Variable sample size of exponentially weighted moving average chart with measurement errors

Document Type : Article

Authors

1 Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, P.O. Box 18151-159, Iran

2 Departement Qualite Logistique Industrielle et Organisation, IUT, Universite de Nantes and LS2N UMR CNRS 6004, Nantes, France

Abstract

The effect of measurement errors on adaptive Shewhart charts have been investigated by several researchers. However, the effect of measurement errors on the performance of variable sample size EWMA control charts has not so far been investigated. In this paper, the performance of the VSS EWMA chart in the presence of measurement errors is investigated using a linear covariate error model and a Markov chain method. It is shown that the performance of the VSS EWMA chart is significantly affected by the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of the VSS EWMA chart is also investigated. Moreover, the performance of the VSS EWMA control chart is compared with several other control charts in the presence of measurement errors. At last, an illustrative example is presented to show the application of the VSS EWMA control chart with measurement errors.

Keywords


References:
1- Prabhu SS, Runger GC and Keats JB. “ X ̅ chart with adaptive sample sizes”, International Journal of Production Research, 31(12), pp. 2895-2909 (1993).
2- Costa AFB. “X ̅ charts with variable sampling size”, Journal of Quality Technology, 26(3), 155–163 (1994).
3- Reynolds MR. “Variable sampling interval control charts with sampling at fixed times”. IIE Transactions, 28(6), pp. 497–510 (1996).
4- Amiri F, Noghondarian K and Noorossana R. “Economic-statistical design of adaptive X ̅ control chart: a Taguchi loss function approach”, Scientia Iranica. Transaction E: Industrial Engineering, 21(3), p. 1096-1104 (2014).
5- Prabhu SS, Montgomery DC and Runger GC. “A combined adaptive sample size and sampling interval X ̅ control scheme”, Journal of Quality Technology, 26(3), pp. 164–176 (1994).
6- Costa A F B. “X̄ chart with variable sample size and sampling intervals”, Journal of Quality Technology, 29(2), pp. 197–204 (1997).
7- Costa AFB. “X̄ charts with variable parameters”. Journal of Quality Technology, 31(4), pp. 408-416 (1999).
8- Saccucci MS, Amin RW and Lucas JM. “Exponentially weighted moving average control schemes with variable sampling intervals”, Communications in Statistics-Simulation and Computation, 21(3), pp. 627-657 (1992).
9- Reynolds MR and Arnold JC. “EWMA control charts with variable sample sizes and variable sampling intervals”, IIE transactions, 33(6), pp. 511-530 (2001).
10- Castagliola P, Celano G and Fichera S. “Evaluation of the statistical performance of a variable sampling interval R EWMA control chart” Quality Technology & Quantitative Management, 3(3), pp. 307-323 (2006).
11- Castagliola P, Celano G, Fichera S and Giuffrida F. “A variable sampling interval S2-EWMA control chart for monitoring the process variance”, International Journal of Technology Management, 37(1-2), pp. 125-146 (2006).
12- Kazemzadeh RB, Karbasian M and Babakhani MA. “An EWMA t chart with variable sampling intervals for monitoring the process mean”, The International Journal of Advanced Manufacturing Technology, 66(1-4), pp. 125-139 (2013).
13- Tran K.P, Castagliola P, Nguyen TH and Cuzol A. “The efficiency of the VSI exponentially weighted moving average median control chart”, Proceeding of 24th ISSAT International Conference on Reliability and Quality in Design, Toronto, Canada (2018).
14- Ugaz W, Sánchez I and Alonso AM. “Adaptive EWMA control charts with time-varying smoothing parameter”, The International Journal of Advanced Manufacturing Technology, 93(9-12), pp. 3847-3858 (2017).
15- Tang A, Castagliola P, Sun J, and Hu X. “Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length.” Quality Technology & Quantitative Management, 16(4), pp. 439-45, (2018). 
16- Amiri A, Nedaie A and Alikhani M. “A new adaptive variable sample size approach in EWMA control chart”, Communications in Statistics-Simulation and Computation, 43(4), pp. 804-812 (2014).
17- Capizzi G and Masarotto G. “An adaptive exponentially weighted moving average control chart”, Technometrics, 45(3), pp. 199-207 (2003).
18- Ong LV, Teoh WL, Khoo MBC, Chong ZL and Yeong WC. “A study on the variable sampling interval EWMA chart when the process parameters are unknown”, In Journal of Physics: Conference Series, 1132(1), pp.012084 IOP Publishing (2018).
19- Tran KP, Castagliola P and Celano G. “Monitoring the ratio of two normal variables using EWMA type control charts”, Quality and Reliability Engineering International, 32(2), pp. 1853–1869 (2015).
20- Chong, ZL, Castagliola P, Khoo MB, Ong LV and Teoh WL. “The Variable Sampling Interval EWMA X¯ Chart with Estimated Process Parameters”. Journal of Testing and Evaluation, published online: https://doi.org/10.1520/JTE20180058
21- Haq A, Khoo MBC. “An adaptive multivariate EWMA chart”, Computers and Industrial Engineering, 131, pp. 459, (2019)
22- Bennett CA. “Effect of measurement error on chemical process control”, Industrial Quality Control, 10(4), pp. 17–20 (1954).
23- Linna KW and Woodall WH. “Effect of measurement error on Shewhart control charts”, Journal of Quality Technology, 33(2), pp. 213-222 (2001).
