Advertisement

Evaluation of the Succession Measures of the Simultaneous Perturbation Stochastic Approximation Algorithm for the Optimization of the Process Capability Index

  • Juan Carlos Castillo García
  • Jesús Everardo Olguín TiznadoEmail author
  • Everardo Inzunza González
  • Claudia Camargo Wilson
  • Juan Andrés López Barreras
  • Enrique Efren García Guerrero
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 209)

Abstract

Simultaneous Perturbation Stochastic Approximation (SPSA) algorithms are alternative methods for optimizing systems where the relationship between the dependent variables and independent variables of a process is unknown. The objective of this research is to determine the optimum succession measure of SPSA that maximizes the Process Capability Index (PCI) through second order regression models by means of experimental simulation. The results show that three out of the ten combinations of the succession measures evaluated in SPSA yield optimum values that maximize the PCI according to the Six Sigma Methodology (DMAIC—Define, Measure, Analyze, Improve, and Control), this because the values have behaviors classified as world-class, this is, processes that generate less than 3.4 defects per million opportunities, which improves customer satisfaction and reduces cycle time and defects.

Keywords

SPSA PCI Optimization Six Sigma DMAIC 

Notes

Acknowledgements

This work was supported by the research project approved at the 18th Internal Call 580 for Research Projects by UABC, with number 485. The researcher J. C. C. G. was supported for his postgraduate studies at Ph.D. level by CONACyT. Thanks to PRODEP (Professional Development Program for Professors) for supporting the new generations and for innovating the application of knowledge.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Abdolshah, M., Ismail, Y.B., Yusuff, R.M., Hong, T.S.: Process capability analysis using Monte Carlo simulation. In: International Conference on Information Management and Engineering, 2009. ICIME’09, pp. 335–339. IEEE (2009)Google Scholar
  2. 2.
    Abdulsadda, A.T., Iqbal, K.: An improved SPSA algorithm for system identification using fuzzy rules for training neural networks. Int. J. Autom. Comput. 8(3), 333–339 (2011).  https://doi.org/10.1007/s11633-011-0589-xGoogle Scholar
  3. 3.
    Ahmad, S., Abdollahian, M., Zeephongsekul, P.: Process capability for a non-normal quality characteristics data. In: Fourth International Conference on Information Technology, 2007. ITNG’07, pp. 420–424. IEEE (2007)Google Scholar
  4. 4.
    Altaf, M.U., Heemink, A.W., Verlaan, M., Hoteit, I.: Simultaneous perturbation stochastic approximation for tidal models. Ocean Dyn. 61(8), 1093–1105 (2011).  https://doi.org/10.1007/s10236-011-0387-6Google Scholar
  5. 5.
    Andradóttir, S.: A stochastic approximation algorithm with varying bounds. Oper. Res. 43(6), 1037–1048 (1995)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Aslam, M., Wu, C.W., Azam, M., Jun, C.H.: Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. Appl. Math. Model. 37(3), 667–675 (2013)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Bai, B., Ju, F., Zhang, J.: Study on process capability index improvement model. In: 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC), pp. 1543–1545. IEEE (2011)Google Scholar
  8. 8.
    Baltcheva, I., Cristea, S., Vázquez-Abad, F.J., De Prada, C.: Simultaneous perturbation stochastic approximation for real-time optimization of model predictive control. In: Proceedings of the First Industrial Simulation Conference (ISC 2003), Valencia, Spain, June 2003, pp. 533–537 (global optimization for model predictive control) (2003)Google Scholar
  9. 9.
    Bangerth, W., Klie, H., Matossian, V., Parashar, M., Wheeler, M.F.: An autonomic reservoir framework for the stochastic optimization of well placement. Cluster Comput. 8(4), 255–269 (2005)Google Scholar
  10. 10.
