Monitoring high complex production processes using process capability indices



The increasing demand and the globalization of the market are leading to increasing levels of quality in production processes, and thus, nowadays, multiple product characteristics must be tested because they are considered critical. In this context, decision makers are forced to interpret a huge amount of quality indicators, when monitoring production processes. This fact leads to a misunderstanding as a result of information overload. The aim of this paper is to help practitioners when monitoring the capability of processes with a huge amount of product characteristics. We propose a methodology that reduces the amount of data in capability analysis by structuring hierarchically the multiple quality indicators obtained in the quality tests. The proposed methodology may help practitioners and decision makers of the industry in three aspects of statistical process monitoring: to identify the part of a complex production process that presents capability problems, to detect worsening over the time in multivariate production processes, and to compare similar production processes. Some illustrative examples based on different kinds of production processes are discussed in order to illustrate the methodology. A case of study based on a real production process of the automotive industry is analyzed using the proposed methodology. We conclude that the proposed methodology reduces the necessary amount of data in capability analysis; and thus, that it provides an added value of great interest for managers and decision makers.


Process monitoring Process capability Multivariate statistics Automotive industry Machining process 


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  1. 1.
    Oborski P (2014) Developments in integration of advanced monitoring systems. Int J Adv Manuf Technol 75(9–12):1613–1632. doi: 10.1007/s00170-014-6123-x CrossRefGoogle Scholar
  2. 2.
    Severson K, Chaiwatanodom P, Braatz RD (2015) Perspectives on process monitoring of industrial systems. IFAC-PapersOnLine 48(21):931–939. doi: 10.1016/j.arcontrol.2016.09.001. doi: 10.1016/j.ifacol.2015.09.646 CrossRefGoogle Scholar
  3. 3.
    Stavropoulos P, Papacharalampopoulos A, Vasiliadis E, Chryssolouris G (2016) Tool wear predictability estimation in milling based on multi-sensorial data. Int J Adv Manuf Technol 82(1–4):509–521. doi: 10.1007/s00170-015-7317-6 CrossRefGoogle Scholar
  4. 4.
    Ostasevicius V, Jurenas V, Augutis V, Gaidys R, Cesnavicius R, Kizauskiene L, Dundulis R (2016) Monitoring the condition of the cutting tool using self-powering wireless sensor technologies. The International Journal of Advanced Manufacturing Technology, pp 1–15. doi: 10.1007/s00170-016-8939-z
  5. 5.
    Seemuang N, McLeay T, Slatter T (2016) Using spindle noise to monitor tool wear in a turning process. International Journal of Advanced Manufacturing Technology, pp 1–10. doi: 10.1007/s00170-015-8303-8
  6. 6.
    Psarakis S (2015) Adaptive control charts: recent developments and extensions. Qual Reliab Eng Int 31 (7):1265–1280. doi: 10.1002/qre.1850 MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yang L, Sheu S H (2006) Integrating multivariate engineering process control and multivariate statistical process control. Int J Adv Manuf Technol 29(1-2):129–136. doi: 10.1007/s00170-014-6641-6 CrossRefGoogle Scholar
  8. 8.
    Bersimis S, Psarakis S, Panaretos J (2007) Multivariate statistical process control charts: an overview. Qual Reliab Eng Int 23(5):517–543. doi: 10.1002/qre.829 CrossRefGoogle Scholar
  9. 9.
    Costa AFB, Machado MAG (2009) A new chart based on sample variances for monitoring the covariance matrix of multivariate processes. Int J Adv Manuf Technol 41(7-8):770–779. doi: 10.1007/s00170-008-1502-9 CrossRefGoogle Scholar
  10. 10.
    Dharmasena LS, Zeephongsekul P (2015) A new process capability index for multiple quality characteristics based on principal components. Int J Prod Res 2015:1–17. doi: 10.1080/00207543.2015.1091520 Google Scholar
  11. 11.
    Sullivan LP (1985) Letters. Qual Prog 18:7–8Google Scholar
  12. 12.
    Kane VE (1986) Process capability indices. J Qual Technol 18(1):41–52Google Scholar
  13. 13.
    Chan LK, Cheng SW, Spiring FA (1988) A new measure of process capability: Cpm. J Qual Technol 20(3):162–175. doi: 10.1108/02656710110396076 Google Scholar
  14. 14.
