On the effect of measurement errors and auto-correlation on the performance of Hotelling’s T2 control chart

Document Type : Research Paper

Authors

1 Department of Industrial Engineering, Shahed University, Tehran, Iran

2 Department of Industrial Engineering, Semnan University, Semnan, Iran

Abstract

Independency of observations is one of the fundamental assumptions in control charts. However, in some processes this assumption is violated and data are auto-correlated. Also, it is assumed that the measurement errors are absent in measurement system while, this assumption is usually violated. The existence of the auto-correlation and measurement errors causes the poor performance of the control charts. In other words, the average run length in the case of out-of-control(OC) situations increases in the presence of auto-correlation and measurement errors. In this paper, the effect of auto-correlation and measurement errors on the performance of Hotelling’s T2 control charts in Phase II in multivariate normal processes is investigated in terms of average run length(ARL) criterion. The first order auto-regressive model as auto-correlation structure between observations within each sample is discussed in this paper. To decrease the effect of auto-correlation and measurement errors on the performance of the Hotelling’s T2 control chart, jump strategy and multiple measurements methods are applied, respectively. The effect of auto-correlation and measurement errors, individually and simultaneously, as well as the performance of the suggested methods to address these effects is appraised through simulation studies and a numerical example. The effect of number of measurements and jumps on the ARL values of the proposed control chart is also evaluated. Results show the acceptable performance of the multiple measurements and jumps methods in diminishing the effect of measurement errors and auto-correlation, respectively. At last, a real case is presented to show the application of the proposed scheme.

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References

Abbasi, S. A. (2010). On the performance of EWMA chart in the presence of two-component measurement error. Quality Engineering, 22(3): 199-213.
Alwan, L. C. & Radson, D. (1992). Time-series investigation of subsample mean charts. IIE Transactions, 24(5): 66-80.
Aparisi, F. (1996). Hotelling’s T2 control chart with adaptive sample sizes. International Journal of Production Research, 34(10), 2853–2862.
Chattinnawat, W., & Bilen, C. (2017). Performance analysis of Hotelling’s T2 under multivariate inspection errors. Quality Technology & Quantitative Management, 14(3), 249-268.
Costa, A. F. B. and P. Castagliola (2011). Effect of measurement error and autocorrelation on the chart Journal of Applied Statistics, 38(4): 661-673.
Ding, G. and L. Zeng (2015). On the effect of measurement errors in regression-adjusted monitoring of multistage manufacturing processes. Journal of Manufacturing Systems, 36: 263-273.
Franco, B. C., Castagliola, P., Celano, G. & Costa, A. F. B. (2014). A new sampling strategy to reduce the effect of autocorrelation on a control chart. Journal of Applied Statistics, 41(7): 1408-1421.
Goswami, A. & Dutta, H. N. (2014). Studies on EWMA Control Chart in Presence of Autocorrelation. International Journal of Scientific & Engineering Research, 5(1): 871-877.
Kalgonda, A. & KulkarniU, S. (2004). Multivariate quality control chart for autocorrelated processes. Journal of Applied Statistics, 31(3): 317-327.
Kazemzadeh, R., Noorossana, R. & Amiri, A. (2010). Phase II monitoring of autocorrelated polynomial profiles in AR(1) processes. Scientia Iranica. Transaction E, Industrial Engineering, 17(1): 12-24.
Khedmati, M. & Niaki, S. T. A. (2016). Phase II monitoring of general linear profiles in the presence of between‐profile autocorrelation. Quality and Reliability Engineering International, 32(2): 443-452.
Leoni, R. C., Costa, A. F. B., Franco, B. C. & Machado, M. A. G. (2015). The skipping strategy to reduce the effect of the autocorrelation on the T2 chart’s performance. The International Journal of Advanced Manufacturing Technology, 80(9-12): 1547-1559.
Linna, K. W. and W. H. Woodall (2001). Effect of measurement error on Shewhart control charts. Journal of Quality Technology, 33(2): 213-222.
Linna, K. W., et al. (2001). The performance of multivariate control charts in the presence of measurement error." Journal of Quality Technology, 33(3): 349-355.
Maravelakis, P., et al. (2004). EWMA chart and measurement error. Journal of Applied Statistics, 31(4): 445-455.
 Maravelakis, P. E. (2012). Measurement error effect on the CUSUM control chart. Journal of Applied Statistics, 39(2): 323-336.
Noorossana, R. and Y. Zerehsaz (2015). Effect of measurement error on phase II monitoring of simple linear profiles. The International Journal of Advanced Manufacturing Technology, 79(9): 2031-2040.
Rakhmawati, D. Y., Kim, K. J., & Sumiati. (2020). Performance comparison of generalized confidence interval and modified sampling distribution approaches for assessing one-sided capability indices with gauge measurement errors. Published online in Communications in Statistics-Theory and Methods, doi: 10.1080/03610926.2020.1752729.
Sabahno, H., Amiri, A. & Castagliola, P. (2019a). Optimal performance of the variable sample sizes Hotelling’s T2 control chart in the presence of measurement errors. Quality Technology & Quantitative Management, 16(5): 588-612.
Sabahno, H., Amiri, A. & Castagliola, P. (2019b). Performance of the variable parameters  control chart in presence of measurement errors. Journal of Testing and Evaluation, 47(1): 480-497.
Sabahno, H., Amiri, A. & Castagliola, P. (2018). Evaluating the effect of measurement errors on the performance of the variable sampling intervals Hotelling's T2 control charts. Quality and Reliability Engineering International, 34 (8): 1785-1799.
Soleimani, P. & Noorossana, R. (2014). Monitoring multivariate simple linear profiles in the presence of between profile autocorrelation. Communications in Statistics-Theory and Methods, 43(3): 530-546.
Soleimani, P., Noorossana, R. & Niaki, S. (2013). Monitoring autocorrelated multivariate simple linear profiles. The International Journal of Advanced Manufacturing Technology, 67(5-8): 1857-1865.
Soleimani, P., Noorossana, R. & Amiri, A. (2009). Simple linear profiles monitoring in the presence of within profile autocorrelation. Computers & Industrial Engineering, 57: 1015-1021.
Shishebori, D., & Zeinal Hamadani, A. (2010). The effect of gauge measurement capability and dependency measure of process variables on the MCp. Journal of Industrial and Systems Engineering, 4(1), 59-76.
Xiaohong, L. and W. Zhaojun (2009). The CUSUM control chart for the autocorrelated data with measurement error. Chinese Journal of Applied Probability and Statistics, 25(5): 461-474.
Journal of Industrial and Systems Engineering
Volume 13, Issue 3
July 2021
Pages 193-215

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History

  • Receive Date: 22 January 2021
  • Revise Date: 13 March 2021
  • Accept Date: 27 March 2021

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