Production
https://www.prod.org.br/article/doi/10.1590/0103-6513.20210092
Production
Research Article

Analysis of deviation from nominal control chart performance on short production runs

Márcio Ricardo Morelli de Meira; Pedro Carlos Oprime; Ricardo Coser Mergulhão

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Abstract

Paper aims: This paper studies the influence of process variation on deviation from nominal control chart performance and proposes some adjustments on the control limits to make it enable on small batches.

Originality: Specific methods were developed to monitor small batches, mainly due to unavailability of data for precise parameters estimation, like the deviation from nominal control charts. However, Montgomery (2014) highlights some essential aspects, such as the influence of process variation on its performance.

Research method: The method used was mathematical modeling and computer simulation.

Main findings: The results validated that there is a significant influence of the process variation on the control chart performance. It has been demonstrated that small adjustments on the control limits can make it enable on lean environments.

Implications for theory and practice: The main contribution is demonstrating the use of deviation from nominal control chart, through the valid control limits definition regardless of the samples size.

Keywords

Control charts for short production runs, Deviation from nominal control chart, Effect of parameters estimation on control charts performance

References

Abbasi, S., & Haq, A. (2019). Enhanced adaptive CUSUM charts for process mean. International Journal of Statistical Computation and Simulation, 89(13), 2562-2582. http://dx.doi.org/10.1080/00949655.2019.1625902.

Ahmad, L., Aslam, M., & Jun, C-H. (2016). The design of a new repetitive sampling control chart based on process capability index. Transactions of the Institute of Measurement and Control, 38(8), 971-980. https://doi.org/10.1177/0142331215571120.

Alwan, L. C. (2007). Effects of autocorrelation on control chart performance. International Journal of Communications in Statistics, 21(4), 1025-1049.

Aykroyd, R. G., Leiva, V., & Ruggeri, F. (2019). Recent developments of control charts, identification of big data sources and future trends of current research. Technological Forecasting and Social Change, 144, 221-232. http://dx.doi.org/10.1016/j.techfore.2019.01.005.

Baker, R. C., & Brobst, R. W. (1978). Conditional double sampling. International Journal of Quality Technology, 10(4), 150-154. http://dx.doi.org/10.1080/00224065.1978.11980843.

Barnard, G. A. (1959). Control charts and stochastic processes. International Journal of the Royal Statistical Society, 21(2), 239-271.

Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of CUSUM rum length. Biometrika, 59(3), 539-549. http://dx.doi.org/10.1093/biomet/59.3.539.

Capizzi, G., & Masarotto, G. (2012). An enhance control charts for startup processes and short runs. International Journal of Quality Technology and Quantitative Management, 9(2), 189-202. http://dx.doi.org/10.1080/16843703.2012.11673285.

Castagliola, P., & Maravelakis, P. E. (2011). A CUSUM control chart for monitoring the variance when parameters are estimated. International Journal of Statistical Planning and Inference, 141(4), 1463-1478. http://dx.doi.org/10.1016/j.jspi.2010.10.013.

Castagliola, P., Celano, G., & Chen, G. (2009). The exact run length distribution and design of the S2 chart when the in-control variance is estimated. International Journal of Reliability Quality and Safety Engineering, 16(1), 23-38. http://dx.doi.org/10.1142/S0218539309003277.

Castagliola, P., Celano, G., & Fichera, S. (2013). Comparison of the X chart ant the t chart when the parameters are estimated. Quality Technology & Quantitative Management, 10(1), 1-16. http://dx.doi.org/10.1080/16843703.2013.11673305.

Castagliola, P., & Wu, S. (2012). Design of the c and np charts when the parameters are estimated. International Journal of Reliability, Quality and Safety Engineering, 19(2), 1-16. https://doi.org/10.1142/S0218539312500106.

Castillo, E. D., & Montgomery, D. (1996). A general model for the optimal economic design of X charts used to control short or long run processes. IIE Transactions, 28(3), 193-201. http://dx.doi.org/10.1080/07408179608966266.

Castillo, E. D., Grayson, J. M., Montgomery, D. C., & Runger, G. C. (1996). A review of statistical process control techniques for short run manufacturing systems. Communications in Statistics, 25(11), 2723-2737. http://dx.doi.org/10.1080/03610929608831866.

