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On the monitoring of multi-attributes high-quality production processes

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Abstract

Over the last decade, there have been an increasing interest in the techniques of process monitoring of high-quality processes. Based upon the cumulative counts of conforming (CCC) items, Geometric distribution is particularly useful in these cases. Nonetheless, in some processes the number of one or more types of defects on a nonconforming observation is also of great importance and must be monitored simultaneously. However, there usually exist some correlations between these two measures, which obligate the use of multi-attribute process monitoring. In the literature, by assuming independence between the two measures and for the cases in which there is only one type of defect in nonconforming items, the generalized Poisson distribution is proposed to model such a problem and the simultaneous use of two separate control charts (CCC & C chats) is recommended.

In this paper, we propose a new methodology to monitor multi-attribute high-quality processes in which not only there exist more than one type of defects on the observed nonconforming item but also there is a dependence structure between the two measures. To do this, first we transform multi-attribute data in a way that their marginal probability distributions have almost zero skewnesses. Then, we estimate the transformed mean vector and covariance matrix and apply the well-known χ2 control chart. In order to illustrate the proposed method and evaluate its performance, we use two numerical examples by simulation and compare the results. The results of the simulation studies are encouraging.

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References

  • Acosta-Mejia C (1999) Improved p charts to monitor process quality. IIE Trans 31:509–516

    Google Scholar 

  • Box GEP, Cox DR (1964) An analysis of transformations. J Roy Stat Soc B 26:211–243

    MATH  MathSciNet  Google Scholar 

  • Cario MC, Nelson BL (1997) Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, USA

    Google Scholar 

  • Collica RS, Ramirez JG, Taam W (1996) Process monitoring in integrated circuit fabrication using both yield and spatial statistics. Qual Reliab Engg Int 12:195–202

    Article  Google Scholar 

  • Consul PC (1989) Generalized Poisson distributions: properties and applications. Marcel Dekker

  • Gadre MP, Rattihalli RN (2005) Some group inspection based multi-attribute control charts to identify process deterioration. Econ Qual Contr 2:151–164

    Google Scholar 

  • Gibra IN (1978) Economically Optimal Determination of the Parameters of np-Control Charts. J Qual Technol 10:12 –19

    Google Scholar 

  • Glushkovsky EA (1994) On-line G-control chart for attribute data. Qual Reliab Engg Int 10: 217–227

    Article  Google Scholar 

  • Goh TN (1987) A control chart for very high yield processes. Qual Assuran 13:18–22

    Google Scholar 

  • Hawkins DM (1991) Regression adjustment for variables in multivariate quality control. J Qual Technol 25:175–182

    Google Scholar 

  • Hawkins DM, Olwell DH (1998) Cumulative sum charts and charting for quality improvements. Springer, Berlin Hidelberg New York, pp129–132

    Google Scholar 

  • Hayter AJ, Tsui KL (1994) Identification and qualification in multivariate quality control problems. J Qual Technol 26:197–208

    Google Scholar 

  • He B, Xie M, Goh TN, Tsui L (2002) Control charts based on generalized Poisson model for count data. Technical Report, Logistics Institute Georgia Tech. and Logistics Institute – Asia Pacific, National University of Singapore

  • Hotelling H (1947) Multivariate quality control. In: Eisenhart, Hastay, Wallis (eds) Techniques of statistical analysis. McGraw-Hill, New York

    Google Scholar 

  • Jarque CM, Bera AK (1987) A test for normality of observations and regression residuals. Int Stat Rev 55:163–172

    Article  MATH  MathSciNet  Google Scholar 

  • Jolayemi JK (2000) An optimal design of multi-attribute control charts for processes subject to a multiplicity of assignable causes. Appl Mathe Comput 114:187–203

    Article  MATH  Google Scholar 

  • Johnson NL, Kotz S (1969) Discrete distributions. Wiley, New York

    MATH  Google Scholar 

  • Jolayemi JK (1994) Convolution of independent binomial variables: An approximation method and a comparative study. Comput Stat Data Analy 18:403–417

    Article  MATH  Google Scholar 

  • Kaminsky FC, Benneyan JC, Davis RD, Burke RJ (1992) Statistical control charts based on a geometric distribution. J Qual Technol 24:63–69

    Google Scholar 

  • Kourti T, MacGregor JF (1996) Multivariate SPC methods for process and product monitoring. J Qual Technol 28:409–428

