In this paper, we present a new control chart for exponentially distributed quality characteristics using variable transformation and exponentially weighted moving average (EWMA). The in-control and out-of-control average run lengths (ARLs) are derived using the normal approximation. The parameters of the proposed control chart are determined by considering the target in-control ARL. The efficiency of the proposed control chart is discussed in terms of ARLs over the existing control chart without using EWMA. The application of the proposed control chart is discussed with the help of a real example.
AbbasiSA (2012) A new nonparametric EWMA sign control chart. Expert Systems with Applications39: 8503.
2.
Acosta-MejiaCA (1998) Monitoring reduction in variability with the range. IIE Transactions30: 515–523.
3.
AhmadLAslamMChi-HyuckJun (2014) Designing of X-bar control charts based on process capability index using repetitive sampling, Transactions of the Institute of Measurement and Control36(3): 367–374.
4.
Al-RefaieA (2011) Evaluating measurement and process capabilities using tabular algorithm procedure with three quality measures. Transactions of the Institute of Measurement and Control34(5): 604–614.
5.
BorrorCMKeatsJBMontgomeryDC (2003) Robustness of the time between events CUSUM. International Journal of Production Research41(5): 3435–3444.
6.
CastagliolaPCelanoGFicheraS (2006a) Monitoring process variability using EWMA. In: PhamH (ed.) Handbook of Engineering Statistics. New York: Springer, pp. 291–325.
7.
CastagliolaPCelanoGFicheraS. (2006b) A variable sampling interval S2 -EWMA control chart for monitoring the process variance. International Journal of Technology Management37(1/2): 125–146.
8.
ChampCWWoodallWH (1987) Exact results for Shewhart control charts with supplementary runs rules. Technometrics29(4): 343–399.
9.
ChanLYXieMGohTN (2000) Cumulative quantity control charts for monitoring production processes. International Journal of Production Research38(2): 397–408.
10.
ChengC-SChenP-W (2010) An ARL-unbiased design of time between events control charts with runs rules. Journal of Statistical Computation and Simulation81(7): 857–871.
11.
FlowersJ (2007) Statistical Process Control Methods in Public Health Intelligence. York: Association of Public Health Observatories.
12.
GanFF (1994) Design of optimal exponential CUSUM control charts. Journal of Quality Technology26(2): 109–124.
13.
GanFF (1998) Designs of one- and two-sided exponential EWMA charts. Journal of Quality Technology30: 55–69.
14.
JensenWABryceGRReynoldsMRJr (2008) Design issues for adaptive control charts. Quality and Reliability Engineering International24(4): 429–445.
15.
JoekesSBarbosaEP (2013) An improved attribute control chart for monitoring non-conforming proportion in high quality processes. Control Engineering Practice21: 107–412.
16.
JohnsonNLKotzS (1970) Continuous Univariate Distributions – I. New York: Wiley.
17.
JonesLAChampCW (2002) Phase I control charts for times between events. Quality and Reliability Engineering International18: 479–488.
18.
KaminskyFCBenneyanJCDavisRD. (1992) Statistical control charts based on a geometric distribution. Journal of Quality Technology24(2): 63–69.
19.
KittlitzRG (1999) Transforming the exponential for SPC applications. Journal of Quality Technology31: 301–308.
20.
KlevensRMEdwardsJRRichardsCL. (2007) Estimating health care- associated infections and deaths in U.S. hospitals, 2002. Public Health Reports122: 160–166.
21.
LiSYTangLCNgSH (2010) Nonparametric CUSUM and EWMA control charts for detecting mean shifts. Journal of Quality Technology42(2): 209–226.
22.
LiuJYXieMGohTN. (2006) A comparative study of exponential time between events charts. Quality Technology and Quantitative Management3(3): 347–359.
23.
LowryCAChampCWWoodallWH (1995) The performance of control charts for monitoring process variation. Communications in Statistics – Simulation and Computation24(2): 409–437.
24.
LucasJMSaccucciMS (1990) Exponentially weighted moving average control schemes: properties and enhancements. Technometrics32(1): 1–12.
25.
MohammedMA (2004) Using statistical process control to improve the quality of health care. Quality and Safety in Health Care13(4): 243–245.
26.
MohammedMALaneyD (2006) Over dispersion in health care performance data: Laney’s approach. Quality and Safety in Health Care15(5): 383–384.
27.
MontgomeryDC (2009) Introduction to Statistical Quality Control. New York: Wiley.
28.
NelsonLS (1984) The Shewhart control chart-tests for special causes. Journal of Quality Technology16: 238–239.
29.
NelsonLS (1994) A control chart for parts-per-million nonconforming items. Journal of Quality Technology26: 239–240.
30.
SantiagoESmithJ (2013) Control charts based on the exponential distribution: adapting runs rules for the t chart. Quality Engineering25(2): 85–96.
31.
SchillingEGNelsonPR (1976) The effect of non-normality on the control limits of X charts. Journal of Quality Technology8: 183–188.
32.
SpiegelMR (1992).Theory and Problems of Probability and Statistics. New York: McGraw-Hill, p. 119.
33.
StoumbosZGReynoldsJrMR (2000) Robustness to non-normality and autocorrelation of individuals control charts. Journal of Statistical Computation and Simulation66(2): 145–187.
34.
SzarkaJLWoodallWH (2011) A review and perspective on surveillance of Bernoulli processes. Quality and Reliability Engineering International27(6): 735–752.
35.
WoodallWH (2006) The use of control charts in health-care and public health surveillance. Journal of Quality Technology38: 89–104.
36.
XieMGohTNKuralmaniV (2002a) Statistical Models and Control Charts for High-Quality Processes. Boston, MA: Kluwer Academic Publisher.
37.
XieMGohTNRanjanP (2002b) Some effective control chart procedures for reliability monitoring. Reliability Engineering & System Safety77: 143–150.
38.
YangS (2013) Using a new VSI EWMA average loss control chart to monitor changes in the difference between the process mean and target and/or the process variability, Applied Mathematical Modeling37: 16–17.
39.
YangSChengTCHungYC. (2012) A new chart for monitoring service process mean. Quality and Reliability Engineering International28(4): 377–386.
40.
YangSLinJChengSW (2011) A new nonparametric EWMA sign control chart. Expert Systems with Applications38: 6239–6243.
41.
ZhangCWXieMGohTN (2005) Economic design of exponential charts for time between events monitoring. International Journal of Production Research43(23): 5019–5032.
42.
ZhangHYXieMGohTN. (2011) Economic design of time-between-events control chart system. Computers and Industrial Engineering60(4): 485–492.
43.
ZhangLChenGCastagliolaP (2009) On t and EWMA t charts for monitoring changes in the process mean. Quality and Reliability Engineering International25(8): 933–945.
