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p Chart¶
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QXL Stat Tools Tab > Control Charts > Attribute Charts > P, NP, and Laney's P'
Want to build one first?
How-To works through a finished chart step by step, from sample data you copy off the page straight into Excel. The data has a point that is out of control, so the result has something to read rather than twenty points in a row.
How-To with GroupBy does the same thing with a GroupBy column, so one run produces a separate chart per group.
A p chart monitors the proportion of defective items in each subgroup. Each inspected item is classified pass or fail, and the chart plots the fraction that failed. Because the fraction is a proportion, the chart handles subgroups of different sizes: it just draws them different limits.
| Panel title on the worksheet | P Chart, one panel only |
| What it plots | defectives divided by sample size, for each subgroup |
| Y axis | Proportion Defective |
| X axis | Subgroup |
| Distribution behind the lines | binomial |
One ribbon entry opens three charts. The button reads P, NP, and Laney's P', and a Variant: radio row at the top of the dialog chooses between them: P, NP and Laney P'. The dialog's title changes with the variant, so the same window is titled P Chart, NP Chart or Laney P' Chart depending on which radio is selected. The worksheet it writes is named for the variant too.
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 where you would rather plot the raw count, the np Chart is the same dialog with one radio moved.
- If the points scatter more than the binomial model predicts, the Laney P' Chart widens the limits to match. Every p chart reports the diagnostic that tells you whether that is happening.
How it works¶
The center line is \(\bar{p}\), the pooled proportion defective: total defectives divided by total items inspected across the baseline subgroups. It is not the average of the subgroup proportions, and the two differ whenever the sample sizes differ.
Each point is that subgroup's own proportion. The limits are three standard deviations either side by default, and because the standard deviation of a proportion depends on the sample size, the limits step in and out with the sample size while the center line stays flat: a bigger sample gives a tighter band. The lower limit is held at zero, since a proportion cannot be negative, and the upper limit is held at one.
Every p chart also reports \(\sigma_Z\), an overdispersion diagnostic. It compares how much the points actually scatter with how much the binomial model says they should. A value near 1 means the model fits. Substantially above 1 means the points scatter more than binomial variation alone explains, and the limits on this chart are then tighter than the process deserves. The diagnostic is computed and printed here but not applied: applying it is what makes the chart a Laney P' Chart.
Two settings change what the limits are estimated from rather than how. Baseline Estimation estimates \(\bar{p}\) from the first few subgroups and extends it. Split Control Limits divides the chart into phases and re-estimates inside each one. A Historical pBar box supplies a known proportion outright.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet named P Chart. Under GroupBy there is one worksheet per group, each named P Chart - {GroupName}.
Worksheets are divided by GroupBy group, not by chart. Every chart belonging to a group is stacked down that one worksheet, one below the other, so selecting three measurement columns without GroupBy produces three charts on a single sheet rather than three sheets. The User Input block is written once at the top of each worksheet; everything after it repeats for each chart on the sheet.
On the sheet, from the top:
- A User Input block in the first two columns, holding the analysis title, the defectives column, the sample size column or constant, the X-axis label column and any GroupBy columns, and whether the calculation type was Excel or GroupBy. Modify Existing Analysis reads it back.
- The P Chart panel, plotting each subgroup proportion with its stepped limits, the zone lines if you asked for them, any reference lines, and phase dividers when the chart is split. Points that broke an enabled out-of-control test are drawn in a different color.
- A summary table to the right, listing p-bar, UCL, LCL, Total subgroups, OOC points and Outliers marked. The UCL and LCL rows, and the center-line row with them, are read at the LAST plotted point, so on a chart with varying sample sizes read the stepped limits off the chart rather than off the table. A split chart adds a Per-Split Breakdown block.
- An Overdispersion Interpretation block below it, headed by the computed \(\sigma_Z\) and then a three-row legend for reading it: near 1.0, significantly above 1.0, and significantly below 1.0, each with a meaning and a recommendation. It is a legend, not a verdict: the table prints all three rows and leaves you to decide which one your \(\sigma_Z\) falls into. On a split chart the pooled \(\sigma_Z\) is not printed at all; each phase reports its own \(\sigma_Z\) in the Per-Split Breakdown instead.
- An optional Z-score plot, off by default, from the Diagnostics group.
There is no capability block and no histogram on an attribute chart worksheet.
When the analysis finishes, the Control Chart task pane opens on the right. See Task Pane for what it can and cannot change.