An integrated model for optimal selection of quality, maintenance, and production parameters with autocorrelated data

Document Type : Article

Authors

1 Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, P.O. BOX 89195-741, Iran.

2 Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, P.O. BOX 89195-741, Iran

3 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

4 Department of Industrial Engineering, Faculty of Technology and Engineering, University of Qom, Qom, Iran

Abstract

Statistical process monitoring, maintenance policy, and production have commonly been studied separately in the literature, whereas their integration can lead to more favorable conditions for the entire production system. Among all studies on integrated models, the underlying process is assumed to generate independent data. However, there are practical examples in which this assumption is violated because of the extraction of correlation patterns. Autocorrelation causes numerous false alarms when the process is in the in-control state or makes the traditional control charts react slowly to the detection of an out-of-control state. The auto-regressive moving average (ARMA) control chart is selected as an effective tool for monitoring autocorrelated data. Therefore, an integrated model subject to some constraints is proposed to determine the optimal decision variables of the ARMA control chart, economic production quantity, and maintenance policy in the presence of autocorrelated data. Due to the complexity of the model, a particle swarm optimization (PSO) algorithm is applied to search for optimal decision variables. An industrial example and some comparisons are provided for more investigations. Moreover, sensitivity analysis is carried out to study the effects of model parameters on the solution of the economic-statistical design.