    Pearn WL, Kotz S, Johnson NL (1992) Distributional and inferential properties of process capability indices. J Qual Technol 24(4):216–231. doi: 10.1080/03610929808832139 Google Scholar
  15. 15.
    Veevers A (1998) Viability and capability indexes for multiresponse processes. J Appl Stat 25(4):545–558. doi: 10.1080/02664769823016 CrossRefMATHGoogle Scholar
  16. 16.
    Gonzalez I, Sanchez I (2009) Capability indices and nonconforming proportion in univariate and multivariate processes. Int J Adv Manuf Technol 44:1036–1050. doi: 10.1007/s00170-008-1907-5 CrossRefGoogle Scholar
  17. 17.
    Zwick D S (1995) A hybrid method for fitting distribution data and its use in computing process capability indices. Qual Eng 7(3):601–613. doi: 10.1080/08982119508918806 CrossRefGoogle Scholar
  18. 18.
    Yang J, Gang T, Cheng Y, Xie M (2015) Process capability indices based on the highest density interval. Qual Reliab Eng Int 31(8):1327–1335. doi: 10.1002/qre.1665 CrossRefGoogle Scholar
  19. 19.
    Lupo T (2015) The new Nino capability index for dynamic process capability analysis. Qual Reliab Eng Int 31(2):305–312. doi: 10.1002/qre.1589 CrossRefGoogle Scholar
  20. 20.
    Eslamipoor R, Hosseini-nasab H (2016) A Modified Process Capability Index Using Loss Function Concept. Qual Reliab Eng Int 32(2):435–442. doi: 10.1002/qre.1761 CrossRefGoogle Scholar
  21. 21.
    Pearn WL, Shiau JJH, Tai YT, Li MY (2011) Capability assessment for processes with multiple characteristics: a generalization of the popular index Cpk. Qual Reliab Eng Int 27(8):1119–1129CrossRefGoogle Scholar
  22. 22.
    Perakis M, Xekalaki E (2011) On the implementation of the principal component analysis-based approach in measuring process capability. Qual Reliab Eng Int 28(4):467–480. doi: 10.1002/qre.1260 CrossRefGoogle Scholar
  23. 23.
    Tano I, Vännman K (2013) A multivariate process capability index based on the first principal component only. Qual Reliab Eng Int 29(7):987–1003. doi: 10.1002/qre.1451 CrossRefGoogle Scholar
  24. 24.
    Shaoxi W, Mingxin W, Xiaoya F, Shengbing Z, Ru H (2013) A multivariate process capability index with a spatial coefficient. J Semicond 34(2). doi: 10.1088/1674-4926/34/2/026001
  25. 25.
    Das N, Dwivedi PS (2013) Multivariate process capability index: a review and some results. Econ Qual Control 28(2):151–166. doi: 10.1515/eqc-2013-0022 CrossRefMATHGoogle Scholar
  26. 26.
    Shiau J, Yen C, Pearn WL, Lee W (2013) Yield-related process capability indices for processes of multiple quality characteristics. Qual Reliab Eng Int 29(4):487–507. doi: 10.1002/qre.1397 CrossRefGoogle Scholar
  27. 27.
    Jalili M, Bashiri M, Amiri A (2012) A new multivariate process capability index underboth unilateral and bilateral quality characteristics. Qual Reliab Eng Int 28(8):925–941. doi: 10.1002/qre.1284 CrossRefGoogle Scholar
  28. 28.
    Ciupke K (2015) Multivariate process capability vector based on one-sided model. Qual Reliab Eng Int 31(2):313–327. doi: 10.1002/qre.1590 CrossRefGoogle Scholar
  29. 29.
    Pan JN, Huang WKC (2015) Developing new multivariate process capability indices for autocorrelated data. Qual Reliab Eng Int 31(3):431–444. doi: 10.1002/qre.1603 CrossRefGoogle Scholar
  30. 30.
    Wang FK, Tamirat Y (2015) Process Yield for Multivariate Linear Profiles with One-sided Specification Limits. Quality and Reliability Engineering International. doi: 10.1002/qre.1834
  31. 31.
    De-Felipe D, Klee T, Folmer J, Benedito E, Vogel-Heuser B (2016) A multivariate process capability index that complies with industry requirements. Paper presented at the Conference of IEEE Industrial Electronics Society (IECON), Florence, doi: 10.1109/IECON.2016.7793509
  32. 32.
    Castagliola P (1996) Evaluation of non-normal process capability indices using Burr’s distributions. Qual Eng 8(4):587–593. doi: 10.1080/08982119608904669 CrossRefGoogle Scholar
  33. 33.
    De-Felipe D, Benedito E (2017) A review of univariate and multivariate process capability indices. The International Journal of Advanced Manufacturing Technology, pp 1–19. doi: 10.1007/s00170-017-0273-6
  34. 34.
    Bothe DR (1999) Composite capability index for multiple product characteristics. Qual Eng 12(2):253–258. doi: 10.1080/08982119908962582 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.Bayerische Motoren Werke AGBMW AGGermany
  2. 2.Department of Management and Institute of Industrial and Control EngineeringUniversitat Politècnica de Catalunya (UPC)BarcelonaSpain

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