Celano, G., & Chakraborti, S. (2021). A distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions. International Journal of Production Research, 59(20), 6069-6086. http://dx.doi.org/10.1080/00207543.2020.1802079.

Celano, G., Castagliola, P., & Trovato, E. (2012). The economic performance of a CUSUM t control chart for monitoring short production runs. International Journal of Quality Technology and Quantitative Management, 9(4), 329-354. http://dx.doi.org/10.1080/16843703.2012.11673297.

Celano, G., Castagliola, P., Fichera, S., & Nenes, G. (2013). Performance of t control charts in short runs with unknown shift sizes. Computers & Industrial Engineering, 64(1), 56-68. http://dx.doi.org/10.1016/j.cie.2012.10.003.

Celano, G., Castagliola, P., Trovato, E., & Fichera, S. (2010). Shewhart and EWMA t control charts for short production runs. Quality and Reliability Engineering International, 27(1), 313-326.

Chakraborti, S. (2000). Run length, average run length and false alarm rate of Shewhart X chart: exact derivations by conditioning. Communications in Statistics. Simulation and Computation, 29(1), 61-81. http://dx.doi.org/10.1080/03610910008813602.

Chakraborti, S. (2006). Parameter estimation and design considerations in prospective applications of the chart. International Journal of Applied Statistics, 33(4), 439-459. http://dx.doi.org/10.1080/02664760500163516.

Chakraborti, S., Human, S. W., & Graham, M. A. (2008). Phase I, statistical process control charts: an overview and some results. International Journal of Quality and Engineering, 21(1), 52-62. http://dx.doi.org/10.1080/08982110802445561.

Crowder, S. V. (1992). An SPC model for short production runs: minimizing expected costs. Technometrics, 34(1), 64-73. http://dx.doi.org/10.2307/1269553.

Cullen, C. C., & Bothe, D. R. (1989). SPC for short production runs. International Quality Institute, 1, 1960-1963.

Deming, W. E. (1986). Out of the crisis. Cambridge: Massachusetts Institute of Technology.

Duarte, B. P. M., & Saraiva, P. M. (2008). An optimization‐based approach for designing attribute acceptance sampling plans. International Journal of Quality & Reliability Management, 25(8), 824-841. https://doi.org/10.1108/02656710810898630.

Elg, M., Olsson, J., & Dahlgaard, J. J. (2008). Implementing statistical process control: an organization perspective. International Journal of Quality & Reliability Management, 25(6), 545-560. http://dx.doi.org/10.1108/02656710810881872.

Farnum, N. R. (1992). Control charts for short run: nonconstant process and measurement error. Journal of Quality Technology, 24(3), 138-144. http://dx.doi.org/10.1080/00224065.1992.11979384.

García-Díaz, J. C., & Aparisi, F. (2005). Economic design of EWMA control charts using regions of maximum and minimum ARL. IIE Transactions, 37(11), 1011-1021. https://doi.org/10.1080/07408170500232214.

Garvin, D. A. (1993). Manufacturing strategic planning. California Management Review, 35(4), 85-106. http://dx.doi.org/10.2307/41166756.

Grant, E. L. (1965). Statistical quality control (3rd ed.). New York: McGraw Hill.

Graves, S. B., Murphy, D. C., & Ringuest, J. L. (1999). Acceptance sampling versus redundancy as alternative means to achieving goals for system reliability. International Journal of Quality & Reliability Management, 16(4), 362-370. http://dx.doi.org/10.1108/02656719910263724.

Gu, K., Jia, X., & You, H. (2011). A study on t chart for short-run and mixed model productions. Advanced Materials Research, 314-316(), 2478-2481. https://doi.org/10.4028/www.scientific.net/AMR.314-316.2478.

Gu, K., Jia, X., You, H., & Zhang, S. (2014). A t-chart for monitoring multi-variety and small batch production run. International Journal of Quality & Reliability Management, 30(10), 287-299. http://dx.doi.org/10.1002/qre.1496.

Hawkins, D. M., & Olwell, D. H. (1998). Cumulative sum charts and charting improvements. New York: Springer. http://dx.doi.org/10.1007/978-1-4612-1686-5.

Hillier, F. S. (1969). X and R chart control limits based on small number of subgroups. International Journal of Quality Technology, 1(1), 17-26. http://dx.doi.org/10.1080/00224065.1969.11980343.

