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Modified short-run statistical process control for test and measurement process

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Abstract

The key characteristics of test and measurement (T&M) manufacturing are short-run, multi-product families and testing at multi-stations. These characteristics render statistical process control (SPC) inefficacious because inherently meagre data do not warrant meaningful control limits. Measurement errors increase the risks of false acceptance and rejection, thereby leading to such consequences as unnecessary process adjustments and loss of confidence in SPC. This study presents a modified SPC model that incorporates measurement uncertainty from guard bands into the \( \overline{\mathrm{Z}} \) and W charts, thereby addressing the implications of short runs, multi-stations and measurement errors on SPC. The implementation of this model involves two phases. Phase I retrospective analysis computes the input parameters, such as the standard deviation of the measurement uncertainty, measurement target and estimate of the population standard deviation. Thereafter, five-band setting and sensitivity factor are proposed to estimate process standard deviation to maximise the opportunity to detect the assignable causes with low false-reject rate. Lastly, the \( \overline{\mathrm{Z}} \) and W charts are generated in Phase II using standardised observation technique that considers the measurement target and estimated process standard deviations. Run tests based on Nelson rules interpret the charts. Validation was performed in three case studies in an actual industry.

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References

  1. Del Castillo E, Grayson JM, Montgomery DC, Runger GC (1996) A review of statistical process control for short run manufacturing systems. Commun Stat Theory Methods 25(11):2723–2737

    Article  MATH  Google Scholar 

  2. Chen G (1997) The mean and standard deviation of the run length distribution of X charts when control limits are estimated. Stat Sin 7:789–798

    MATH  Google Scholar 

  3. Tsai TR, Lin JJ, Wu SJ, Lin HC (2005) On estimating control limits of X chart when the number of subgroups is small. Int J Adv Manuf Technol 26:1312–1316

    Article  Google Scholar 

  4. Montgomery DC (2013) Statistical quality control: a modern introduction, 7th edn. Wiley, Singapore

    MATH  Google Scholar 

  5. Costa AFB, Castagliola P (2011) Effect of measurement error and autocorrelation on the X̄ chart. J Appl Stat 38(4):611–673

    Article  MathSciNet  Google Scholar 

  6. Chakraborty A, Khurshid A (2013) Measurement error effect on the power of control chart for zero-truncated Poisson distribution. Int J Qual Res 7(3):3–14

    Google Scholar 

  7. Chandra MJ (2001) Statistical quality control. CRC Press LLC, Florida

    Book  Google Scholar 

  8. Kanazuka T (1986) The effects of measurement error on the power of X - R charts. J Qual Technol 18:91–95

    Article  Google Scholar 

  9. Tricker A, Coates E, Okell E (1998) The effect on the R chart of precision of measurement. J Qual Technol 30(3):232–239

    Article  Google Scholar 

  10. Khoo MBC, Moslim NH (2010) A study on Q chart for short runs production. Proceedings of the Regional Conference on Statistical Sciences (RCSS’10). June 2010, 1–8

  11. Jin J, Shi J (1999) State space modeling of sheet metal assembly for dimensional control. J Manuf Sci Eng 121:756–762

    Article  Google Scholar 

  12. Camelio J, Hu SJ, Ceglarek D (2003) Modeling variation propagation of multistation assembly systems with compliant parts. J Mech Des 125(4):673–681

    Article  Google Scholar 

  13. Djurdjanovic D, Ni J (2006) Stream of variations (SoV)-based measurement scheme analysis in multistation machining system. IEEE Trans Autom Sci Eng 3(4):407–422

    Article  Google Scholar 

  14. Zhang M, Djurdjanovic D, Ni J (2007) Diagnosibility and sensitivity analysis for multi-station machining processes. Int J Mach Tools Manuf 47(3–4):646–657

    Article  Google Scholar 

  15. Abellan-Nebot JV, Liu J, Subiron FR (2011) Design of multi-station manufacturing processes by integrating the stream-of-variation model and shop-floor data. J Manuf Syst 30(2):70–82

    Article  Google Scholar 

  16. Jiao Y, Djurdjanovic D (2011) Compensability of errors in product quality in multistage manufacturing processes. J Manuf Syst 30(4):204–213

    Article  Google Scholar 

  17. Linna KW, Woodall WH (2001) Effect of measurement error on Shewhart control charts. J Qual Technol 33(2):213–222

    Article  Google Scholar 

  18. ILAC-G8:03/2009 (2009) Guidelines on assessment and reporting of compliance with specification. International Laboratory Accreditation Cooperation. Retrieved from https://ilac.org/publications-and-resources/ilac-guidance-series

