Statistical process control (SPC) charts monitor process metrics over time against statistically derived control limits. The X̄ chart tracks the process mean; the R-chart tracks variability within subgroups; the CUSUM chart detects small sustained shifts. Points outside control limits signal special causes requiring investigation. They are indispensable in manufacturing, healthcare, and service quality management.

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sample	value	mean	ucl	lcl
1	500.2	500	503	497
2	499.6	500	503	497
3	501.1	500	503	497
4	500.8	500	503	497
5	503.8	500	503	497
6	499.3	500	503	497
7	500.5	500	503	497
8	498.9	500	503	497
9	504.2	500	503	497
10	499.7	500	503	497

{
  "title": {
    "text": "Tablet Weight — X̄ Control Chart (mg)"
  },
  "data": [
    {
      "sample": 1,
      "value": 500.2,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 2,
      "value": 499.6,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 3,
      "value": 501.1,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 4,
      "value": 500.8,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 5,
      "value": 503.8,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 6,
      "value": 499.3,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 7,
      "value": 500.5,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 8,
      "value": 498.9,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 9,
      "value": 504.2,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 10,
      "value": 499.7,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 11,
      "value": 500.4,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 12,
      "value": 501.6,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 13,
      "value": 496.4,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 14,
      "value": 500.1,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    },
    {
      "sample": 15,
      "value": 499.9,
      "mean": 500,
      "ucl": 503,
      "lcl": 497
    }
  ],
  "series": [
    {
      "type": "line",
      "xKey": "sample",
      "yKey": "value",
      "stroke": "#6366f1",
      "strokeWidth": 2,
      "marker": {
        "enabled": true,
        "fill": "#6366f1"
      }
    },
    {
      "type": "line",
      "xKey": "sample",
      "yKey": "mean",
      "stroke": "#10b981",
      "strokeWidth": 1.5,
      "lineDash": [
        4,
        4
      ],
      "marker": {
        "enabled": false
      }
    },
    {
      "type": "line",
      "xKey": "sample",
      "yKey": "ucl",
      "stroke": "#f43f5e",
      "strokeWidth": 1.5,
      "lineDash": [
        6,
        3
      ],
      "marker": {
        "enabled": false
      }
    },
    {
      "type": "line",
      "xKey": "sample",
      "yKey": "lcl",
      "stroke": "#f43f5e",
      "strokeWidth": 1.5,
      "lineDash": [
        6,
        3
      ],
      "marker": {
        "enabled": false
      }
    }
  ],
  "axes": [
    {
      "position": "bottom",
      "title": {
        "text": "Sample Number"
      }
    },
    {
      "position": "left",
      "title": {
        "text": "Weight (mg)"
      }
    }
  ],
  "legend": {
    "enabled": true,
    "position": "bottom"
  }
}

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An X-bar control chart for a manufacturing process. Points outside the UCL/LCL control limits flag out-of-control conditions.

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