×
Yazdi, Ahmad Ahmadi; Hamadani, Ali Zeinal; Gavareshki, Mohammad Hosein Karimi; Amiri, Amirhossein

Phase II monitoring of multivariate profiles with estimated parameters and optimal phase I subgroups. (English) Zbl 1497.62367

Commun. Stat., Simulation Comput. 50, No. 10, 2858-2884 (2021).
Summary: In this paper, we investigate the effect of parameter estimation from in-control Phase I samples on the in-control and out-of-control performance of the four Phase II control charts used for monitoring multivariate multiple linear profiles. These methods are evaluated in terms of out-of-control performance using corrected limits. The monitoring approaches investigated are then compared using the statistical properties of the ARL distribution. Furthermore, two optimization models are proposed for finding the optimum number of Phase I samples needed to achieve proper parameter estimations of desired accuracy and solved by using a novel hybrid simulation algorithm named HBSO.

Cited in 1 Document

MSC:

62P30 Applications of statistics in engineering and industry; control charts

Keywords:

estimation effect; multivariate multiple linear profiles; phase II; profile monitoring; statistical process monitoring

Software:

spcadjust
Cite Review PDF
Full Text: DOI

References:

[1] Adibi, A.; Montgomery, D. C.; Borror, C. M., A P-value approach for phase II monitoring of multivariate profiles, International Journal of Quality Engineering and Technology, 4, 2, 133-43 (2014) · doi:10.1504/IJQET.2014.060432
[2] Albers, W.; Kallenberg, W. C. M., New corrections for old control charts, Quality Engineering, 17, 3, 457-73 (2005)
[3] Albers, W.; Kallenberg, W. C. M.; Nurdiati, S., Exceedance probabilities for parametric control charts, Statistics, 39, 5, 429-43 (2005) · Zbl 1089.62146 · doi:10.1080/02331880500310181
[4] Aly, A. A.; Mahmoud, M. A.; Hamed, R., The performance of the multivariate adaptive exponentially weighted moving average control chart with estimated parameters, Quality and Reliability Engineering International, 32, 3, 957-67 (2016) · doi:10.1002/qre.1806
[5] Aly, A. A.; Mahmoud, M. A.; Woodall, W. H., A comparison of the performance of phase ii simple linear profile control charts when parameters are estimated, Communications in Statistics - Simulation and Computation, 44, 6, 1432-40 (2015) · Zbl 1331.62377 · doi:10.1080/03610918.2013.821484
[6] Amiri, A.; Jensen, W. A.; Kazemzadeh, R. B., A case study on monitoring polynomial profiles in the automotive industry, Quality and Reliability Engineering International, 26, 5, 509-20 (2009) · doi:10.1002/qre.1071
[7] Atkinson, K. E., An introduction to numerical analysis (2008), New York. NY: John Wiley & Sons, New York. NY
[8] Ayoubi, M.; Kazemzadeh, R.; Noorossana, R., Estimating multivariate linear profiles change point with a monotonic change in the mean of response variables, The International Journal of Advanced Manufacturing Technology, 75, 9-12, 1537-56 (2014) · doi:10.1007/s00170-014-6208-6
[9] Burroughs, T.; Rigdon, S.; Champ, C. (1993)
[10] Castagliola, P.; Maravelakis, P. E.; Figueiredo, F. O., The EWMA median chart with estimated parameters, IIE Transactions, 48, 1, 66-74 (2016) · doi:10.1080/0740817X.2015.1056861
[11] Chakraborti, S., Run length, average run length and false alarm rate of Shewhart X-bar chart: Exact derivations by conditioning, Communications in Statistics-Simulation and Computation, 29, 1, 61-81 (2000) · Zbl 0968.62558 · doi:10.1080/03610910008813602
[12] Champ, C. W.; Jones-Farmer, L. A.; Rigdon, S. E., Properties of the T^2 control chart when parameters are estimated, Technometrics, 47, 4, 437-45 (2005) · doi:10.1198/004017005000000229
[13] Chen, G., The mean and standard deviation of the run length distribution of X charts when control limits are estimated, Statistica Sinica, 7, 3, 789-98 (1997) · Zbl 0876.62086
[14] Ding, Y.; Zeng, L.; Zhou, S., Phase I analysis for monitoring nonlinear profiles in manufacturing processes, Journal of Quality Technology, 38, 3, 199-216 (2006) · doi:10.1080/00224065.2006.11918610
[15] Epprecht, E. K.; Loureiro, L. D.; Chakraborti, S., Effect of the amount of phase I data on the phase II performance of S^2 and S control charts, Journal of Quality Technology, 47, 2, 139-55 (2015) · doi:10.1080/00224065.2015.11918121