24- Kanazuka T. “The effect of measurement error on the power of X ̅-R charts”, Journal of Quality Technology, 18(2), pp. 91-95 (1986).
25- Costa AF and Castagliola P. “Effect of measurement error and autocorrelation on the  chart”, Journal of Applied Statistics, 38(4), pp. 661-673 (2011).
26- Hu X, Castagliola P, Sun J and Khoo M.B. “The effect of measurement errors on the synthetic   chart”, Quality and Reliability Engineering International, 31(8), pp. 1769-1778 (2014).
27- Linna KW, Woodall WH and Busby KL. “The performance of multivariate control charts in the presence of measurement error”, Journal of Quality Technology, 33(3), pp. 349-355 (2018).
28- Hu X, Castagliola P, Sun J and Khoo M.B. “The performance of variable sample size   chart with measurement errors”, Quality and Reliability Engineering International; 32(3), pp. 969-983 (2015).
29- Hu X, Castagliola P, Sun J and Khoo M.B. “Effect of measurement errors on the VSI    chart”, European J. Industrial Engineering, 10(2), pp. 224–242 (2016).
30- Sabahno H and Amiri A. “The effect measurement errors on the performance of variable sample size and sampling interval  control chart”, International Journal of Engineering-Transactions A: Basics, 30(7), pp. 995-1004 (2017).
31- Sabahno H, Amiri A and Castagliola P. “Performance of the variable parameters   control chart in presence of measurement errors”, Journal of Testing and Evaluation, 47(1), pp. 480-497 (2019).
32- Sabahno H, Amiri A and Castagliola P. “Optimal performance of the variable sample sizes Hotelling’s T2 control chart in the presence of measurement errors”, Quality Technology & Quantitative Management,  16(5), pp. 588-612 (2019).
33- Sabahno H, Amiri A and Castagliola P. “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), pp. 1785-1799 (2018).
34- Ghashghaei R, Bashiri M, Amiri A and Maleki MR. “Effect of measurement error on joint monitoring of process mean and variability under ranked set sampling”, Quality and Reliability Engineering International, 32(8), pp. 3035-3050 (2016).
35- Amiri A, Ghashghaei R and Maleki MR. “On the effect of measurement errors in simultaneous monitoring of mean vector and covariance matrix of multivariate processes”. Transactions of the Institute of Measurement and Control, 40(1), pp. 318-330 (2018).
36- Maleki MR, Amiri A and Ghashghaei R. “Simultaneous monitoring of multivariate process mean and variability in the presence of measurement error with linearly increasing variance under additive covariate model”, International Journal of Engineering-Transactions A: Basics, 29(4), pp. 471-480 (2016).
37- Nguyen, HD, Nguyen QT, Tran KP, and Ho DP.” On the performance of VSI Shewhart control chart for monitoring the coefficient of variation in the presence of measurement errors”. Published online in The International Journal of Advanced Manufacturing Technology, (2019). doi: 10.1007/s00170-019-03352-7.
38- Tran K P, Heuchenne C and Balakrishnan, N. “On the performance of coefficient of variation charts in the presence of measurement errors”. Quality and Reliability Engineering International, 35(1), 329-350, (2019).
39- Stemann D and Weihs C. “The EWMA-X-S-control chart and its performance in the case of precise and imprecise data”, Statistical Papers, 42(2), pp. 207–223 (2001).
40- Maravelakis P, Panaretos J and Psarakis S. “EWMA chart and measurement error”, Journal of Applied Statistics ; 31(4):445-455 (2004).
41- Yang S F, Ho HW and Rahim MA. “Effects of measurement error on controlling two dependent process steps”, Economic Quality Control, 22(1), pp. 127–139 (2007).
42- Haq A, Brown J, Moltchanova E and Al-Omari AI. “Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes”, Journal of Statistical Computation and Simulation, 85(6), pp. 1224-1246 (2014).
43- Abbasi SA. “On the performance of EWMA chart in the presence of two-component measurement error”, Quality Engineering, 22(3), pp. 199-213 (2010).
44- Abbasi SA. “Exponentially weighted moving average chart and two‐component measurement error”, Quality and Reliability Engineering International, 32(2), pp. 499-504 (2015).
45- Saghaei A, Fatemi Ghomi SMT and Jaberi S. “Economic design of exponentially weighted moving average control chart based on measurement error using genetic algorithm”, Quality and Reliability Engineering International, 30(8), pp. 1153-1163(2014).
46- Cheng X.B and Wang FK. “The performance of EWMA median and CUSUM median control charts for a normal process with measurement errors”, Quality and Reliability Engineering International, 34(2), pp. 203-213 (2017).
47- Tang A, Castagliola P, Sun J and Hu X. “The effect of measurement errors on the adaptive EWMA chart”, Quality and Reliability Engineering International, 34(4), pp. 609-630 (2018).
48- Maleki M.R, Amiri A and Castagliola P. “Measurement errors in statistical process monitoring: a literature review”, Computers & Industrial Engineering, 103, pp. 316-329 (2016).
49- Lucas JM and Saccucci MS. “Exponentially weighted moving average control schemes: properties and enhancements”, Technimetrics, 32, pp. 1–12 (1990).
50- Montgomery DC and Runger GC. “Gauge capability and designed experiments. Part I: basic methods”. Quality Engineering, 6(1), pp. 115–135 (1994).
Volume 28, Issue 4
Transactions on Industrial Engineering (E)
July and August 2021
Pages 2386-2399
  • Receive Date: 17 January 2019
  • Revise Date: 01 October 2019
  • Accept Date: 10 November 2019