Ho, L., & Trindade, A. L. (2009). Economic design of an X chart for short run production. International Journal of Production Economics, 120(2), 613-624. http://dx.doi.org/10.1016/j.ijpe.2009.04.012.

Jensen, W. A., Jones-Farmer, L. A., Champ, C. W., & Woodall, W. H. (2006). Effects of parameter estimation on control chart properties: a literature review. International Journal of Quality Technology, 38(4), 349-364. http://dx.doi.org/10.1080/00224065.2006.11918623.

Jones-Farmer, L. A., Woodall, W. H., Steiner, S. H., & Champ, C. W. (2014). An overview of phase I analysis for process improvement and monitoring. International Journal of Quality Technology, 46(3), 265-280. http://dx.doi.org/10.1080/00224065.2014.11917969.

Juran, J. M., & Gryna, F. M. (1988). Quality control handbook (4th ed..). New York: McGraw-Hill.

Kemp, K. W. (1961). The average run length of the cumulative sum chart when a V mask is used. International Journal of the Royal Statistical Society, 23(1), 149-153. http://dx.doi.org/10.1111/j.2517-6161.1961.tb00398.x.

Kanji, G. K. (1994). Total quality management and statistical understanding. Total Quality Management, 5(3), 105-114. https://doi.org/10.1080/09544129400000030.

Khoo, M. B. C., Quah, S. H., Low, H. C., & Ch’ng, C. K. (2005). Short runs multivariate control chart for process dispersion. International Journal of Reliability Quality and Safety Engineering, 12(2), 127-147. http://dx.doi.org/10.1142/S0218539305001732.

Kim, G. C., & Schniederjans, M. J. (2000). Use of short run statistical process control techniques: a comparison of US and Japanese manufacturing. American Journal of Business, 15(1), 21-30. http://dx.doi.org/10.1108/19355181200000002.

Kim, K., Mahmoud, M. A., & Woodall, W. H. (2003). On the monitoring of linear profiles. Journal of Quality Technology, 35(3), 317-328. https://doi.org/10.1080/00224065.2003.11980225.

Korzenowski, A. L., & Werner, L. (2012). Probabilidade de erro do tipo I nas cartas de Shewhart sob não normalidade. Production, 22(4), 807-816. http://dx.doi.org/10.1590/S0103-65132012005000059.

Li, Z., Zou, C., Gong, Z., & Wang, Z. (2014). The computation of average run length and average time to signal: an overview. Journal of Statistical Computation and Simulation, 84(8), 1779-1802. http://dx.doi.org/10.1080/00949655.2013.766737.

Lizarelli, F. L., Bessi, N. C., Oprime, P. C., Amaral, R. M., & Chakraborti, S. (2016). A bibliometric analysis of 50 years of worldwide research on statistical process control. Gestão & Produção, 23(4), 853-870. http://dx.doi.org/10.1590/0104-530x1649-15.

Lucas, J. M., & Saccucci, M. S. (1990). Exponentially Weighted Moving Average control schemes: properties and enhancements. Technometrics, 32(1), 1-12. http://dx.doi.org/10.1080/00401706.1990.10484583.

McCracken, A. K., & Chakraborti, S. (2013). Control charts for joint monitoring of mean and variance: an overview. Quality Technology & Quantitative Management, 10(1), 17-36. https://doi.org/10.1080/16843703.2013.11673306.

Michel, R., & Fogliatto, F. S. (2002). Economic project of adaptive charts for process monitoring. Gestão & Produção, 9(1), 17-31. http://dx.doi.org/10.1590/S0104-530X2002000100003.

Montgomery, D. C. (2014). Introdução ao controle estatístico da qualidade (4. ed.). São Paulo: Editora LTC.

Mood, A. M., Graybill, F. A., & Boes, D. C. (1974). Introduction to the theory of statistics (3. ed.). New York: McGraw-Hill.

Nenes, G., & Tagaras, G. (2007). The economically designed two-sided Bayesian X control chart. European Journal of Operational Research, 183(1), 263-277. http://dx.doi.org/10.1016/j.ejor.2006.09.074.

Oprime, P. C., & Ganga, G. M. D. (2013). A framework for continuous inspection plans using multivariate mathematical methods. Quality and Reliability Engineering International, 29(7), 937-949. http://dx.doi.org/10.1002/qre.1446.

