Controlo Estatístico de Processo em Contextos “Short Run”: Modelo de Decisão
Controlo Estatístico de Processo em Contextos “Short Run”: Modelo de Decisão
Índice
1. Introdução
2. Revisão da literatura
3. Modelo de decisão
4. Caso de estudo
5. Conclusões
Para além de cada vez mais exigirem produtos com melhor qualidade e ao mais baixo custo possível, os clientes procuram também soluções com maiores níveis de personalização. Face a isto, as empresas industriais procuram adoptar sistemas de produção flexíveis, incluindo estratégias de personalização em massa, o que coloca novos e sem precedentes desafios em termos de procedimentos de controlo da qualidade a adoptar. O controlo estatístico do processo (SPC) abrange um amplo leque de métodos para monitorizar o desempenho de processos e detectar situações anómalas no seu comportamento, mas a sua utilização tradicional não fornece soluções adequadas ao exercício das actividades de controlo da qualidade durante a produção de pequenos lotes, no arranque de um processo, ou quando existe uma grande diversidade de artigos a produzir. Situações como estas encontram-se no âmbito da chamada produção de pequenas séries (“short-run”). Vários métodos de SPC têm sido propostos para lidar com diferentes ambientes de “short run”; cada um com as suas vantagens, limitações e especificidades. Este artigo fornece uma revisão da literatura completa e actualizada sobre o tópico, distingue diferentes classes de abordagens de SPC para pequenas séries e, a partir daqui, apresentar um modelo de decisão conducente à selecção do melhor método de “SPC short run” para uma determinada realidade. O modelo foi testado numa empresa têxtil e incorporado numa solução de software.
Pedro Alexandre Marques, licenciado (2001) e doutorado (2013) em Engenharia Industrial pela FCT-NOVA; Six Sigma Black Belt certificado pela American Society for Quality (ASQ); Consultor Sénior no ISQ – Instituto de Soldadura e Qualidade (2006-); Professor Auxiliar na Universidade Lusófona de Humanidades e Tecnologias (2014-); Professor Assistente convidado na Faculdade de Engenharia da Universidade Católica Portuguesa (2008-2012); Membro do Conselho Editorial de publicações nacionais e internacionais, incluindo o International Journal of Business and Industrial Marketing. Orador convidado em diversos eventos; Autor e co-autor de várias publicações, incluindo capítulos de livros; Coordenador do projecto vencedor do Prémio Equipas de Melhoria atribuído pela Associação Portuguesa para a Qualidade (2015); vencedor do Prémio Boléo Tomé para o melhor artigo publicado na revista Qualidade da APQ (2014).
António de Sousa Ribeiro, Mestre em Engenharia Electrotécnica pela Faculdade de Engenharia da Universidade do Porto, Diretor da SISTRADE, S.A. desde Julho de 2000. Participou em vários projetos de investigação, como por exemplo o MAPPLE e acompanhou os projetos PSI, PTI, I9Source e FADIS.
Aminnayeri, M., Torkamani, E.A., Davodi, M. e Ramtin, M. (2010). “Short-run process control based on non-conformity degree”. Proceedings of the World Congress in Engineering, London, UK, 30 June 30 – 2 July of 2010, vol. III, pp. 2273-2276.
Bothe, D.R. (1988). SPC for Short Production Runs, International Quality Institute, Northville, MI.
Calzada, M.E. e Scariano, S.M. (2013). The synthetic t and synthetic EWMA t charts. Quality Technology & Quantitative Management, 10: 37-56.
Capizzi, G. e Masarotto, G. (2012). An enhanced control chart for start-up processes and short runs. Quality Technology & Quantitative Management, 9: 189-202.
Castagliola, P., Celano, G., Fichera, S. e Nenes, G. (2013). The variable sample size t control chart for monitoring short production runs. International Journal on Advanced Manufacturing Technology, 66: 1353-1366.
Celano, G., Costa, A. e Fichera, S. (2008). “One-Sided Bayesian S2 Control Charts for the Control of Process Dispersion in Finite Production Runs”. International Journal of Reliability, Quality and Safety Engineering. 15: 305-327.
