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Laney U' Chart

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

The Laney U' chart ("U-prime") is a u Chart corrected for overdispersion. When defect counts vary between subgroups more than the Poisson model predicts, an ordinary u chart draws limits that are too tight. The Laney U' chart widens the limits by an overdispersion factor so the signals are meaningful.

When to use it

  • You would use a u Chart, but the overdispersion diagnostic σ_Z is well above 1.
  • The subgroup sizes are known per subgroup; the Laney correction needs a size for each subgroup, so a single constant size is not used for this chart.

How it works

The center line and the plotted defects-per-unit are the same as the u chart. The ordinary Poisson standard deviation is multiplied by the overdispersion factor σ_Z, estimated from the moving range of the standardized subgroup values, and the limits are placed three of these adjusted standard deviations from the center line by default, with the lower limit floored at zero. 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).
  • Defects column: the count of defects; selecting several columns produces several charts.
  • Inspection size: the area of opportunity per subgroup, taken from a column (this chart needs a per-subgroup size, so a single constant is not 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 defects-per-unit rate instead of estimating it from the data.
  • Force straight limits: substitute a single assumed inspection size so the limits are level.
  • 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 U' 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