c chart

Each point is a count: how many defects were found in one period's fixed amount of work. The centre line is the average count. Because counts of rare events behave in a known way, the limits come straight from that average: three times its square root either side.

One item can carry several defects, and each one counts. That is the difference from a p chart, which counts each failed item once.

Use it when you count defects and the amount of opportunity is the same every period: the same number of records audited, the same length of report checked, the same number of rooms inspected. Errors per audit, complaints per thousand contacts at steady volume, faults per inspection round.

If the amount of work checked changes from period to period, use a u chart, which divides each count by the amount checked and plots the rate. If what matters is whether each item passed or failed, not how many things were wrong with it, use a p chart. And if the counts are large, in the hundreds, an individuals chart of the counts often fits the data better than the c chart's assumption.

Average the counts to get the centre line. The upper limit is the centre line plus three times its square root; the lower limit is the centre line minus three times its square root, and if that comes out below zero, the lower limit is zero. With small averages it usually does, which means only a high count can signal on its own; a fall has to show as a run below the centre line.

A case management team audited 100 records each week for 20 weeks and counted every error it found: a missing date, a wrong code, an unsigned note. The figures are illustrative, built to show the method.

The average is 5.0 errors a week. The upper limit is 11.71, and the lower limit works out at minus 1.71, so it is set to zero. Week 15 found 13 errors, above the limit: a special cause. Every other week sits between 2 and 7, with no long run on either side of the centre line.

Week 15 is worth a conversation; weeks 4 and 5, with five and seven errors, are not. If the team wanted fewer errors overall, the chart says that chasing individual weeks will not get there: the process produces about five errors per hundred records as a matter of course, and only a change to the process itself, such as a required field or a checklist at the point of entry, will move the centre line.

Two steps: the average count, and the limits from it. Stated in words first, then written out, then worked with the 20 weeks above.

One row per period with its count. Average the counts, take the square root of the average, and work out the two limits. Draw the counts as a line with the centre and limits as flat lines. Keep the amount checked the same every period, and write it on the chart; if it has to change, switch to a u chart.

In Measure it sets the baseline for an error count, and it often feeds a Pareto chart: the c chart shows how many defects there are and whether the count is stable; a Pareto chart of the same defects by type shows which kinds to work on first.