Celano, G., Castagliola, P., Trovato, E. e Fichera, S. (2011). Shewhart and EWMA t control charts for short production runs. Quality & Reliability Engineering International, 27: 313-326.
Celano, G., Castagliola, P., Fichera, S. e Nenes, G. (2013). “Performance of t control charts in short runs with unknown shift sizes”. Computers & Industrial Engineering, 64: 56-68.
Chan, L.K. e Cui, H.J. (1996). “Linear Transformation Control Charts for Short Run or Long Run Processes”.
Technical Report, Department of Management Sciences, City University of Hong Kong.
Crowder, S.V. e Eshleman, L. (2000). “Small sample properties of an adaptive filter applied to low volume SPC. Journal of Quality Technology, 33: 29-46.
Del Castillo, E. e Montgomery, D.C. (1994). Short run statistical process control: Q-chart enhancements and alternative methods. Quality and Reliability Engineering International, 10: 87-97.
Elam, M.E. (2001). Investigation, Extension, and Generalization of a Methodology for Two Stage
Short Run Variables Control Charting. Ph.D. Thesis, Department of Industrial Engineering and Management, Oklahoma State University, Stillwater, 276 pp.
Elam, M.E. (2008). Control charts for short production runs. Encyclopedia of Statistics in Quality and Reliability.
Elam, M.E. e Case, K.E. (2001). A computer program to calculate two-stage short-run control chart factors for (X-bar ,R) charts. Quality Engineering. 14: 77-102.
Elam, M.E. e Case, K.E. (2003a). A computer program to calculate two-stage short-run control charts for (Xbar, n) and (Xbar, n ) charts. Quality Engineering. 15: 609-638.
Elam, M.E. e Case, K.E. (2003b). Two-stage short-run (Xbar, n) and (Xbar, n ) control charts. Quality Engineering. 15: 441-448.
Elam, M.E. e Case, K.E. (2004). Two-stage short-run (Xbar, s) control charts. Quality Engineering. 17: 95- 107.
Elam. M.E. e Case, K.E. (2005). A computer program to calculate two-stage short-run control chart factors for (Xbar , s) charts. Quality Engineering. 17: 259-277.
Elam, M.E. e Case, K.E. (2008). Two-stage short-run (X, MR) control charts. Journal of Modern Applied Statistical Methods. 7: 95-107.
Fonseca, D.J., Elam, M.E. e Tibbs, L. (2007). “Fuzzy Short-Run Control Charts”. Mathware & Soft Computing. 14: 81-101.
Garjani, M., Noorossana, R. e Saghaci, A. (2010). “A neural network-based control scheme for monitoring start-up processes and short runs”. International Journal of Advanced Manufacturing Technology. 51: 1023-1032.
Gu, K, Jia, X., You, H. e Zhang, S. (2013). A t-chart for monitoring multi-variety and small batch production run. Quality and Reliability Engineering International. 30: 287-299.
Guo, R. e Dunne, T. (2006). “Grey predictive process control charts”. Communications in Statistics – Theory and Methods. 35: 1857-1868.
Hawkins, D.M. (1987). Self-starting CUSUM charts for location and scale. Journal of the Royal Statistical Society. Series D (The Statistician). 36: 299-316.
Hawkins, D.M., Qiu, P. e Kang, C.W. (2003). The change point model for statistical process control. Journal of Quality Technology. 35: 355-366.
Hawkins, D.M. e Zamba, K.D (2005a). A change point model for a shift in variance. Journal of Quality Technology. 37: 21-31.
Hawkins, D.M. e Zamba, K.D. (2005b). Statistical process control for shifts in mean or variance using a change point formulation. Technometrics, 47: 164-172.
Hawkins, D.M., Qiu, P. e Zamba, K.D. (2008). “Change-point Methods”. Encyclopedia of Quality and Reliability. Wiley.
He, F., Jiang, W. e Shu, L. (2008). Improved self-starting control charts for short runs. Quality Technology & Quantitative Management. 3: 289-308.