Keywords


References:
1. Cheng, L., Tsou, C.-S., and Yang, D.-Y. "Cost -service tradeoff analysis of reorder-point-lot-size inventory models", J. Manuf. Syst., 37, pp. 217-226 (2015).
2. Zhou, X., Wu, C., Li, Y., et al. "A preventive maintenance model for leased equipment subject to internal degradation and external shock damage", Reliab. Eng. Syst. Saf., 154, pp. 1-7 (2016).
3. Lee, P.-H., Torng, C.-C., and Liao, L.-F. "An economic design of combined double sampling and variable sampling interval X control chart", Int. J. Prod. Econ., 138(1), pp. 102-106 (2012).
4. Woodall, W.H. and Montgomery, D.C. "Some current directions in the theory and application of statistical process monitoring", J. Qual. Technol., 46(1), pp. 78- 94 (2014).
5. Jafarian-Namin, S., Goli, A., Qolipour, M., et al. "Forecasting the wind power generation using Box-Jenkins and hybrid artificial intelligence: A case study", Int. J. Energy Sect. Manag., 13(4), pp. 1038- 1062 (2019).
6. Triantafyllopoulos, K. and Bersimis, S. "Phase II control charts for autocorrelated processes", Qual. Technol. Quant. Manag., 13(1), pp. 88-108 (2016).
7. Alwan, L.C. and Roberts, H.V. "The problem of misplaced control limits", J. R. Stat. Soc. C-Appl., 44(3), pp. 269-278 (1995).
8. Psarakis, S. and Papaleonida, G.E.A. "SPC procedures for monitoring autocorrelated processes", Qual. Technol. Quant. Manag., 4(4), pp. 501-540 (2007).
9. Thaga, K. and Sivasamy, R. "Single variables control charts: A further overview", Indian J. Sci. Technol, 8, pp. 518-528 (2015).
10. Alwan, L.C. and Roberts, H.V. "Time-series modeling for statistical process control", J. Bus. Econ. Stat., 6(1), pp. 87-95 (1988).
11. Vasilopoulos, A.V. and Stamboulis, A.P. "Modification of control chart limits in the presence of data correlation", J. Qual. Technol., 10(1), pp. 20-30 (1978).
12. Karaoglan, A.D. "Control chart for autocorrelated processes: a review", Eng. Sci., 5, pp. 243-259 (2010).
13. Osei-Aning, R., Abbasi, S.A., and Riaz, M. "Monitoring of serially correlated processes using residual control charts", Sci. Iran., 24(3), pp. 1603-1614 (2017).
14. Chen, S. and Yu, J. "Deep recurrent neural networkbased residual control chart for autocorrelated processes", Qual. Reliab. Eng. Int., 35(8), pp. 2687-2708 (2019).
15. Wang, F.-K. and Cheng, X.-B. "Exponentially weighted moving average chart with a likelihood ratio test for monitoring autocorrelated processes", Qual. Reliab. Eng. Int., 36(2), pp. 753-764 (2020).
16. Jiang, W., Tsui, K., and Woodall, W.H. "A new SPC monitoring method: The ARMA chart", Technometrics, 42(4), pp. 399-410 (2000).
17. Zhang, N.F. "A statistical control chart for stationary process data", Technometrics, 40(1), pp. 24-38 (1998).
18. Wardell, D.G., Moskowitz, H., and Plante, R.D. "Control charts in the presence of data correlation", Manage. Sci., 38(8), pp. 1084-1105 (1992).
19. Low, C. and Lin, W.Y. "Consideration of weibull distribution under the assignable causes for economic design of the ARMA control chart", J. Qual., 17(5), pp. 365-387 (2010).
20. Lin, S.-N., Chou, C.-Y., Wang, S.-L., et al. "Economic design of autoregressive moving average control chart using genetic algorithms", Expert Syst. Appl., 39(2), pp. 1793-1798 (2012).
21. Costa, A. and Fichera, S. "Economic statistical design of ARMA control chart through a modified fitnessbased self-adaptive  differential evolution", Comput. Ind. Eng., 105, pp. 174-189 (2017).
22. Costa, A. and Fichera, S. "Economic-statistical design of adaptive arma control chart for autocorrelated data", J. Stat. Comput. Simul., 91(3), pp. 623-647 (2021).
23. Ben-Daya, M. "The economic production lot-sizing problem with imperfect production processes and imperfect maintenance", Int. J. Prod. Econ., 76(3), pp. 257-264 (2002).
24. Hadidi, L.A., Al-Turki, U.M., and Rahim, A. "Integrated models in production planning and scheduling, maintenance and quality: a review", Int. J. Ind. Syst. Eng., 10(1), pp. 21-50 (2012).
25. Rahim, M.A. "Joint determination of production quantity, inspection schedule, and control chart design", IIE Trans., 26(6), pp. 2-11 (1994).
26. Rahim, M.A. and Ben-Daya, M. "A generalized economic model for joint determination of production run, inspection schedule and control chart design", Int. J. Prod. Res., 36(1), pp. 277-289 (1998).
27. Rahim, M.A. and Ohta, H. "An integrated economic model for inventory and quality control problems", Eng. Optim., 37(1), pp. 65-81 (2005).
28. Cheng, J.-C. and Chou, C.-Y. "A real-time inventory decision system using Western Electric run rules and ARMA control chart", Expert Syst. Appl., 35(3), pp. 755-761 (2008).
29. Pan, E., Jin, Y., and Wang, Y. "Integration of economic production quantity in optimization design of control chart based on loss function and random process shift", J. Manuf. Technol. Manag., 22(7), pp. 929-946 (2011).
30. Gunay, E.E. and Kula, U. "Integration of production quantity and control chart design in automotive manufacturing", Comput. Ind. Eng., 102, pp. 374-382 (2016).
31. Tagaras, G. "An integrated cost model for the joint optimization of process control and maintenance", J. Oper. Res. Soc., 39(8), pp. 757-766 (1988).
32. Ben-Daya, M. and Rahim, M.A. "Effect of maintenance on the economic design of x-control chart", Eur. J. Oper. Res., 120(1), pp. 131-143 (2000).
33. Wu, J. and Makis, V. "Economic and economicstatistical design of a chi-square chart for CBM", Eur. J. Oper. Res., 188(2), pp. 516-529 (2008).
34. Zhou, W.-H. and Zhu, G.-L. "Economic design of integrated model of control chart and maintenance management", Math.  omput. Modell., 47(11), pp. 1389-1395 (2008).
35. Panagiotidou, S. and Nenes, G. "An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart", Reliab. Eng. Syst. Saf., 94(3), pp. 732-741 (2009).
