applications to Engineering Problems. Studies in Computational Intelligence, 357. Springer, Berlin, Heidelberg.  II. Kumar, J., Bansal, S.A., Mehta, M. and Singh, H. (2020). Reliability analysis in process industries – an overview. GIS Sci J., 7(5), 151-168. III. Kumari, K. and Poonia, M.S. (2023). Availability optimization of cylinder block in cast iron manufacturing plant using GA. European Chemical Bulletin, 12(4), 17784-17792.  IV. Kumari, S., Khurana, P. and Singla, S. (2022). Behaviour and profit analysis of a thresher plant under steady state. International Journal of System Assurance Engineering and Management, 13, 166-171.  V. Kumari, S., Singla, S. and Khurana, P. (2022). Particle swarm optimization for constrained cost reliability of rubber plant. Life Cycle Reliability and Safety Engineering, 11(3), 273-277.  VI. Malik, S., Verma, S., Gupta, A., Sharma, G. and Singla, S. (2022). Performability evaluation, validation and optimization for the steam generation system of a coal-fired thermal power plant. MethodsX, 9.  VII. Naithani, A., Khanduri, S. and Gupta, S. (2022). Stochastic analysis of main unit with two non-identical replaceable sub-units working with partial failure. International Journal of System Assurance Engineering and Management, 13, 1467-1473.  VIII. Naithani, A., Parashar, B., Bhatia, P.K. and Taneja G. (2013). Cost benefit analysis of a 2-out-of-3 induced draft fans system with priority for operation to cold standby over working at reduced capacity. Advanced Modelling and Optimization, 15(2), 499-509.  IX. Sachdeva, K., Taneja, G, and Manocha, A. (2022). Sensitivity and economic analysis of an insured system with extended conditional warranty. Reliability: Theory and Applications, 17, 24–31.  X. Singla, S. and Dhawan, P. (2022). Mathematical analysis of regenerative point graphical technique (RPGT). Mathematical Analysis and its Contemporary Applications, 4(4), 49-56.  XI. Taj, S. Z. and Rizwan, S. M. (2022). Reliability analysis of a 3-unit parallel system with single maintenance facility. Advanced Mathematical Models &amp; Applications, 7(1), 93-103. View Download  Journal Vol – 19 No -1, January 2024 CONSTRUCTION OF A SPLINE FUNCTION WITH MIXED NODE VALUES

The present paper deals with the lacunary interpolation problem called the mixed values problem or (0, 3; 0, 2) problem for which known data points are function values at all the points, third derivatives at even knots, and second derivatives at odd knots of the unit interval I = [0,1]. For this problem, we obtained an interpolating function. The paper is divided into two parts, where we have shown that the spline function exists and is convergent.