{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "VYM8AJ8111"
    }
  ],
  "body": "\n## Summary\n\nCUSUM, short for cumulative sum, is a sequential procedure for detecting a change in the distribution of a stream of observations.\nIt adds up evidence for a change and resets the sum to zero whenever it becomes negative.\nIt raises an alarm when the sum crosses a threshold.\nE. S. Page introduced it in 1954, and it is the standard solution of the [[change detection|Z5H8ZZHVMC]] problem in quality control.\n\n## Explanations\n\n### L1 human\n\nPicture a machine that fills bottles with $500$ ml on average, and suppose a fault would raise the average.\nAfter each bottle, add how much it exceeds $500$ ml plus a small allowance, and subtract when it falls short, but never let the running total go below zero.\nWhile the machine is fine, the total keeps hitting zero and stays small.\nAfter a fault, the excesses pile up and the total soon crosses the alarm level.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "62L10",
      "62P30"
    ],
    "name": "CUSUM",
    "same_as": {
      "wikidata": "Q1024555",
      "wikipedia": "CUSUM"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/CUSUM"
      }
    ],
    "tag": "1VXZHAHT6K"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/1VXZHAHT6K/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/1VXZHAHT6K.md",
  "msc": [
    "62L10",
    "62P30"
  ],
  "name": "CUSUM",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/1VX/1VXZHAHT6K.md",
  "status": null,
  "tag": "1VXZHAHT6K",
  "uri": "m2://1VXZHAHT6K",
  "url": "https://tamnd.github.io/math2/wiki/cusum/",
  "writing": {
    "tag": "1VXZHAHT6K",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}