Authors:
Parveen Kumar,Gulshan Taneja,Anil Kumar Taneja,DOI NO:
https://doi.org/10.26782/jmcms.2025.05.00007Keywords:
Cold Standby unit(s),Comparative Analysis,Major/Minor failure,Operative unit,Regenerative Point Technique,Abstract
A system with a single functional unit and one or two cold standby units is studied by developing two Models. In one of the two models, there is a provision for one cold standby unit, whereas in the other, the provision is for two cold standby units. The operative unit, whenever it fails, may either fail due to a major fault or a minor fault, which is revealed by carrying out an inspection. When the operative unit fails, the cold standby becomes operational with an activation time between the operative unit failing and the standby operating state. Reliability and profit analysis have been carried out for both two models. A comparative study has also been made between the two models to decide whether one or two cold standby units should be used for such a system, as far as the profitability aspect is concerned. The models have been examined using the regenerating point method.Refference:
I. A. Kumar, S. Baweja: ‘Cost-benefit analysis of a cold standby system with preventive maintenance subject to the arrival time of the server’. Int J Agriculture Stat Sci, Vol 11, No. 2, (2015), pp 375–380. https://connectjournals.com/file_full_text/2414202H_375-380.pdf
II. A. Manocha, and G. Taneja: ‘Stochastic analysis of a two-unit cold standby system with arbitrary distribution for life, repair, and waiting times’. International Journal of Performability Engineering, Vol11,No.3,(2015),pp293-299. 10.23940/ijpe.15.3.p293.mag
III. A. Roy, and N. Gupta: ‘A study on the utilization of a cold standby component to enhance the mean residual life function of a coherent system’. Communications in Statistics-Theory and Methods, Vol 53,No.19,(2024),pp6977-6996. 10.1080/03610926.2023.2255323
IV. K. Murari, and V. Goyal: ‘Reliability of a system with two types of repair facilities’. Microelectronic Reliability, Vol 23, (1983), pp 1015–1025. 10.1016/0026-2714(85)90400-7
V. L.R. Goel, A. Kumar, and A.K. Rastogi: ‘Stochastic behavior of man-machine systems operating under different weather conditions’. Microelectronic Reliability, Vol 25, (1985), pp 87–91. 10.1016/0026-2714(85)90447-0
VI. M.A.W. Mahmoud, and M.E. Mosherf: ‘On a two-unit cold standby system considering hardware, human error failures, and preventive maintenance’. Mathematical and Computer Modeling, Vol 5, No. (5-6),(2010),pp736-745. 10.1016/j.mcm.2009.10.019
VII. M.S. EL-Sherbeny, M.A.W. Mahmoud, & Z.M. Hussien: ‘Reliability analysis of a two-unit cold standby system with arbitrary distributions and change in units’. Life Cycle Reliable Safe Eng, Vol 9, (2020), pp 261–272. 10.1007/s41872-020-00127-y
VIII. L. Munda, G. Taneja, K. Sachdeva: ‘Reliability and economic analysis of a system comprising three units, i.e., operative, hot standby, and warm standby’. Journal of Mechanics of Continua and Mathematical Sciences Vol 20, No.-1, January (2025), pp 17 – 33. 10.26782/jmcms.2025.01.00002
IX. P. Kumar, & A. Sirohi: ‘Profit analysis of a two-unit cold standby system with the delayed repair of the partially failed unit and better utilization of units’. International Journal of Computer Applications, Vol 117, No. 1, (2015), pp 41-46. 10.5120/20522-2633
X. P.K. Tyagi, and K. Agarwal: ‘Cost-benefit analysis of a two-unit cold standby system with correlated failures and repairs and inspection time’. International Journal of Engineering, Management & Technology (IJEMT), Volume 1, No 5, (2022), pp 9-16. 10.1108/13552519710161544
XI. Parveen, D. Singh, A.K. Taneja: ‘Redundancy Optimization of N+1-Unit Cold Standby System Working with a Single Operative Unit with Activation Time’. International Journal of Engineering Trends and Technology, Vol 71, No. 8, August (2023), pp 458-466. 10.14445/22315381/IJETT-V71I8P239
XII. Parveen, D. Singh, A.K. Taneja: ‘Redundancy Optimization for a System Comprising One Operative Unit and N Warm Standby Units with Switching Time’. International Journal of Agricultural & Statistical Sciences, Vol 19, (2023), pp 1339-1350. 10.59467/IJASS.2023.19.1339
XIII. Parveen, D. Singh, A.K. Taneja: ‘Redundancy Optimization for a System Comprising One Operative Unit and N Hot Standby Units’.Reliability: Theory & Applications, Vol 18, No. 4, (2023), pp 547-562. https://www.gnedenko.net/Journal/2023/042023/RTA_4_2023-46.pdf
XIV. R. Singh and R. K. Bhardwaj: ‘Steady-state performance of a cold standby system with conditional server replacement’. Journal of Statistics Applications & Probability, Vol 3, (2021), pp 759-766. 10.18576/jsap/100314
XV. S. Batra and G. Taneja: ‘Reliability and Optimum Analysis for Number of Standby Units in a System Working with One Operative Unit’. International Journal of Applied Engineering Research, Vol 13, No.5, (2018),pp2791-2797. https://www.ripublication.com/ijaer18/ijaerv13n5_93.pdf
XVI. S. Batra, and G. Taneja: ‘Optimization of the Number of Hot Standby Units through Reliability Models for a System Operative with One Unit’. International Journal of Agricultural and Statistical Sciences, Vol 14, No. 1, (2018), pp 365-370. https://connectjournals.com/file_html_pdf/2838401H_365-370a.pdf
XVII. S. Batra and G. Taneja: A ‘Reliability Model for the Optimum Number of Standby Units in a System Working with Two Operative Units’. Ciencia e Tecnica Vitivinicola, Vol 33, No. 8, (2018), pp 20-49. https://www.academia.edu/download/79254481/ijaerv13n5_93.pdf
XVIII. S.K. Singh, and A.K. Mishra: ‘Profit evaluation of a two-unit cold standby redundant system with two operating systems’. Microelectronic Reliability, Vol 34, No. 4, (1994), pp 747–750. 10.1016/0026-2714(94)90040-X
XIX. S.K. Singh, B. Srinivasu: ‘Stochastic analysis of a two-unit cold standby system with preparation time for repair’. Microelectronics Reliability, Volume 27, No. 1, (1987), pp 55-60. 10.1016/0026-2714(87)90620-2
XX. V. Singh, P. Poonia: ‘Probabilistic assessment of two-unit parallel system with correlated lifetime under inspection using regenerative point technique’. Int J Reliabil Risk Safety Theory Appl, Vol 2, No. 1, (2019) pp 5–14. 10.30699/IJRRS.2.1.2