    Bartkute, V., Sakalauskas, L.: Simultaneous perturbation stochastic approximation of nonsmooth functions. Eur. J. Oper. Res. 181, 1174–1188 (2005)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Brittanti, S., Lovera, M., Moiraghi, L.: Application of non-normal process capability indices to semiconductor quality control. IEEE Trans. Semicond. Manuf. 11(2), 296–303 (1998)Google Scholar
  12. 12.
    Broadie, M., Cicek, D., Zeevi, A.: General bounds and finite-time improvement for the Kiefer-Wolfowitz stochastic approximation algorithm. Oper. Res. 59(5), 1211–1224 (2011)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Brooks, O.: Solving discrete resource allocation problems using the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. In: SpringSim, no 3, pp. 55–62 (2007)Google Scholar
  14. 14.
    Cao, X.: Preliminary results on non-bernoulli distribution of perturbations for simultaneous perturbation stochastic approximation. In: Proceedings of the 2011 American Control Conference, pp. 2669–2670 (2011).  https://doi.org/10.1109/acc.2011.5991550
  15. 15.
    Chin, D.C.: Comparative study of stochastic algorithms for system optimization based on gradient approximations. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 27(2), 244–249 (1997)Google Scholar
  16. 16.
    Cipriani, E., Florian, M., Mahut, M., Nigro, M.: A gradient approximation approach for adjusting temporal origin–destination matrices. Transp. Res. Part C: Emerg. Technol. 19(2), 270–282 (2011).  https://doi.org/10.1016/j.trc.2010.05.013Google Scholar
  17. 17.
    de Felipe, D., Benedito, E.: A review of univariate and multivariate process capability indices. Int. J. Adv. Manuf. Technol. 92(5–8), 1687–1705 (2017)Google Scholar
  18. 18.
    Dellino, G., Kleijnen, J.P., Meloni, C.: Robust optimization in simulation: Taguchi and Krige combined. INFORMS J. Comput. 24(3), 471–484 (2012)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Ding, S., Xia, N., Wang, P., Li, S., Ou, Y.: Optimization algorithm based on SPSA in multi-channel multi-radio wireless monitoring network. In: 2015 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, pp. 517–524 (2015).  https://doi.org/10.1109/cyberc.2015.84
  20. 20.
    Ebadi, M., Shahriari, H.: A process capability index for simple linear profile. Int. J. Adv. Manuf. Technol. 64(5–8), 857–865 (2013)Google Scholar
  21. 21.
    Finck, S., Beyer, H.G.: Performance analysis of the simultaneous perturbation stochastic approximation algorithm on the noisy sphere model. Theoret. Comput. Sci. 419, 50–72 (2012)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Fu, M.C., Ho, Y.C.: Using perturbation analysis for gradient estimation, averaging and updating in a stochastic approximation algorithm. In: Proceedings of the 20th Conference on Winter Simulation, pp. 509–517 (1988)Google Scholar
  23. 23.
    García, M.R.: Algoritmo de Aproximaciones Estocásticas para el Mejoramiento del Índice de Capacidad Real de Procesos CPK. Tesis de Doctorado en Ingeniería Industrial, Instituto Tecnológico de Cd. Juárez (2000)Google Scholar
  24. 24.
    Gedi, M.A., Bakar, J., Mariod, A.A.: Optimization of supercritical carbon dioxide (CO2) extraction of sardine (Sardinella lemuru Bleeker) oil using response surface methodology (RSM). Grasas Aceites 66(2), 074 (2015)Google Scholar
  25. 25.
    Haghighat Sefat, M., Muradov, K.M., Elsheikh, A.H., Davies, D.R.: Proactive optimization of intelligent-well production using stochastic gradient-based algorithms. SPE Reserv. Eval. Eng. 19(02), 239–252 (2016)zbMATHGoogle Scholar
  26. 26.
    Hosseinifard, S.Z., Abbasi, B., Ahmad, S., Abdollahian, M.: A transformation technique to estimate the process capability index for non-normal processes. Int. J. Adv. Manuf. Technol. 40(5–6), 512 (2009)Google Scholar
  27. 27.
    Ito, K., Dhaene, T.: Adaptive initial step size selection for Simultaneous Perturbation Stochastic Approximation. SpringerPlus 5(1), 200 (2016).  https://doi.org/10.1186/s40064-016-1823-3Google Scholar
  28. 28.
    Jalali, H., Nieuwenhuyse, I.V.: Simulation optimization in inventory replenishment: a classification. IIE Trans. 47(11), 1217–1235 (2015)Google Scholar
  29. 29.