  19. JCGM 100:2008 (2008) Evaluation of measurement data– guide to the expression of uncertainty in measurement (GUM 1995 with minor corrections). Joint Committee for Guides in Metrology. Retrieved from https://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

  20. Cheatle KR (2006) Fundamentals of test measurement instrumentation. ISA, North Carolina

    Google Scholar 

  21. Nielsen HS (2017) Estimating measurement uncertainty. Metrology Consulting Inc. Web. https://www.hn-metrology.com/uncertaintytraining.htm. Accessed 6 October 2017

  22. ISO/IEC 17025:2017 (2017) General requirements for the competence of testing and calibration laboratories (3rd Ed.). International Organization for Standardization/ International Electrotechnical Commission. Retrieved from https://www.iso.org/standard/66912.html

  23. ANSI/NCSL Z540.3:2006 (2006) Requirements for the calibration of measuring and test equipment. American National Standard Institute/ National Conference of Standards Laboratories. Retrieved from http://www.ncsli.org/i/i/sp/z540/z540s/iMIS/Store/z540s.aspx

  24. Castrup H (2007) Risk analysis methods for complying with Z540.3. Proceedings of the NCSLI International Workshop and Symposium, August 2007. St. Paul, MN

  25. Sediva S, Havlikova M (2013) Comparison of GUM and Monte Carlo method for evaluation measurement uncertainty of indirect measurements. Proceedings of the 14th International Carpathian Control Conference (ICCC), 26–29 May 2013 Ryto 325–329

  26. Deaver D (1995) Using guardbands to justify TURs less than 4:1. Proceedings of ASQC 49th Annual Quality Congress, 136–141

  27. Mezouara H, Dlimi L, Salih A, Afechcar M (2015) Determination of the guard banding to ensure acceptable risk decision in the declaration of conformity. Int J Metrol Qual Eng 6:206

    Article  Google Scholar 

  28. Pou JM, Leblond L (2015) Control of customer and supplier risks by the guardband method. Int J Metrol Qual Eng 6:205

    Article  Google Scholar 

  29. Williams RH, Hawkins CF (1993) The effect of guardbands on error in production testing. In European Test Conference. Proceedings of ETC 93, Third, 19–22 April 1993. Rotterdam. 2–7

  30. Hossain A, Choudhury ZA, Suyut S (1996) Statistical process control of an industrial process in real time. IEEE Trans Ind Appl 32(2):243–249

    Article  Google Scholar 

  31. Koons GF, Luner JJ (1991) SPC in low-volume manufacturing: a case study. J Qual Technol 23(4):287–295

    Article  Google Scholar 

  32. Quesenberry CP (1991) SPC Q charts for start-up processes and short or long runs. J Qual Technol 23(3):213–224

    Article  Google Scholar 

  33. Celano G, Castagliola P, Trovato E, Fichera S (2011) Shewhart and EWMA t control charts for short production runs. Qual Reliab Eng Int 27:313–326

    Article  Google Scholar 

  34. Teoh WL, Chuah SK, Khoo MBC, Castagliola P, Yeong WC (2017) Optimal designs of the synthetic t chart with estimated process mean. Comput Ind Eng 112:409–425

    Article  Google Scholar 

  35. Gu K, Jia XZ, You HL, Zhang SH (2014) A t-chart for monitoring multi-variety and small batch production run. Qual Reliab Eng Int 30(2):287–299

    Article  Google Scholar 

  36. Cullen JM (1987) The use of statistical process control in one-off and small batch production. Proceedings of 8th International Conference on Automated Inspection and Product Control, June 1987. Chicago 63–68

  37. Bothe DR (1988) SPC for short production runs. Quality 27(12):58

    Google Scholar 

  38. Montgomery DC (1991) Introduction to statistical quality control, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  39. Moore SS, Murphy E (2013) Process visualization in medical device manufacture: an adaptation of short run SPC techniques. Qual Eng 25(3):247–265

    Article  Google Scholar 

  40. Marques PA, Cardeira CB, Paranhos P, Ribeiro S, Gouveia H (2015) Selection of the most suitable statistical process control approach for short production runs: a decision-model. Int J Inform Educ Technol 5(4):303–310