36. Yin, Z. and Makis, V. "Economic and economicstatistical design of a multivariate Bayesian control chart for condition-based maintenance", IMA J. Manage. Math., 22(1), pp. 47-63 (2010).
37. Ho, L.L. and Quinino, R.C. "Integrating on-line process control and imperfect corrective maintenance: An economical design", Eur. J. Oper. Res., 222(2), pp. 253-262 (2012).
38. Xiang, Y. "Joint optimization of X control chart and preventive maintenance policies: A discrete-time Markov chain approach", Eur. J. Oper. Res., 229(2), pp. 382-390 (2013).
39. Yin, H., Zhang, G., Zhu, H., et al. "An integrated model of statistical process control and maintenance based on the delayed monitoring", Reliab. Eng. Syst. Saf., 133, pp. 323-333 (2015).
40. Abouei Ardakan, M., Zeinal Hamadani, A., Sima, M., et al. "A hybrid model for economic design of MEWMA control chart under maintenance policies", Int. J. Adv. Manuf. Technol., 83(9), pp. 2101-2110 (2016).
41. Rasay, H., Fallahnezhad, M.S., and Zare Mehrjerdi, Y. "An integrated model for economic design of chi-square control chart and maintenance planning", Commun. Stat.-Theor. M., 47(12), pp. 2892-2907 (2018).
42. Salmasnia, A., Namdar, M., and Abdzadeh, B. "An integrated quality and maintenance model for twounit series systems", Commun. Stat.-Simul. Comput., 49(4), pp. 886-917 (2020).
43. Salmasnia, A., Abdzadeh, B., and Rahimi, A. "Joint optimization of double warning T2-Hotelling chart and maintenance policy with multiple assignable causes", J. Stat. Comput. Simul., 90(3), pp. 465-488 (2020).
44. Farahani, A. and Tohidi, H. "Integrated optimization of quality and maintenance: A literature review", Comput. Ind. Eng., 151, p. 106924 (2021).
45. Ben-Daya, M. and Makhdoum, M. "Integrated production and quality model under various preventive maintenance policies", J. Oper. Res. Soc., 49(8), pp. 840-853 (1998).
46. Lam, K.K. and Rahim, M.A. "A sensitivity analysis of an integrated model for joint determination of economic design of control charts, economic production quantity and production run length for a deteriorating production system", Qual. Reliab. Eng. Int., 18(4), pp. 305-320 (2002).
47. Pan, E., Jin, Y., Wang, S., et al. "An integrated EPQ model based on a control chart for an imperfect production process", Int. J. Prod. Res., 50(23), pp. 6999-7011 (2012).
48. Salmasnia, A., Abdzadeh, B., and Namdar, M. "A joint design of production run length, maintenance policy and control chart with multiple assignable causes", J. Manuf. Syst., 42, pp. 44-56 (2017).
49. Salmasnia, A., Kaveie, M., and Namdar, M. "An integrated production and maintenance planning model under VP-T2 Hotelling chart", Comput. Ind. Eng., 118, pp. 89-103 (2018).
50. Salmasnia, A., Hajihosseini, Z., Namdar, M., et al. "A joint determination of production cycle length, maintenance policy, and control chart parameters considering time value of money under stochastic shift size", Sci. Iran., 27(1), pp. 427-447 (2020).
51. Salmasnia, A., Soltani, F., Heydari, E., et al. "An integrated model for joint determination of production run length, adaptive control chart parameters and maintenance policy", J. Ind. Prod. Eng., 36(6), pp. 401-417 (2019).
52. Salmasnia, A., Soltany, F., Noroozi, M., et al. "An economic-statistical model for production and maintenance planning under adaptive non-central chi-square control chart", J. Ind. Syst. Eng., 12, pp. 35-65 (2019).
53. Niaki, S.T.A., Toosheghanian, M., and Gazaneh, F.M. "Economic design of VSI X control chart with correlated non-normal data under multiple assignable causes", J. Stat. Comput. Simul., 83(7), pp. 1279-1300 (2013).
54. Jafarian-Namin, S., Fallahnezhad, M.S., Tavakkoli-Moghaddam, R., et al. "Robust economic-statistical design of acceptance control chart", Journal of Quality Engineering and Production Optimization, 4(1), pp. 55-72 (2019).
55. Kennedy, J. and Eberhart, R. "Particle swarm optimization", Proceedings of ICNN'95-Int. Conf. on Neural Networks, 4, Perth, WA, Australia, pp. 1942- 1948 (1995).
56. Chih, M., Yeh, L.-L., and Li, F.-C. "Particle swarm optimization for the economic and economic statistical designs of the X control chart", chart", Appl. Soft Comput., 11(8), pp. 5053-5067 (2011).
57. Morabi, Z.S., Owlia, M.S., Bashiri, M., et al. "Multiobjective design of X/ control charts with fuzzy process parameters using the hybrid epsilon constraint PSO", Appl. Soft Comput., 30, pp. 390-399 (2015).
58. Salmasnia, A., Namdar, M., and Noroozi, M. "Robust design of a VP-NCS chart for joint monitoring mean and variability in series systems under maintenance policy", Comput. Ind. Eng., 124, pp. 220-236 (2018).
59. Shojaee, M., Jafarian Namin, S., Fatemi Ghomi, S.M.T., et al. "Applying SVSSI sampling scheme on np-chart to decrease the time of detecting shifts- Markov chain approach, and Monte Carlo simulation", Sci. Iran., 29(6), pp. 3369-3387 (2022). DOI: 10.24200/sci.2020.52677.2833.
60. Jafarian-Namin, S., Fallahnezhad, M.S., Tavakkoli-Moghaddam, R., et al. "Robust modeling of acceptance control chart to specify best design parameters", In Studies in Fuzziness and Soft Computing, Shabazova, S., Kacprzyk J., Balas V. and Kreinovich V., Eds., pp. 321-332, Springer, Switzerland (2021).
61. Jafarian-Namin, S., Fallahnezhad, M.S., Tavakkoli-Moghaddam, R., et al. "An integrated quality, maintenance and production model based on the delayed monitoring under the ARMA control chart", J. Stat. Comput. Simul., 91(13), pp. 2645-2669 (2021). DOI:10.1080/00949655.2021.1904241.
Volume 31, Issue 3 - Serial Number 3
Transactions on Industrial Engineering (E)
January and February 2024
Pages 206-227
  • Receive Date: 26 July 2020
  • Revise Date: 31 May 2021
  • Accept Date: 02 August 2021