[16] Eyvazian, M.; Noorossana, R.; Saghaei, A.; Amiri, A., Phase II monitoring of multivariate multiple linear regression profiles, Quality and Reliability Engineering International, 27, 3, 281-96 (2011) · doi:10.1002/qre.1119
[17] Gandy, A.; Kvaløy, J. T., Guaranteed conditional performance of control charts via bootstrap methods, Scandinavian Journal of Statistics, 40, 4, 647-68 (2013) · Zbl 1283.62239 · doi:10.1002/sjos.12006
[18] Jardim, F. S.; Chakraborti, S.; Epprecht, E. K., \(####\) chart with estimated parameters: the conditional ARL distribution and new insights, Published Online in Production and Operations Management. (2018) · doi:10.1111/poms.12985
[19] Jensen, W. A.; Birch, J. B., Profile monitoring via nonlinear mixed models, Journal of Quality Technology, 41, 1, 18-34 (2009) · doi:10.1080/00224065.2009.11917757
[20] Jensen, W. A.; Jones-Farmer, L. A.; Champ, C. W.; Woodall, W. H., Effects of parameter estimation on control chart properties: A literature review, Journal of Quality Technology, 38, 4, 349-64 (2006) · doi:10.1080/00224065.2006.11918623
[21] Jin, J.; Shi, J., Feature-preserving data compression of stamping tonnage information using wavelets, Technometrics, 41, 4, 327-39 (1999) · doi:10.1080/00401706.1999.10485932
[22] Jones, L. A., The statistical design of EWMA control charts with estimated parameters, Journal of Quality Technology, 34, 3, 277-88 (2002) · doi:10.1080/00224065.2002.11980158
[23] Jones, L. A.; Champ, C. W.; Rigdon, S. E., The performance of exponentially weighted moving average charts with estimated parameters, Technometrics, 43, 2, 156-67 (2001) · doi:10.1198/004017001750386279
[24] Jones, L. A.; Champ, C. W.; Rigdon, S. E., The run length distribution of the CUSUM with estimated parameters, Journal of Quality Technology, 36, 1, 95-108 (2004) · doi:10.1080/00224065.2004.11980254
[25] Kang, L.; Albin, S. L., On-line monitoring when the process yields a linear profile, Journal of Quality Technology, 32, 4, 418-26 (2000) · doi:10.1080/00224065.2000.11980027
[26] Khoo, M. B. C., A control chart based on sample median for the detection of a permanent shift in the process mean, Quality Engineering, 17, 2, 243-57 (2005) · doi:10.1081/QEN-200057329
[27] Kim, K.; Mahmoud, M. A.; Woodall, W. H., On the monitoring of linear profiles, Journal of Quality Technology, 35, 3, 317-28 (2003) · doi:10.1080/00224065.2003.11980225
[28] Loureiro, L. D.; Epprecht, E. K.; Chakraborti, S.; Jardim, F. S., In-control performance of the joint Phase II \(####− S\) control charts when parameters are estimated, Quality Engineering, 30, 2, 253-67 (2018) · doi:10.1080/08982112.2017.1349914
[29] Lowry, C. A.; Woodall, W. H.; Champ, C. W.; Rigdon, S. E., A multivariate exponentially weighted moving average control chart, Technometrics, 34, 1, 46-53 (1992) · Zbl 0761.62144 · doi:10.2307/1269551
[30] Mahmoud, M. A., Phase I analysis of multiple linear regression profiles, Communications in Statistics—Simulation and Computation, 37, 10, 2106-30 (2008) · Zbl 1149.62101 · doi:10.1080/03610910802305017
[31] Mahmoud, M. A., The performance of phase II simple linear profile approaches when parameters are estimated, Communications in Statistics-Simulation and Computation, 41, 10, 1816-33 (2012) · Zbl 1272.62152 · doi:10.1080/03610918.2011.621570
[32] Mahmoud, M. A.; Morgan, J. P.; Woodall, W. H., The monitoring of simple linear regression profiles with two observations per sample, Journal of Applied Statistics, 37, 8, 1249-63 (2010) · Zbl 1511.62466 · doi:10.1080/02664760903008995
[33] Mahmoud, M. A.; Parker, P. A.; Woodall, W. H.; Hawkins, D. M., A change point method for linear profile data, Quality and Reliability Engineering International, 23, 2, 247-68 (2007) · doi:10.1002/qre.788
[34] Mahmoud, M. A.; Woodall, W. H., Phase I analysis of linear profiles with calibration applications, Technometrics, 46, 4, 380-91 (2004) · doi:10.1198/004017004000000455
[35] Maleki, M.; Castagliola, P.; Amiri, A.; Khoo, M. B. C., The effect of parameter estimation on phase II monitoring of Poisson regression profiles, Communications in Statistics-Simulation and Computation, 1-15 (2018) · Zbl 07551930 · doi:10.1080/03610918.2018.1429619
[36] Montgomery, D. C., Introduction to statistical quality control (2005), New York. NY: John Wiley and Sons, New York. NY · Zbl 1059.62125
