手法を比較

	多変量CUSUM管理図	CUSUM管理図	多変量EWMA管理図
分野	統計学	統計学	統計学
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1988	1954	1992
提唱者	Robert Crosier	E. S. Page	Lowry, Woodall, Champ & Rigdon
種類	Multivariate sequential monitoring chart	Statistical process control chart for small shifts	Multivariate sequential monitoring chart
原典	Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291–303.	Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100–115.	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.
別名	Multivariate Cumulative Sum Chart, MCUSUM Control Chart, Crosier MCUSUM Scheme, Çok Değişkenli CUSUM Kontrol Grafiği	cumulative sum chart, CUSUM control chart, Page's CUSUM, kümülatif toplam kontrol kartı	Multivariate Exponentially Weighted Moving Average Chart, MEWMA Control Chart, Vector EWMA Chart, Çok Değişkenli EWMA Kontrol Grafiği
関連	2	4	2
概要	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.	The cumulative sum (CUSUM) control chart, introduced by E. S. Page in 1954, monitors a process by accumulating the deviations of observations from a target value rather than judging each point in isolation. Because small persistent shifts add up over time, the running sum makes them visible far sooner than a Shewhart chart, making CUSUM the tool of choice for detecting small, sustained changes in the process mean.	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.