The effect of Phase I sample size on the run length performance of control charts for autocorrelated data

Köksal G., Kantar B., Ula T. A., Testik M. C.

JOURNAL OF APPLIED STATISTICS, cilt.35, ss.67-87, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1080/02664760701683619
  • Dergi Adı: JOURNAL OF APPLIED STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.67-87
  • Anahtar Kelimeler: autocorrelated data, sample size, residual chart, EWMAST chart, modified Shewhart chart, ARMA chart, run length, STATISTICAL PROCESS-CONTROL, STATIONARY PROCESS DATA, TIME-SERIES, ESTIMATED PARAMETERS, LIMITS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Traditional control charts assume independence of observations obtained from the monitored process. However, if the observations are autocorrelated, these charts often do not perform as intended by the design requirements. Recently, several control charts have been proposed to deal with autocorrelated observations. The residual chart, modified Shewhart chart, EWMAST chart, and ARMA chart are such charts widely used for monitoring the occurrence of assignable causes in a process when the process exhibits inherent autocorrelation. Besides autocorrelation, one other issue is the unknown values of true process parameters to be used in the control chart design, which are often estimated from a reference sample of in-control observations. Performances of the above-mentioned control charts for autocorrelated processes are significantly affected by the sample size used in a Phase I study to estimate the control chart parameters. In this study, we investigate the effect of Phase I sample size on the run length performance of these four charts for monitoring the changes in the mean of an autocorrelated process, namely an AR(1) process. A discussion of the practical implications of the results and suggestions on the sample size requirements for effective process monitoring are provided.