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u Chart

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QXL Stat Tools Tab > Control Charts > u Chart

A u chart monitors defects per unit when the area of opportunity varies from subgroup to subgroup. Like the c chart it counts defects (a single item can have several), but it divides by the size of each subgroup so subgroups of different sizes can be compared on one chart.

When to use it

  • You count defects and the area of opportunity varies between subgroups (different sample sizes, inspection areas, or time windows).
  • If the area of opportunity is constant, the c Chart is simpler because it plots raw counts.
  • If the counts are overdispersed relative to the Poisson model, prefer the Laney U' Chart; the u chart reports the σ_Z diagnostic to help you decide.

How it works

The center line is the pooled defects per unit over the baseline subgroups and stays flat. Each point is the subgroup's defects divided by its size. The control limits sit three standard deviations from the center line by default, with the lower limit held at zero; because the standard deviation depends on the subgroup size, the limits step in and out with the size. The Force Straight Limits option substitutes a single assumed size to keep the limits level. 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.
  • Inspection size: the area of opportunity per subgroup, 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 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 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 u chart and a summary listing the center line (ū), the control limits, the number of subgroups, the count of out-of-control points, and the σ_Z overdispersion diagnostic.

See Also