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Variable sampling plan for resubmitted lots based on process capability index and Bayesian approach

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Abstract

Acceptance sampling plans are applied for quality inspection of products. Among the design approaches of sampling plan, the most important one is to use process capability indices in order to improve the quality of manufacturing processes and the quality inspection of products. But, selection of estimators of process capability index and their sampling distribution is very important. Bayesian statistical technique can be used to obtain the sampling distribution. In this paper, a variable sampling plan is developed for resubmitted lots based on process capability index and Bayesian approach. In the proposed sampling plan, lots are inspected several times depending on the quality level of the process. In addition, this paper presents an optimization model for determining the decision parameters of developed sampling plan with regards to the constraints related to the risk of consumer and producer. Two comparison studied have been done including: First, the methods of double sapling plan (DSP), multiple dependent state (MDS) sampling plan, and repetitive group sampling (RGS) plan are elaborated, and also in order to comparing developed sampling plans, an expected number of products as average sample number (ASN) is used for different developed plans; second, a comparison study between Bayesian approach and exact probability distribution is carried out and their results are analyzed. It is observed that the ASN values of MDS sampling plan is less than ASN values of other methods, and also the ASN values of different variable sampling plans based on Bayesian approach is less than ASN values obtained using exact approach.

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References

  1. Duncan AJ (1959) Quality control and industrial statistics. Homewood Illinois

  2. Montgomery DC (1976) Introduction statistical quality control, 5th ed. Wiley

  3. Aslam M, Chi HJ, Azam M (2013) Multiple dependent state sampling plan based on process capability index. J Test Eval 41(2):340–346

    Article  Google Scholar 

  4. Govindaraju K, Ganesalingam S (1997) Sampling inspection for resubmitted lots. Commun Stat Simul 26(3):1163–1176

    Article  MATH  Google Scholar 

  5. Sherman RE (1965) Design and evaluation of repetitive group sampling plans. Technometrics 7:11–21

    Article  MathSciNet  MATH  Google Scholar 

  6. Aslam M, Azam M, Chi HJ (2013) A mixed repetitive sampling plan based on process capability index. Appl Math Model 37(24):10027–10035

    Article  MathSciNet  Google Scholar 

  7. Aslam M, Wu CW, Azam M, Chi HJ (2013) Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. Appl Math Model 37:667–675

    Article  MathSciNet  MATH  Google Scholar 

  8. Balamurali S, Jun CH (2006) Repetitive group sampling procedure for variables inspection. J Appl Stat 33:327–338

    Article  MathSciNet  MATH  Google Scholar 

  9. Balamurali S, Subramani J (2010) Designing of variables repetitive group sampling plan indexed by point of control. J Manuf Eng 5:166–169

    Google Scholar 

  10. Aslam M, Azam M, Chi HJ (2015) Various repetitive sampling plans using process capability index of multiple quality characteristics. Appl Stoch Models Bus Ind

  11. Soundararajan V, Vijayaraghavan R (1990) Construction and selection of multiple dependent (deferred) state sampling plan. J Appl Stat 17:397–409

    Article  Google Scholar 

  12. Vaerst R (1982) A procedure to construct multiple deferred state sampling plan. Meth Oper Res 37:477–485

    Google Scholar 

  13. Balamurali S, Jun CH (2007) Multiple dependent state sampling plan for lot acceptance based on measurement data. Eur J Oper Res 180:1221–1230

    Article  MATH  Google Scholar 

  14. Fallah Nezhad MS, Seifi S (2016) Designing optimal double-sampling plan based on process capability index. J Commun Stat Theory Methods

  15. Moskowitz H, Tang K (1992) Bayesian variables acceptance sampling plans: quadratic loss function and step loss function. Technometrics 34:340–347

    Article  MathSciNet  MATH  Google Scholar 

  16. Tagaras G (1994) Economic acceptance sampling by variables with quadratic quality costs. IIE Trans 26:29–36

    Article  Google Scholar 

  17. Arizono I, Kanagawa A, Ohta H, Watakabe K, Tateishi K (1997) Variable sampling plans for normal distribution indexed by Taguchi’s loss function. Nav Res Logist 44:591–603

    Article  MATH  Google Scholar 

  18. Fallah Nezhad MS, Hosseini Nasab H (2012) A new Bayesian acceptance sampling plan considering inspection errors. Sci Iran 19(6):1865–1869

    Article  Google Scholar 

  19. Wu CW (2006) Assessing process capability based on Bayesian approach with subsamples. Eur J Oper Res 184(1):207–228

    Article  MATH  Google Scholar 

  20. Wu CW, Aslam M, Chi HJ (2012) Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. Eur J Oper Res 217:560–566

    Article  MATH  Google Scholar 

  21. Miao R, Zhang X, Yang D, Zhao Y, Jiang Z (2011) A conjugate Bayesian approach for calculating process capability indices. Expert Syst Appl 38:8099–8104

    Article  Google Scholar 

  22. Pearn WL, Wu CW (2005) A Bayesian approach for assessing process precision based on multiple samples. Eur J Oper Res 165(3):685–695

    Article  MathSciNet  MATH  Google Scholar 

  23. Yen CH, Chang CH (2009) Designing variables sampling plans with process loss consideration. Commun Stat Simul Comput 38:1579–1591

    Article  MathSciNet  MATH  Google Scholar 

  24. Negrin I, Parmet Y, Schechtman E (2009) Developing a sampling plan based on Cpk. Qual Eng 21:306–318

    Article  Google Scholar 

  25. Pearn WL, Lin PC (2004) Testing process performance based on capability index Cpk with critical value. Comput Ind Eng 47:351–369

    Article  Google Scholar 

  26. Wu CW, Pearn WL (2008) A variables sampling plan based on Cpmk for product acceptance determination. Eur J Oper Res 184:549–560

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Industrial Engineering, Yazd University, Yazd, Iran

    Sina Seifi & Mohammad Saber Fallah Nezhad

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  1. Sina Seifi
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  2. Mohammad Saber Fallah Nezhad
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Correspondence to Mohammad Saber Fallah Nezhad.

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Seifi, S., Nezhad, M.S.F. Variable sampling plan for resubmitted lots based on process capability index and Bayesian approach. Int J Adv Manuf Technol 88, 2547–2555 (2017). https://doi.org/10.1007/s00170-016-8958-9

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  • DOI: https://doi.org/10.1007/s00170-016-8958-9

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