    Jianfeng, Y.: Process capability evaluation in skew distributed processes based on SWV method. In: International Conference on Wireless Communications, Networking and Mobile Computing, 2007. WiCom 2007, pp. 5919–5922. IEEE (2007)Google Scholar
  30. 30.
    Kane, V.E.: Process capability indices. J. Qual. technol. 18(1), 41–52 (1986)Google Scholar
  31. 31.
    Kashif, M., Aslam, M., Jun, C.H., Al-Marshadi, A.H., Rao, G.S.: The efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals. Arab. J. Sci. Eng. 42(11), 4941–4955 (2017)zbMATHGoogle Scholar
  32. 32.
    Khong, S.Z., Tan, Y., Manzie, C., Nešić, D.: Extremum seeking of dynamical systems via gradient descent and stochastic approximation methods. Automatica 56, 44–52 (2015)MathSciNetzbMATHGoogle Scholar
  33. 33.
    Kotz, S., Johnson, N.L. Process capability indices—a review, 1992–2000. J. Qual. Technol. 34(1), 2–19 (2002)Google Scholar
  34. 34.
    L’Ecuyer, P., Giroux, N., Glynn, P.W.: Stochastic optimization by simulation: numerical experiments with the M/M/1 queue in steady-state. Manage. Sci. 40(10), 1245–1261 (1994)zbMATHGoogle Scholar
  35. 35.
    Lee, K.K., Ro, Y.C., Han, S.H.: Tolerance optimization of a lower arm by using genetic algorithm and process capability index. Int. J. Precis. Eng. Manuf. 15(6), 1001–1007 (2014)Google Scholar
  36. 36.
    Lin, C.J., Pearn, W.L.: Process selection for higher production yield based on capability index Spk. Qual. Reliab. Eng. Int. 26(3), 247–258 (2010)Google Scholar
  37. 37.
    Lofthouse, T.: The Taguchi loss function. Work Study 48(6), 218–223 (1999)Google Scholar
  38. 38.
    Maryak, J.L., Chin, D.C.: Global random optimization by simultaneous perturbation stochastic approximation. IEEE Trans. Autom. Control 53, 780–783 (2008)MathSciNetzbMATHGoogle Scholar
  39. 39.
    McClary, D.W., Syrotiuk, V.R., Kulahci, M.: Steepest-ascent constrained simultaneous perturbation for multiobjective optimization. ACM Trans. Model. Comput. Simul. 21(1), 1–22 (2010).  https://doi.org/10.1145/1870085.1870087Google Scholar
  40. 40.
    Méndez-González, L.C., Rodríguez-Picón, L.A., Quezada-Carreón, A.E., Romero-López, R., Garcia, V.: Process capability index for AC transformer under electrical harmonics. Electr. Eng. 100(2), 347–353 (2018)Google Scholar
  41. 41.
    Miranda, A.K., Del Castillo, E.: Robust parameter design optimization of simulation experiments using stochastic perturbation methods. J. Oper. Res. Soc. 62(1), 198–205 (2011)Google Scholar
  42. 42.
    Montgomery, D.C.: Design and Analysis of Experiments. Wiley (2008)Google Scholar
  43. 43.
    Olguín, J.: Algoritmo de aproximaciones estocásticas para la optimización de procesos industriales. Ingeniería e investigación 31(3), 100–111 (2011)Google Scholar
  44. 44.
    Parnianifard, A., Azfanizam, A.S., Ariffin, M.K.A., Ismail, M.I.S.: An overview on robust design hybrid metamodeling: advanced methodology in process optimization under uncertainty. Int. J. Ind. Eng. Comput. 1–32 (2017)Google Scholar
  45. 45.
    Pearn, W.L., Shiau, J.J., Tai, Y.T., Li, M.Y.: Capability assessment for processes with multiple characteristics: a generalization of the popular index Cpk. Qual. Reliab. Eng. Int. 27(8), 1119–1129 (2011)Google Scholar
  46. 46.
    Prashanth, L.A., Bhatnagar, S., Fu, M., Marcus, S.: Adaptive system optimization using random directions stochastic approximation. IEEE Trans. Autom. Control 62(5), 2223–2238 (2017)MathSciNetzbMATHGoogle Scholar
  47. 47.
    Radenković, M.S., Stanković, M.S., Stanković, S.S.: On stochastic extremum seeking via adaptive perturbation-demodulation loop. J. Optim. Theory Appl. 179(3), 1008–1024 (2018)MathSciNetzbMATHGoogle Scholar
  48. 48.
    Ramakrishnan, B., Sandborn, P., Pecht, M.: Process capability indices and product reliability. Microelectron. Reliab. 41(12), 2067–2070 (2001)Google Scholar
  49. 49.
    Reardon, B.E., Lloyd, J.M., Perel, R.Y.: Tuning missile guidance and control algorithms using simultaneous perturbation stochastic approximation. Johns Hopkins APL Tech. Digest 29(1), 85–100 (2010)Google Scholar
  50. 50.
    Rodriguez, R.N.: Discussion-process capability indices—a review, 1992–2000. J. Qual. Technol. 34(1), 28–31 (2002)Google Scholar