[37] Montgomery, D. C., Design and analysis of experiments (2017), New York. NY: John Wiley & Sons, New York. NY
[38] Noorossana, R.; Aminmadani, M.; Saghaei, A., Effect of phase I estimation error on the monitoring of simple linear profiles in phase II, The International Journal of Advanced Manufacturing Technology, 84, 5-8, 873-84 (2016)
[39] Noorossana, R.; Eyvazian, M.; Amiri, A.; Mahmoud, M. A., Statistical monitoring of multivariate multiple linear regression profiles in phase I with calibration application, Quality and Reliability Engineering International, 26, 3, 291-303 (2010) · doi:10.1002/qre.1066
[40] Noorossana, R.; Eyvazian, M.; Vaghefi, A., Phase II monitoring of multivariate simple linear profiles, Computers & Industrial Engineering, 58, 4, 563-70 (2010) · doi:10.1016/j.cie.2009.12.003
[41] Parker, P. A.; Finley, T. D., Advancements in aircraft model force and attitude instrumentation by integrating statistical methods, Journal of Aircraft, 44, 2, 436-43 (2007)
[42] Parker, P., Morton, M., Draper, N., and Line, W.. 2001. A single-vector force calibration method featuring the modern design of experiments. AIAA 2001-0170, Paper presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada.
[43] Quesenberry, C. P., The effect of sample size on estimated limits for \(####\) and X control charts, Journal of Quality Technology, 25, 4, 237-47 (1993) · doi:10.1080/00224065.1993.11979470
[44] Rencher, A. C., Methods of multivariate analysis, 492 (2003), New York. NY: John Wiley & Sons, New York. NY
[45] Saghaei, A.; Mehrjoo, M.; Amiri, A., A CUSUM-based method for monitoring simple linear profiles, The International Journal of Advanced Manufacturing Technology, 45, 11-12, 1252-60 (2009) · doi:10.1007/s00170-009-2063-2
[46] Saleh, N. A.; Mahmoud, M. A.; Jones-Farmer, L. A.; Zwetsloot, I.; Woodall, W. H., Another look at the EWMA control chart with estimated parameters, Journal of Quality Technology, 47, 4, 363-82 (2015) · doi:10.1080/00224065.2015.11918140
[47] Steiner, S.; Jensen, W. A.; Grimshaw, S. D.; Espen, B., Nonlinear profile monitoring for oven-temperature data, Journal of Quality Technology, 48, 1, 84-97 (2016) · doi:10.1080/00224065.2016.11918153
[48] Stoer, J.; Bulirsch, R., Introduction to numerical analysis, 12 (2013), New York. NY: Springer Science & Business Media, New York. NY · Zbl 0423.65002
[49] Vaghefi, A.; Tajbakhsh, S. D.; Noorossana, R., Phase II monitoring of nonlinear profiles, Communications in Statistics—Theory and Methods, 38, 11, 1834-51 (2009) · Zbl 1167.62102 · doi:10.1080/03610920802468707
[50] Walker, E.; Wright, S., Comparing curves using additive models, Journal of Quality Technology, 34, 1, 118-29 (2002) · doi:10.1080/00224065.2002.11980134
[51] Wang, K.; Tsung, F., Using profile monitoring techniques for a data‐rich environment with huge sample size, Quality and Reliability Engineering International, 21, 7, 677-88 (2005)
[52] Wilkinson, J. H., The algebraic eigenvalue problem, 87 (1965), Oxford: Clarendon Press Oxford, Oxford · Zbl 0258.65037
[53] Woodall, W. H., Current research on profile monitoring, Production, 17, 3, 420-5 (2007) · doi:10.1590/S0103-65132007000300002
[54] Woodall, W. H. S.; Dan, J.; Montgomery, Douglas, C..; Gupta, S., Using control charts to monitor process and product quality profiles, Journal of Quality Technology, 36, 3, 309-20 (2004) · doi:10.1080/00224065.2004.11980276
[55] Woodall, W. H.; Montgomery, D. C., Some current directions in the theory and application of statistical process monitoring, Journal of Quality Technology, 46, 1, 78-94 (2014) · doi:10.1080/00224065.2014.11917955
[56] Zhang, J.; Li, Z.; Wang, Z., Control chart based on likelihood ratio for monitoring linear profiles, Computational Statistics & Data Analysis, 53, 4, 1440-8 (2009) · Zbl 1452.62983 · doi:10.1016/j.csda.2008.12.002
[57] Zou, C.; Ning, X.; Tsung, F., LASSO-based multivariate linear profile monitoring, Annals of Operations Research, 192, 1, 3-19 (2012) · Zbl 1236.62168 · doi:10.1007/s10479-010-0797-8
[58] Zwetsloot, I. M.; Woodall, W. H., A head-to-head comparative study of the conditional performance of control charts based on estimated parameters, Quality Engineering, 29, 2, 244-53 (2017) · doi:10.1080/08982112.2016.1237651
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.