    Article  Google Scholar 

  41. Nelson LS (1989) Standardization of Shewhart control charts. J Qual Technol 21:287–289

    Article  Google Scholar 

  42. Bothe DR (1989) A powerful new control chart for job shops. Proceedings of the 43rd Annual Quality Congress Transactions, May 1989. Toronto 265–270

  43. Cullen CC, Bothe DR (1989) SPC for short production runs. Proceedings of the IEEE National Aerospace and Electronics Conference, 22–26 May 1989. Dyton, OH. 1960–1963

  44. Wasserman GS (1994) Short run SPC using dynamic control chart. Comput Ind Eng 27(1–4):353–356

    Article  Google Scholar 

  45. Wheeler DJ (1991) Short run SPC. SPC Press, Inc, Knoxville

    Google Scholar 

  46. Noskievičová D, Jarošová E (2013) Complex application of statistical process control in conditions of profile bars production. Proceedings of METAL2013, 15–17 May 2013. Brno, Czech Republic

  47. Zhou X, Govindaraju K, Jones G (2017) Monitoring fractional nonconformance for short-run production. Qual Eng. https://doi.org/10.1080/08982112.2017.1360499

  48. Farnum NR (1992) Control charts for short runs: nonconstant process and measurement error. J Qual Technol 24(2):138–144

    Article  Google Scholar 

  49. Kirkup L, Frenkel B (2006) An introduction to uncertainty measurement. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  50. Weckenmann A, Rinnagl M (2000) Acceptance of processes: do we need decision rules? Precis Eng 24:264–269

    Article  Google Scholar 

  51. Quesenberry CP (1998) Statistical gymnastics. Qual Prog 31(9):78–79

  52. UKAS (2007) The expression of uncertainty and confidence in measurement. M3003, 2nd edn. United Kingdom Accreditation Service, Staines-upon-Thames

    Google Scholar 

  53. Taylor BN, Kuyatt CE (1994) Guidelines for evaluating and expressing the uncertainty of NIST measurement results. National Institute of Standards and Technology, Maryland

    Book  Google Scholar 

  54. Bell S (2001) Measurement good practice guide no 11 (issue 2): a beginner’s guide to uncertainty of measurement. National Physical Laboratory, Middlesex

    Google Scholar 

  55. Instone I (1996) Simplified method for assessing uncertainties in a commercial production environment. Teste and measurement. Proceeding of Metrology Forum, 10 Oct. London. 1–7

  56. Dobbert M (2008) A guard-band strategy for managing false-accept risk. NCSLI Measure J Meas Sci 3(4):44–48

    Article  Google Scholar 

  57. Hoaglin DC, Mosteller F, Tukey JW (1983) Understanding robust and exploratory data analysis. Wiley, New York

    MATH  Google Scholar 

  58. Nelson LS (1984) The Shewhart control chart-tests for special causes. J Qual Technol 16(4):237–239

    Article  Google Scholar 

  59. Noskievičová D (2013) Complex control chart interpretation. Int J Eng Bus Manag 5(13):1–7

    Google Scholar 

  60. Shapiro SS, Wilk MB (1965) An analysis of variance test for normality. Biometrika 52(3–4):591–611

    Article  MathSciNet  MATH  Google Scholar 

  61. Scrucca L, Snow G, Bloomfield P (2017) Package ‘qcc’ (Version 2.7) [Source code]. https://cran.r-project.org/web/packages/qcc

  62. Venables WN, Smith DM, the R Core Team (2017) An introduction to R. version 3.4.3. Retrieved from https://cran.r-project.org/doc/manuals/r-release/R-intro.pdf

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Acknowledgement

This work was supported by Research University Grant (RUI), Universiti Sains Malaysia [grant number 8014069].

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Authors and Affiliations

  1. School of Mechanical Engineering, Engineering Campus, Universiti Sains Malaysia, Room 330, 14300, Nibong Tebal, Penang, Malaysia

    Chin Kok Koh & Jeng Feng Chin

  2. Department of Mechanical Engineering, Universiti Teknologi Petronas, Seri Iskandar, Perak, Malaysia

    Shahrul Kamaruddin

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  1. Chin Kok Koh
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  2. Jeng Feng Chin
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Correspondence to Jeng Feng Chin.

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Koh, C.K., Chin, J.F. & Kamaruddin, S. Modified short-run statistical process control for test and measurement process. Int J Adv Manuf Technol 100, 1531–1548 (2019). https://doi.org/10.1007/s00170-018-2776-1

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