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p Chart

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QXL Stat Tools Tab > Control Charts > p Chart

A p chart monitors the proportion of defective items in each subgroup. It is an attribute chart: each inspected item is classified pass or fail, and the chart plots the fraction that failed. Use it when the subgroup size can vary from one sample to the next.

When to use it

  • The data are counts of defective items out of a sample, and you want the proportion defective.
  • Subgroup sizes may differ (for a constant subgroup size that plots the raw count instead, use the np Chart).
  • If the points vary more than the binomial model predicts (overdispersion), prefer the Laney P' Chart. Quantum XL reports an overdispersion diagnostic on the p chart to help you decide.

How it works

The center line is the pooled proportion defective across the baseline subgroups. Each point is the subgroup proportion, defectives divided by subgroup size. The control limits are placed three standard deviations from the center line by default, and because the standard deviation depends on the subgroup size, the limits step in and out with the sample size rather than forming straight lines. The lower limit is held at zero, since a proportion cannot be negative. 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).
  • 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 diagnostic: compute the σ_Z statistic, and optionally a secondary Z-score probability plot, to judge whether the Laney P' 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 p chart and a summary that lists the center line (p̄), the control limits, the number of subgroups, the count of out-of-control points, and the σ_Z overdispersion diagnostic with its interpretation.

See Also