Determination of Optimum Sample Size for Lot Acceptance Attribute Sampling under Life Tests Based On Rayleigh Distribution Using Graphical Evaluation Review Technique (GERT)

Document Type : Original Research Article

Authors

Department of Statistics Bharathiar University, India

Abstract

This paper presents the graphical evaluation and review technique (GERT) exploration of performance measures for lot acceptance sampling procedures having attribute characteristics following life tests based on percentiles of Rayleigh Distribution and henceforth determining optimum sampling size.  The advantageous implications of GERT analysis in this framework is primarily to visualize the dynamics of the sampling inspection system and secondly, critical analysis of sampling procedure characteristics. The formula of operating characteristics (OC) function and average sample number (ASN) function is derived and illustrated numerically. Lastly, tables have been provided to determine the optimum sample size assuring certain mean life or quality of the product.

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Main Subjects


  • Abubakar M.I and Singh,V.V. (2019). Performance assessment of African textile manufacturers, LTD, in Kano state, Nigeria, through Multi failure and repair using copula. Oper Res Decis 29(4):1–18
  • Anand, J and Malik, S.C. 2012. Analysis of a Computer System with Arbitrary Distributions for H/W and S/W Replacement Time and Priority to Repair Activities of H/W over Replacement of the S/W, International Journal of Systems Assurance Engineering and Management, Vol.3 (3), pp. 230-236.
  • Ashok Kumar, D. Pawar1 & S. C. Malik. (2020). Reliability Analysis of a Redundant System with ‘FCFS’ Repair Policy Subject to Weather Conditions, International Journal of Advanced Science and Technology, 29(3),,7568 – 7578
  • Bisht, S and Singh, S. B. (2019), Reliability analysis od acyclic transmission network based on minimal cuts using copula in repair, Proceedings of the Jangjeon Mathematical Society,22(2019), No. 1, pp. 163-173.
  • Kumar, A. and Malik, S. C. 2012. Stochastic Modeling of a Computer System with Priority to PM over S/W the Replacement Subject to Maximum Operation and Repair Times. International Journal of Computer Applications, Vol.43 (3), pp. 27-34.
  • Kumar, Ashish; Anand, Jyoti and Malik, S.C. 2013. Stochastic Modeling of a Computer System with Priority to Up-gradation of Software over Hardware Repair Activities. International Journal of Agricultural and Statistical Sciences, Vol. 9(1), pp. 117-126.
  • Kumar, A. & Malik, S.C. 2014. Reliability modelling of a computer system with priority to H/w repair over replacement of H/w and up-gradation of S/w subject to MOT and MRT, Jordan Journal of Mechanical and Industrial Engineering, Vol.8 (4), pp. 233-241.
  • Kumar, A., Saini, M. and Malik, S.C. 2015. Performance Analysis of a Computer System with Fault Detection of Hardware, Procedia computer science,45, 602-610.
  • Lado, A.K., Singh, V.V., Ismail K.H and Ibrahim, Y. (2018). Performance and cost assessment of repairable complex system with two subsystems connected in the series configuration. Int J Reliabil Appl 19(1):27–42
  • Lado, A. and Singh, V. (2019), "Cost assessment of complex the repairable system consisting two subsystems in the series configuration using Gumbel Hougaard family copula", International Journal of Quality & Reliability Management, Vol. 36 No. 10, pp. 1683-1698. https://doi.org/10.1108/IJQRM-12-2018-0322
  • Liu, Y and Peng, Y.(2016). The application of computer network and research under the new media environment, evaluation of the computer network technology application tutorial (fourth edition). J Youth Press; 32:104–104. 1007/s11263-011-0495-210.1049/iet-cta.2013.0676
  • Malik, S. C. and Anand, J.2010. Reliability and Economic Analysis of a Computer System with Independent Hardware and Software Failures, Bulletin of Pure and Applied Sciences,Vol.29 E (Math. & Stat.), No. 1, pp.141-153.
  • Malik, S.C. and Sureria, J.K. 2012. Profit Analysis of a Computer System with H/W Repair and S/W Replacement. International Journal of Computer Applications, Vol.47(1), pp.19-26.
  • Malik, S.C. 2013. Reliability Modelling of a computer System with Preventive Maintenance and Priority Subject to Maximum Operation and Repair Times. International Journal of System Assurance Engineering and Management, Vol. 4 (1), pp. 94-100.
  • Malik, S.C. and Munday, V.J. 2014. Stochastic Modeling of a Computer System with Hardware Redundancy, International Journal of Computer Applications, Vol. 89 (7), pp. 26-30.
  • Niwas, R. and Garg, H. (2018), “An approach for analyzing the reliability and profit of an industrial system based on the cost-free warranty policy”, Journal of the Brazilian Society of Mechanics and Engineering, Vol. 40 No. 5, pp. 1-9.
  • Singh, V.V., Poonia, P.K and Abdullahi, A.H. (2020). Performance analysis of a complex repairable system with two subsystems in series configuration with imperfect switch, Journal of Mathematical and Computational Science, 10(2). 359-383.
  • Singh, V.V and Poonia, P. K.. (2019). Probabilistic Assessment of Two-Unit Parallel System with Correlated Lifetime under Inspection Using Regenerative Point Technique, IJRRS,2(1),5-14
  • Temraz, N.S.Y.(2019). Availability and reliability of a parallel system under imperfect repair and replacement: analysis and cost optimization. Int J Syst Assur Eng Manag10, 1002–1009 (2019). https://doi.org/10.1007/s13198-019-00829-2
  • Wang, K,-H and Kuo, C,-C. 2000. Cost and probabilistic analysis of series systems with mixed standby components, Applied Mathematical Modelling, 24: 957-967.
  • Wang,K., Hsieh, C and Liou, C. 2006. Cost benefit analysis of series systems with cold standby components and a repairable service station. Journal of quality technology and quantitative management, 3(1): 77-92.
  • Yang, D. Y and Tsao, C. L. (2019). Reliability and availability analysis of standby systems with working vacations and retrial of failed components. Reliability Engineering & System Safety, 182, 46-55.
  • Yen, T, -C and Wang, K, -H. (2018). Cost-benefit analysis of three systems with imperfect coverage and standby switching failures, IJMOR, 12(2),253-272.DOI: 1504/IJMOR.2018.089680
  • Yang, S.(2019)Analysis for the reliability of the computer network by using intelligent cloud computing method,International Journal of Computers and Applications,41:4,306-311,DOI: 1080/1206212X.2017.1417770
  • Yusuf, I., Yusuf, B., Babagana, M., Sani, B and Lawan, M.A. (2018). Some reliability characteristics of a linear consecutive 2-out-of-4system connected to a 2-out-of-4 supporting device for operation. Int J Eng Technol 7(1):135–139.
  • Yusuf I, Yufus B, Suleiman K (2019) Reliability assessment of a repairable system under online and offline preventive maintenance. Life Cycle Reliability Saf Eng 8(4):391–406.
  • Zhao, B., Xie, L., Li, H., Zhang, S., Wang, B., and Li, C. (2020). Reliability analysis of aero-engine compressor rotor system considering cruise characteristics. IEEE Trans Reliab 68(4):245–259
  • Zhang, F. (2019). Research on reliability analysis of computer network based on intelligent cloud computing method, International Journal of Computers and Applications, 41:4, 283-288, DOI: 1080/1206212X.2017.1402622.