Hillier, F.S. (1969). X-bar and R-chart control limits based on a small number of subgroups. Journal of Quality Technology. 1:17-26.
Huang, Q., Fang, W. e Liu, J. (2011). “Comparison of Two Quality Control Models for Short Run Process Based on Bayesian Analysis”. Proceedings of the International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. Xian, China, June 17-19, pp. .
Jarošová, E. (2012). “Comparison of Two Bayesian Approaches to SPC”. Journal of Applied Mathematics. 5: 259 268.
Jaupi, L., Herwindiati, D.E., Durant, P. e Ghorbanzadeh, D. (2013). “Short-run multivariate control charts for process mean and variability”. Proceedings of the World Congress on Engineering. London, UK, 3-5 July 2013, pp. 1-5.
Kawamura, H., Nishina, K., Higashide, M. e Suzuki, T. (2013). Application of Q charts for short run autocorrelated data. International Journal of Innovative Computing, Information and Control. 9: 3667- 3676.
Khoo, M. e Quah, S. (2002). “Proposed short runs multivariate control charts for the process mean. Quality Engineering, 14: 603–621.
Khoo, M.B. e Gan, H.L. (2005). “An improved multivariate short-run control chart based on the CUSUM statistic” Proceedings of the 1st IMT-GT Regional Conference on Mathematics Statistics and Their Applications. Lake Toba, Indonesia, 13-15 June 2005, pp. 287-292.
Khoo, M.B., Quah, S.H, Low, H.C. e Ch’ng, C.K. (2005). “Short Runs Multivariate Control Chart for Process Dispersion”. International Journal of Reliability, Quality and Safety Engineering, 12: 127-147.
Koning, A.J. e Does, R.J (2000). CUSUM Charts for Preliminary Analysis of Individual Observations. Journal of Quality Technology. 32: 122-132.
Li, Z., Luo, Y. e Wang, Z. (2010a). CUSUM of Q chart with variable sampling intervals for monitoring the process mean. International Journal of Production Research. 48: 5861-4876.
Li, Z. e Wang, Z. (2010b). Adaptive CUSUM of Q chart. International Journal of Production Research, 48: 1287-1301.
Nedumaran, G. e Leon, J.V. (1998). “p-chart Control Limits Based on a Small Number of Subgroups. Quality Engineering. 11: 1-9.
Makis, V. (2009). “Multivariate bayesian process control for a finite production run”. European Journal of Operational Research, 194: 795-806.
Marques, P.A., Cardeira, C.B., Paranhos, P., Ribeiro, S. e Goouveia, H. (2010). Selection of the most suitable statistical process control approach for short production runs: a decision-model. International Journal of Information and Education Technology. 5: 303-310.
Montgomery, D.C. (2009). Introduction to Statistical Quality Control. Sixth Edition, John Wiley & Sons.Hoboken, NJ.
Quesenberry, C.P. (1991a). SPC Q Charts for start-up processes and short or long runs. Journal of Quality Technology. 23: 213-224.
Quesenberry, C.P. (1991b). SPC Q charts for a Binomial parameter p: short or long runs. Journal of Quality Technology, 23: 213-224.
Quesenberry, C.P. (1991c). SPC Q charts for a Poisson parameter l: short or long runs. Journal of Quality Technology. 23: 239-246.
Quesenberry, C.P. (1995a). On properties of Q-Charts for variables. Journal of Quality Technology. 27: 184- 203.
Quesenberry, C.P. (1995b). On properties of Binomial Q-charts for attributes”, Journal of Quality Technology.27: 204-213.
Quesenberry, C.P. (1995c). On properties of Poisson Q-charts for attributes”, Journal of Quality Technology.27: 293-303.
Quesenberry, C.P. (1995d). Geometric Q charts for high quality processes. Journal of Quality Technology. 27: 304-315.
Quesenberry, C.P. (2001). “The multivariate short-run snapshot Q chart”. Quality Engineering. 13: 679-683. Pan, R. (2002). Statistical Process Adjustment Methods for Quality Control in Short-Run Manufacturing. Ph.D.
