مقایسهٔ روش‌ها

	نمودار MEWMA	نمودار کنترل میانگین متحرک وزنی نمایی (EWMA)	نمودار MCUSUM
حوزه	آمار	آمار	آمار
خانواده	Process / pipeline	Process / pipeline	Process / pipeline
سال پیدایش	1992	1959	1988
پدیدآور	Lowry, Woodall, Champ & Rigdon	S. W. Roberts	Robert Crosier
نوع	Multivariate sequential monitoring chart	Statistical process control chart for small shifts	Multivariate sequential monitoring chart
منبع بنیادین	Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46–53.	Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239–250.	Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291–303.
نام‌های دیگر	Multivariate Exponentially Weighted Moving Average Chart, MEWMA Control Chart, Vector EWMA Chart, Çok Değişkenli EWMA Kontrol Grafiği	exponentially weighted moving average chart, EWMA control chart, geometric moving average chart, EWMA kontrol kartı	Multivariate Cumulative Sum Chart, MCUSUM Control Chart, Crosier MCUSUM Scheme, Çok Değişkenli CUSUM Kontrol Grafiği
مرتبط	2	3	2
خلاصه	The Multivariate EWMA (MEWMA) control chart is a statistical process monitoring method designed to detect small and sustained shifts in the mean vector of a multivariate process. Introduced by Lowry, Woodall, Champ, and Rigdon in 1992, it extends the univariate EWMA chart to p-dimensional observation vectors by computing an exponentially weighted moving average of successive measurement vectors and charting a Hotelling-type quadratic form against a control limit determined by a target average run length.	The exponentially weighted moving average (EWMA) control chart, introduced by S. W. Roberts in 1959, monitors a process using a weighted average that gives the most recent observation the greatest weight while letting older observations fade geometrically. Like CUSUM, this memory makes it highly effective at detecting small, sustained shifts in the process mean, with a single smoothing parameter λ controlling how much past information the chart retains.	The Multivariate CUSUM (MCUSUM) Chart is a sequential monitoring scheme designed to detect small, persistent mean shifts in a process characterized by multiple correlated quality variables simultaneously. Introduced by Robert Crosier in 1988, it extends the classical univariate CUSUM principle to the multivariate setting by accumulating a vector-valued sum of deviations from the in-control mean, scaled by the process covariance structure, and comparing a scalar norm of that cumulative sum against a control limit.