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c Chart

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QXL Stat Tools Tab > Control Charts > c Chart

A c chart monitors the number of defects in each subgroup, where every subgroup represents the same, constant area of opportunity (for example one panel, one hour of production, or one square meter). A single item can have several defects, so this chart counts defects rather than defective items.

When to use it

  • You count defects (not defective items) and the area of opportunity is constant across subgroups.
  • If the area of opportunity varies from subgroup to subgroup, use the u Chart, which plots defects per unit.
  • If the counts are overdispersed relative to the Poisson model, prefer the Laney U' Chart; the c chart reports the σ_Z diagnostic to help you decide.

How it works

The center line is the average defect count over the baseline subgroups. Each point is the raw defect count. Because the area of opportunity is constant, the control limits are straight, placed three standard deviations from the center line by default, with the lower limit held at zero. The Poisson model sets the standard deviation equal to the square root of the mean count. The exact formulas are on the Math Details page.

Options

Data

  • Data source: an Excel range, or GroupBy (each value of the grouping column produces a separate chart).
  • Defects column: the count of defects; selecting several columns produces several charts. Each subgroup is one constant area of opportunity, so no size column is used.
  • X-axis labels (optional): a column of dates, text, or numbers to label the points.

Control limits

  • Limit type: Shewhart (calculated), Manual (you enter the upper limit, center, and lower limit), or None (center line only).
  • Number of standard deviations: the sigma multiplier for the limits (default 3).
  • Historical mean: supply a known mean defect count instead of estimating it from the data.
  • Baseline subgroups: estimate the center from all subgroups or from the first N subgroups.
  • Split control limits: break the chart into phases with separate limits, split at the changes in a column's value or at manual break rows, with an optional label per phase.

Tests and display

  • Out-of-control tests: the point-pattern rules that flag signals; attribute charts use rules 1 through 4, and the run length for rules 2, 3, and 4 is adjustable. See Out-of-Control tests.
  • Zones: show the one- and two-sigma zone lines.
  • Reference lines: add horizontal lines at chosen values, each with a label, color, and thickness.
  • Overdispersion diagnostic: compute the σ_Z statistic, and optionally a secondary Z-score probability plot, to judge whether the Laney U' chart is warranted.

After creation

The Control Chart task pane lets you scroll and zoom the visible window, toggle the zone, out-of-control, and outlier markers, and edit the phase splits.

For the shared steps of building and updating a control chart, see Create Control Charts and Data Sources.

Output

Quantum XL draws the c chart and a summary listing the center line (c̄), the control limits, the number of subgroups, the count of out-of-control points, and the σ_Z overdispersion diagnostic.

See Also