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np Chart¶
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QXL Stat Tools Tab > Control Charts > Attribute Charts > P, NP, and Laney's P'
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The np chart is the p Chart with one radio moved, so the walkthroughs live there. p Chart How-To and p Chart with GroupBy use the same dialog, and the plain one ends with a bullet showing exactly what changes when you switch Variant: to NP.
An np chart monitors the number of defective items in each subgroup. Each inspected item is classified pass or fail, and the chart plots the raw count that failed rather than the fraction.
| Panel title on the worksheet | NP Chart, one panel only |
| What it plots | the count of defectives in each subgroup |
| Y axis | Count 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 the Variant: radio row at the top of the dialog selects which one you get. Choosing NP retitles the window NP Chart and names the worksheet NP Chart.
When to use it¶
- The data are counts of defective items out of a sample, and the count is what people actually talk about: "eleven bad units", not "5.5 percent".
- Best suited to a constant sample size. It works with varying sizes, but see the warning below about what that does to the center line.
- If you want the fraction instead, that is the p Chart, the same dialog with the variant on P. If the points scatter more than the binomial model predicts, the Laney P' Chart is the third radio.
How it works¶
The proportion \(\bar{p}\) is estimated exactly as on a p chart: total defectives over total items inspected, pooled across the baseline subgroups. What differs is what gets drawn from it. The expected count in a subgroup of \(n_i\) items is \(n_i\bar{p}\), so:
On an np chart the center line moves with the sample size
A p chart has a flat center line and stepped limits. An np chart has both stepped, because the expected count depends on how many items you inspected. If your sample sizes vary, the center line is a staircase, and a point sitting above it may only mean that subgroup was larger.
Two ways out, both in the dialog. Keep the sample size constant, which is what this chart is designed for. Or tick Force Straight Limits and give an Assumed n:, which substitutes one size everywhere and flattens the center line and the limits together. That control reaches the np variant and, deliberately, neither of the other two.
The limits are three standard deviations either side of the stepped center line by default, floored at zero and capped at the sample size, since a count of defectives can be neither negative nor larger than the number inspected.
Every np chart also reports \(\sigma_Z\), the overdispersion diagnostic, computed and printed but not applied. Applying it is what the Laney P' Chart does.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet named NP Chart. Under GroupBy there is one worksheet per group, each named NP 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.
The sheet carries a User Input block, the NP Chart panel, a summary table listing np-bar, UCL, LCL, Total subgroups, OOC points and Outliers marked, and an Overdispersion Interpretation block headed by the computed \(\sigma_Z\) and then a three-row legend for reading it, which is a guide rather than a verdict on yours. With sample sizes read from a column the np-bar row is the center line at the last plotted point, that point's \(n\) times \(\bar{p}\), not a chart-wide average, and the UCL and LCL rows are read at that same point, so read the staircase off the chart. 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. A split chart adds a Per-Split Breakdown block. 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.