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| 多変量CUSUM管理図× | CUSUM管理図× | |
|---|---|---|
| 分野 | 統計学 | 統計学 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1988 | 1954 |
| 提唱者≠ | Robert Crosier | E. S. Page |
| 種類≠ | Multivariate sequential monitoring chart | Statistical process control chart for small shifts |
| 原典≠ | Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291–303. DOI ↗ | Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100–115. DOI ↗ |
| 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 |
| 関連≠ | 2 | 4 |
| 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. |
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