    Google Scholar 

  • Kuralmani V, Xie M, Goh TN, Gan FF (2002) A conditional decision procedure for high yield processes. IIE Trans 34:1021–1030

    Google Scholar 

  • Lambert D (1992) Zero-inflated regression with an application to defects in manufacturing. Technometrics, 34:1–14

    Article  MATH  Google Scholar 

  • Larpkiattaworn S (2003) A neural network approach for multi-attribute process control with comparison of two current techniques and guidelines for practical Use. Ph.D. Thesis, University of Pittsburgh, USA

    Google Scholar 

  • Lowry CA, Montgomery DC (1995) A review of multivariate control charts. IIE Transa 27:800–810

    Article  Google Scholar 

  • Lu XS, Xie M, Goh TN, Lai CD (1998) Control chart for multivariate attribute processes. Int J Product Res 36:3477–3489

    Article  MATH  Google Scholar 

  • Marcucci M (1985) Monitoring multinomial processes. J Qual Technol 17:86–91

    Google Scholar 

  • Montgomery DC (2003) Introduction to statistical quality control. 5th edn, J Wiley, New York

    Google Scholar 

  • Nelson LS (1994) A control chart for parts-per-million nonconforming items. J Qual Technol 26:239–240

    Google Scholar 

  • Niaki STA, Abbasi B (2006) A symmetric rectangular region for multi-attribute C control chart. In: Proceedings of the 36th international conference on computer and industrial engineering, Taipei, Taiwan

  • Niaki STA, Abbasi B (2005) Fault diagnosis in multivariate control charts using artificial neural networks. J Qual Reliab Engg Int 21:825–840

    Article  Google Scholar 

  • Niaki STA, Abbasi B (2006) NORTA and neural networks based method to generate random vectors with arbitrary marginal distributions and correlation matrix. In: Proceedings of the 17th IASTED international conference on modeling and simulation, Montreal, Canada

  • Patel HI (1973) Quality control methods for multivariate binomial and Poisson distributions. Technometrics, 15:103–112

    Article  MATH  MathSciNet  Google Scholar 

  • Quesenberry CP (1995) Geometric Q-charts for high quality processes. J Qual Technol 27:304–315

    Google Scholar 

  • Runger GC (1996) Projections and the U2 multivariate control chart. J Qual Technol 2:313–319

    Google Scholar 

  • Ryan TP (1989) Statistical methods for quality improvement. J Wiley, New York

    Google Scholar 

  • Ryan TP, Schwertman NC (1997) Optimal limits for attributes control charts. J Qual Technol 29:86–96

    Google Scholar 

  • Thisted RA (2000) Elements of statistical computing, numerical computation. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

  • Woodall WH (1997) Control charts based on attribute data: Bibliography and review. J Qual Technol 29:172–183

    Google Scholar 

  • Xie M, Goh TN, Tang Y (2000) Data transformation for geometrically distributed quality characteristics. Qual Reliab Engg Int 16:9–15

    Article  Google Scholar 

  • Xie M, Goh TN (1993) SPC of a near zero-defect process subject to random shock. Qual Reliabi Engg Int 9:89–93

    Article  Google Scholar 

  • Xie M, Goh TN (1995) Some procedures for decision making in controlling high yield processes. Qual Reliabi Engg Int 8:355–360

    Article  Google Scholar 

  • Xie M, Goh TN (1997) The use of probability limits for process control based on geometric distribution. Int J Qual Relia Manage 14:64–73

    Article  Google Scholar 

  • Yang ZH, Xie M, Kuralmani V, Tsui K (2002) On the performance of geometric charts with estimated control limits. J Qual Technolo 34:448–458

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Industrial Engineering, Sharif University of Technology, P.O. Box 11365-9414, Azadi Ave., Tehran, Iran

    Seyed Taghi Akhavan Niaki & Babak Abbasi

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  1. Seyed Taghi Akhavan Niaki
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  2. Babak Abbasi
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Correspondence to Seyed Taghi Akhavan Niaki.

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Akhavan Niaki, S.T., Abbasi, B. On the monitoring of multi-attributes high-quality production processes. Metrika 66, 373–388 (2007). https://doi.org/10.1007/s00184-006-0117-0

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  • DOI: https://doi.org/10.1007/s00184-006-0117-0

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