手法を比較

	EWMA管理図	CUSUM管理図	シュワート管理図（Xバー / R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	1959	1954	1931
提唱者	S. W. Roberts	E. S. Page	Walter A. Shewhart
種類	Statistical process control chart for small shifts	Statistical process control chart for small shifts	Statistical process control chart for variables
原典	Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239–250.	Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100–115.	Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. D. Van Nostrand Company. ISBN: 978-0-87389-076-2
別名	exponentially weighted moving average chart, EWMA control chart, geometric moving average chart, EWMA kontrol kartı	cumulative sum chart, CUSUM control chart, Page's CUSUM, kümülatif toplam kontrol kartı	X-bar and R chart, Shewhart chart, variables control chart, process control chart
関連	3	4	4
概要	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 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 Shewhart control chart, invented by Walter Shewhart at Bell Labs in the 1920s and set out in his 1931 book, is the foundational tool of statistical process control. It plots a process statistic — typically the subgroup mean (X-bar) and range (R) — over time against a center line and three-sigma control limits, distinguishing the natural common-cause variation inherent in a stable process from special-cause variation that signals something has changed and warrants investigation.