Controlling the conditional false alarm rate for the MEWMA control chart
Küçük Resim Yok
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor & Francis Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
An integral part of the design of control charts, including the multivariate exponentially weighted moving average (MEWMA) control chart, is the determination of the appropriate control limits for prospective monitoring. Methods using Markov chain analyses, integral equations, and simulation have been proposed to determine the MEWMA chart limits when the limits are based on a specified in-control average run length (ARL) value. A drawback of the usual approach is that the conditional false alarm rate (CFAR) for these charts varies over time in what might be in an unexpected and undesirable way. We define the CFAR as the probability of a false alarm given no previous false alarm. We do not condition on the results of a Phase I sample, as done by others, in studies of the effect of estimation error on control chart performance. We propose the use of dynamic probability control limits (DPCLs) to keep the CFAR constant over time at a specified value. The CFAR at any time, however, could be controlled to be any specified value using our approach. Using simulation, we determine the DPCLs for the MEWMA control chart being used to monitor the mean vector with an assumed known variance-covariance matrix. We consider cases where the sample size is both fixed and time-varying. For varying sample sizes, the DPCLs adapt automatically to any change in the sample size distribution. In all cases, the CFAR is held closely to a fixed value and the resulting in-control run length performance follows closely to that of the geometric distribution.
Açıklama
Anahtar Kelimeler
Average run length, dynamic probability control limits, exponentially weighted moving average, multivariate quality control, statistical process monitoring, Probability Control Limits, Average Run-Length, Poisson Count Data, Integral-Equation, Arl, Program, Model
Kaynak
Journal Of Quality Technology
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
54
Sayı
5