Oprime, P. C., & Mendes, G. H. S. (2017). The X-bar control chart with restriction of the capability indices. International Journal of Quality & Reliability Management, 34(1), 38-52. http://dx.doi.org/10.1108/IJQRM-08-2014-0103.

Oprime, P. C., Lizarelli, F. L., Pimenta, M. L., & Achcar, J. A. (2019). Acceptance X-bar chart considering the sample distribution of capability indices, Cp and Cpk: a practical and economical approach. International Journal of Quality & Reliability Management, 36(6), 875-894. http://dx.doi.org/10.1108/IJQRM-11-2017-0239.

Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1-2), 100-115. http://dx.doi.org/10.2307/2333009.

Psarakis, S., Vyniou, A. K., & Castagliola, P. (2014). Some recent development on the effect of parameter estimation on control chart. International Journal of Quality and Reliability Engineering, 30(8), 1113-1129. http://dx.doi.org/10.1002/qre.1556.

Qin, S. J. (2003). Statistical process monitoring: basics and beyond. International Journal of Chemistry, 17(8‐9), 480-502.

Quesenberry, C. P. (1991). SPC Q charts for start-up processes and short or long runs. International Journal of Quality Technology, 23(3), 213-224. http://dx.doi.org/10.1080/00224065.1991.11979327.

Ryan, T. P. (2011). Statistical methods for quality improvement (3. ed.). New Jersey: Willey.

Samohyl, R. W. (2009). Controle estatístico de qualidade. Rio de Janeiro: Elsevier.

Shepardson, K., Runger, G. C., & Sullo, P. (1992). SPC for short runs using a Kalman filter (Technical report, Decision Sciences and Engineering Systems). Rensselaer Polytechnic Institute.

Shewhart, W. A. (1931). Statistical method from an engineering viewpoint. Journal of the American Statistical Association, 26(175), 262-269. http://dx.doi.org/10.1080/01621459.1931.10502545.

Singh, S., & Prajapati, D. R. (2013). Performance of CUSUM and EWMA charts for serial correlation. International Journal of Total Quality Management, 25(3), 309-324. http://dx.doi.org/10.1108/17542731311307474.

Smith, E. S. (1947). Control charts: introduction to statistical quality control (1st ed.). New York: McGraw Hill.

Sower, V. E., Motwani, J. G., & Savoie, M. J. (1994). Delta charts for short run statistical process control. International Journal of Quality & Reliability Management, 11(6), 50-56. http://dx.doi.org/10.1108/02656719410064658.

Toledo, J. C., Borrás, M. A. A., Mergulhão, R. C., & Mendes, G. H. S. (2013). Qualidade: gestão e métodos. Rio de Janeiro: LTC.

Wasserman, G. S. (1994). Short run SPC using dynamic control chart. Computers & Industrial Engineering, 27(1), 353-356. http://dx.doi.org/10.1016/0360-8352(94)90307-7.

Wiederhold, M., Greipel, J., Ottone, R., & Schmitt, R. (2016). Clustering of similar processes for the application of statistical process control in small batch and job production. International Journal of Metrology and Quality Engineering, 7(4), 404-411. http://dx.doi.org/10.1051/ijmqe/2016018.

Woodall, W. H. (1985). The statistical design of quality control charts. International Journal of Royal Statistical Society, 34(2), 155-160. http://dx.doi.org/10.2307/2988154.

Woodall, W. H. (2000). Controversies and contradictions in statistical process control. International Journal of Quality Technology, 32(4), 341-350. http://dx.doi.org/10.1080/00224065.2000.11980013.

Woodall, W. H., & Montgomery, D. C. (2014). Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology, 46(1), 78-94. http://dx.doi.org/10.1080/00224065.2014.11917955.

Yang, M., Wu, Z., Lee, K. M., & Khoo, M. B. C. (2012). The X control chart for monitoring process shifts in mean and variance. International Journal of Production Research, 50(3), 893-907. https://doi.org/10.1080/00207543.2010.539283.

Yu, J., & Liu, J. (2011). LRProb control chart based on logistic regression for monitoring mean shifts of auto-correlated manufacturing processes. International Journal of Production Research, 49(8), 2301-2326. https://doi.org/10.1080/00207541003694803.
 


Submitted date:
08/05/2021

Accepted date:
12/13/2021

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