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Laney P' Chart

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QXL Stat Tools Tab > Control Charts > Laney P' Chart

The Laney P' chart ("P-prime") is a p Chart corrected for overdispersion. When a process has real variation between subgroups beyond what the binomial model predicts (common with very large subgroups), an ordinary p chart draws limits that are too tight and flags too many points. The Laney P' chart widens the limits by an overdispersion factor so the signals are meaningful.

When to use it

  • You would use a p Chart, but the overdispersion diagnostic σ_Z is well above 1, indicating between-subgroup variation the binomial model does not capture.
  • The subgroup sizes are known per subgroup (the correction is estimated from the point-to-point variation).

How it works

The center line and the plotted proportion are the same as the p chart. The difference is in the limits: the ordinary binomial standard deviation is multiplied by the overdispersion factor σ_Z, which is estimated from the moving range of the standardized subgroup values. The limits are then placed three of these adjusted standard deviations from the center line by default, floored at zero and capped at one. The exact formulas are on the Math Details page, and σ_Z is defined in Laney Overdispersion.

Options

Data

  • Data source: an Excel range, or GroupBy (each value of the grouping column produces a separate chart).
  • Defectives column: the count of defective items; selecting several columns produces several charts.
  • Sample size: taken from a column or entered as a constant.
  • 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 proportion: supply a known proportion defective 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: the σ_Z factor is applied to the limits automatically on this chart; a secondary Z-score probability plot can also be shown.

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 Laney P' chart and a summary listing the center line, the overdispersion-adjusted control limits, the number of subgroups, the count of out-of-control points, and the σ_Z factor used.

See Also