  51. 51.
    Ros-Roca, X., Montero, L., Schneck, A., Barceló, J.: Investigating the performance of SPSA in simulation-optimization approaches to transportation problems. Transp. Res. Procedia 34, 83–90 (2018)Google Scholar
  52. 52.
    Sadegh, P., & Spall, J.C.: Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation. In: Proceedings of the 1997 American Control Conference (Cat. No. 97CH36041), vol. 6, pp. 3582–3586 (1997).  https://doi.org/10.1109/acc.1997.609490
  53. 53.
    Seyedpoor, S.M., Salajegheh, J., Salajegheh, E., Gholizadeh, S.: Optimal design of arch dams subjected to earthquake loading by a combination of simultaneous perturbation stochastic approximation and particle swarm algorithms. Appl. Soft Comput. 11(1), 39–48 (2011).  https://doi.org/10.1016/j.asoc.2009.10.014Google Scholar
  54. 54.
    Shiau, J.J.H., Hung, H.N., Chiang, C.T.: A note on Bayesian estimation of process capability indices. Stat. probab. lett. 45(3), 215-224 (1999)MathSciNetzbMATHGoogle Scholar
  55. 55.
    Sidorov, K.A., Richmond, S., Marshall, D.: An efficient stochastic approach to groupwise non-rigid image registration. In: 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 2208–2213 (2009).  https://doi.org/10.1109/cvpr.2009.5206516
  56. 56.
    Śliwiński, P., Wachel, P.: A simple model for on-sensor phase-detection autofocusing algorithm. J. Comput. Commun. 1(06), 11 (2013)Google Scholar
  57. 57.
    Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 37(3), 332–341 (1992)MathSciNetzbMATHGoogle Scholar
  58. 58.
    Spall, J.C.: Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Trans. Aerosp. Electron. Syst. 34(3), 817–823 (1998)Google Scholar
  59. 59.
    Spall, J.C.: An overview of the simultaneous perturbation method for efficient optimization. Johns Hopkins APL Tech. Digest 19(4), 482–492 (1998)Google Scholar
  60. 60.
    Spall, J.C.: A stochastic approximation algorithm for large-dimensional systems in the Kiefer-Wolfowitz setting. In: Proceedings of the 27th IEEE Conference on Decision and Control, 1988, pp. 1544–1548. IEEE (1988)Google Scholar
  61. 61.
    Spall, J.C.: Stochastic optimization. In: Handbook of Computational Statistics, pp. 173–201. Springer, Berlin, Heidelberg (2012)Google Scholar
  62. 62.
    Stoumbos, Z.G.: Process capability indices: overview and extensions. Nonlinear Anal.: Real World Appl. 3(2), 191–210 (2002)MathSciNetzbMATHGoogle Scholar
  63. 63.
    Tang, S., Wang, F.Y.: A PCI-based evaluation method for level of services for traffic operational systems. IEEE Trans. Intell. Transp. Syst. 7(4), 494–499 (2006)MathSciNetGoogle Scholar
  64. 64.
    Venkatesh, Y.V., Kassim, A.A., Zonoobi, D.: Medical Image Reconstruction from Sparse Samples Using Simultaneous Perturbation Stochastic Optimization, pp. 3369–3372. National University of Singapore, Singapore (2010)Google Scholar
  65. 65.
    Wang, L.-F., Shi, L.-Y.: Simulation optimization: a review on theory and applications. Acta Automatica Sinica 39(11), 1957–1968 (2013)Google Scholar
  66. 66.
    Wang, Q.: Stochastic approximation for discrete optimization of noisy loss measurements. In: 2011 45th Annual Conference on Information Sciences and Systems, pp. 1–4 (2011)Google Scholar
  67. 67.
    Wu, C.W., Pearn, W.L., Kotz, S.: An overview of theory and practice on process capability indices for quality assurance. Int. J. Prod. Econ. 117(2), 338–359 (2009)Google Scholar
  68. 68.
    Yum, B.J., Kim, K.W.: A bibliography of the literature on process capability indices: 2000–2009. Qual. Reliab. Eng. Int. 27(3), 251–268 (2011)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Juan Carlos Castillo García
    • 1
  • Jesús Everardo Olguín Tiznado
    • 1
    Email author
  • Everardo Inzunza González
    • 1
  • Claudia Camargo Wilson
    • 1
  • Juan Andrés López Barreras
    • 2
  • Enrique Efren García Guerrero
    • 1
  1. 1.Faculty of Engineering, Architecture, and DesignAutonomous University of Baja CaliforniaEnsenadaMexico
  2. 2.Faculty of Chemical Sciences and EngineeringAutonomous University of Baja CaliforniaTijuanaMexico

Personalised recommendations