Abstract
We propose a variable sampling interval exponentially weighted moving average (VSI c EWMA) chart for the average number of nonconformities in the sample, with the objective of improved detection of small to moderate increases in the process nonconformities rate. Using a Markov chain model for the calculations, we obtain optimal designs for this chart as well as for the fixed sampling interval c EWMA chart and compare the performances of the two control schemes in terms of their expected times to signal an out-of-control condition. The designs are optimal in the sense that they minimize the expected delay in the detection of upward shifts of a specified magnitude in the process nonconformities rate, while keeping the false alarm rate and the average sampling frequency at specified levels. The results reveal considerable gains in detection speed with the use of the VSI scheme. The optimal parameters found for each case are tabulated and may be used directly in practice. The results of the analysis, including the optimal design parameters tabulated, can also be extended to a VSI np EWMA chart for improved detection of small to moderate increases in the fraction nonconforming of the process provided that in-control fraction nonconforming is small.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Annadi HP, Keats JB, Runger GC, Montgomery DC (1995) An adaptive sample size CUSUM control chart. Int J Prod Res 33:1605–1616
Arnold JC, Reynolds MR Jr (1994) CUSUM charts with variable sample size and variable interval size. Proceedings, Section on Quality and Productivity, ASA, pp 132–137
Borror CM, Champ CW, Rigdon SE (1998) Poisson EWMA control charts. J Qual Technol 30(4):352–361
Brook D, Evans DA (1972) An approach to the probability distribution of CUSUM run length. Biometrika 59(3):539–549
Capizzi G, Masarotto G (2003) An adaptive exponentially weighted moving average control chart. Technometrics 45(3):199–207
Costa AFB (1994) \( \overline X \) charts with variable sample size. J Qual Technol 26(3):155–163
Costa AFB (1997) \( \overline X \) charts with variable sample size and sampling intervals. J Qual Technol 29(2):197–204
Costa AFB (1998) Joint \( \overline X \) and R charts with variable parameters. IIE Trans 30:505–514
Costa AFB (1998) VSSI Xbar charts with sampling at fixed times. Commun Stat Theory Methods 27(11):2853–2869
Costa AFB (1999) Joint \( \overline X \) and R charts with variable sample size and sampling intervals. J Qual Technol 31:387–397
Costa AFB (1999) \( \overline X \) charts with variable parameters. J Qual Technol 31(4):408–416
Epprecht EK, Costa AFB (2001) Adaptive sample size control charts for attributes. Qual Eng 13(3):465–473
Epprecht EK, Costa AFB, Mendes FCT (2003) Adaptive control charts for attributes. IIE Trans 35(6):567–582
Gan FF (1990) Monitoring observations generated from a binomial distribution using modified exponentially weighted moving average control chart. J Stat Comput Simul 37(1):45–60
Gan FF (1990) Monitoring Poisson observations using modified exponentially weighted moving average control charts. Commun Stat Simul Comput 19(1):103–124
Lucas JM, Saccucci MS (1990) Exponentially weighted moving average control schemes: properties and enhancements. Technometrics 32(1):1–12
Luo H, Wu Z (2002) Optimal np control charts with variable sample sizes or variable sampling intervals. Econ Qual Control 17(1):39–61
Montgomery DC (2001) Introduction to statistical quality control, 4th edn. Wiley, New York
Prabhu SS, Runger GC, Keats JB (1993) \( \overline X \) chart with adaptive sample sizes. Int J Prod Res 31(12):2895–2909
Prabhu SS, Montgomery DC, Runger GC (1994) A combined adaptative sample size and sampling interval \( \overline x \) control scheme. J Qual Technol 26(3):164–176
Reynolds MR Jr (1989) Optimal variable sampling interval control charts. Seq Anal 8:361–379
Reynolds MR Jr (1995) Evaluating properties of variable sampling interval control charts. Seq Anal 14:59–97
Reynolds MR Jr (1996) Shewhart and EWMA variable sampling interval control charts with sampling at fixed times. J Qual Technol 28:199–212
Reynolds MR Jr, Arnold JC (1989) Optimal one-sided Shewhart control charts with variable sampling intervals. Seq Anal 8:51–77
Reynolds MR Jr, Arnold JC (2001) EWMA control charts with variable sample sizes and variable sampling intervals. IIE Trans 33:511–530
Reynolds MR, Amin RW, Arnold JC, Nachlas JA (1988) \( \overline X \) charts with variable sampling intervals. Technometrics 30(2):181–192
Reynolds MR, Amin RW, Arnold JC (1990) CUSUM charts with variable sampling intervals. Technometrics 32:371–384
Runger GC, Pignatiello JJ Jr (1991) Adaptive sampling for process control. J Qual Technol 23:135–155
Runger GC, Montgomery DC (1993) Adaptive sampling enhancements for Shewhart control charts. IIE Trans 25:41–51
Saccucci MS, Amin RW, Lucas JM (1992) Exponentially weighted moving average control schemes with variable sampling intervals. Commun Stat Simul Comput 21:627–657
Sawalapurkar U, Reynolds MR Jr, Arnold JC (1990) Variable sampling size \( \overline X \) control charts. Presented at the Winter Conference of the American Statistical Association, Orlando FL
Tagaras G (1998) A survey of recent developments in the design of adaptive control charts. J Qual Technol 30(3):212–231
Trevanich A, Bourke P (1993) EWMA control charts using attributes data. The Statistician 42(3):215
Vaughan TS (1993) Variable sampling interval np process control chart. Commun Stat Theory Methods 22(1):147–167
Zimmer LS, Montgomery DC, Runger GC (1998) Three-state sample size \( \overline X \) chart. Int J Prod Res 36:733–743
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Epprecht, E.K., Simões, B.F.T. & Mendes, F.C.T. A variable sampling interval EWMA chart for attributes. Int J Adv Manuf Technol 49, 281–292 (2010). https://doi.org/10.1007/s00170-009-2390-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-009-2390-3