Thesis. Department Industrial and Manufacturing Engineering, Pennsylvania State University, 218 pp. Pereira, Z.L. e Requeijo, J.G. (2008). Qualidade: Planeamento e Controlo Estatístico de Processos. Editora Prefácio, Lisboa.
Pyzdek, T. (1993). Process control for short and small runs. Quality Progress. 26: 51–60.
Requeijo, J.G. (2003). Técnicas Avançadas do Controlo Estatístico do Processo. Tese de Douramento em Engenharia Industrial, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, 313 pp.
Ryan, T.P. (2011). Statistical Methods for Quality Improvement. Third Edition, John Wiley & Sons, Hoboken, NJ.
Snoussi, A. (2011). “SPC for short-run multivariate autocorrelated processes”. Journal of Applied Statistics. 38: 2303-2312.
Snoussi, A., Ghourabi, M.E. e Limam, M. (2005). ”On SPC for short run autocorrelated data”.
Communications in Statistics – Simulation and Computation. 34: 219-234.
Snoussi, A. e Limam, M. (2007). “The change point model: SPC method for short run autocorrelated data”. Quality Technology & Quantitative Management, 4: 313-329.
Sower, V.E, Motwani, J.G. e Savoie, M.J. (1994). “d charts for short run statistical process control,” International Journal of Quality & Reliability Management. 11: 50-56.
Tang, P.F. (1996). Statistical Process Control with Special Reference to Multivariate Processes and Short Runs. Ph.D. Thesis. Department of Computer & Mathematical Sciences, Victoria University of Technology, Australia, 251 pp.
Tang, P.F. e Barnett, N. (1994). “A Comparison of Mean and Range Charts with Pre-Control having a Particular Reference to Short Run Production”. Quality and Reliability Engineering International, 10: 477-485.
Torng, C., Liao, H., Lee, P. e Wu, J. (2009). “Performance Evaluation of a Tukey’s Control Chart in Monitoring Gamma Distribution and Short Run Processes”. Proceedings of the International MultiConference of Engineers and Computer Scientists, Hong Kong, 18-20 March.
Tsiamyrtzis, P. e Hawkins, D.M. (2008). A bayesian EWMA method to detect jumps at the start-up phase of a process”. Quality and Reliability Engineering International. 24: 721-735.
Wheeler, D. (1991). Short Run SPC, SPC Press, Knoxville, TN.
Wright, C.M. (2003). “A note on the joint estimation method for short-run autocorrelated data”. Communications in Statistics – Simulation and Computation, 32: 1105-1114.
Wright, C.M., Booth, D.E. e Hu, M.Y. (2001). “Joint estimation: SPC method for short-run autocorrelated data”. Journal of Quality Technology, 33: 365-377.
Wu, B. e Yu, J. (2010). “A neural network ensemble model for on-line monitoring of process mean and variance shifts in correlated processes”. Expert Systems with Applications. 37: pp. 4058-4065.
Yang, C.H. e Hillier, F.S. (1970). Mean and variance control chart limits based on a small number of subgroups. Journal of Quality Technology, 2: 9-16.
Zamba, K.D. e Hawkins, D.M. (2006). A multivariate change point model for statistical process control. Technometrics. 48: 539-549.
Zhang, L., Chen, G. e Castagliola, P. (2009). On t and EWMA t charts for monitoring changes in the process mean. Quality and Reliability Engineering International, 25: 933-945.
Zhou, C., Zou, C., Zhang, Y. e Wang, Z. (2009). “Nonparametric control chart based on change-point model”. Statistical Papers. 50: pp. 13-28.
Zou, C. e Tsung, F. (2010). “Likelihood ratio-based distribution-free EWMA control charts. Journal of Quality Technology. 42: 174-196.
Zou, C., Wang, Z. e Tsung, F. (2012). A spatial rank-based multivariate EWMA control chart. Naval Research Logistics. 59: 91-82.
Cartas de controlo; Controlo estatístico do processo (SPC); Modelo de decisão; Short-Run.