Home / Statistical Tools / Control Charts
Control Charts¶
A control chart plots a process statistic in the order the data was collected, against a center line and a pair of control limits estimated from the data itself. Quantum XL writes the chart to its own worksheet, together with the numbers behind it, and opens a task pane you can use to change the analysis afterwards.
Every chart is launched the same way, from QXL Stat Tools Tab > Control Charts, and the groups below match the chart groups on that menu. The menu also carries the Control Chart Wizard at the top, a Multivariate group whose three commands all open T² and Generalized Variance, and an Outliers group covered by Marking Outliers. Start with Create Control Charts if you have not run one before: it covers the Data Selection window, how to lay out your data, and the parts of the finished worksheet, all of which are the same whichever chart you pick.
Pick a Chart¶
Each chart has its own set of pages: an index page describing what the chart plots and what lands on the worksheet, an Options page covering every control in its dialog, a Task Pane page for what can be changed after the run, a Math Details page, and, for most charts, one or two step-by-step How-To walkthroughs with data you can copy into Excel.
Variables: Charts in Subgroups¶
For measured values collected in subgroups, where each plotted point summarizes a group of readings.
| Chart | What it plots | Pages |
|---|---|---|
| Xbar-R and Xbar-S | Subgroup means, over a companion panel of subgroup ranges (Xbar-R) or subgroup standard deviations (Xbar-S). | Chart · How-To · GroupBy · Options · Task Pane · Math |
| I-MR-R/S | Three panels: the individual subgroup means, the moving range between them, and the within-subgroup range or standard deviation. | Chart · How-To · GroupBy · Options · Task Pane · Math |
| Xbar | The Xbar panel alone. The ribbon's Xbar entry opens the Xbar-R dialog; the Xbar-S dialog offers the same Xbar only variant with an Sbar estimate. | Chart · Options · Task Pane · Math |
| R | The range panel alone. | Chart · Options · Task Pane · Math |
| S | The standard deviation panel alone. | Chart · Options · Task Pane · Math |
Variables: Charts as Individuals¶
For measured values where each reading is plotted on its own.
| Chart | What it plots | Pages |
|---|---|---|
| I-MR | Each reading, over a panel of the moving ranges between consecutive readings. | Chart · How-To · GroupBy · Options · Task Pane · Math |
| Individuals | The individuals panel alone, from the same dialog as I-MR. | Chart · Options · Task Pane · Math |
| Moving Range | The moving range panel alone. | Chart · Options · Task Pane · Math |
| Levey-Jennings | Each reading against limits built from the overall standard deviation, tested with the six Westgard rules instead of the numbered ones. | Chart · How-To · GroupBy · Options · Task Pane · Math |
Short Run¶
| Chart | What it plots | Pages |
|---|---|---|
| Z-MR | Readings from several different parts standardized onto one scale, so short runs of each can share a chart, over a moving range panel. | Chart · How-To · GroupBy · Options · Task Pane · Math |
Time Weighted Charts¶
Each point carries the influence of the points before it, so these charts offer Rule 1 only.
| Chart | What it plots | Pages |
|---|---|---|
| EWMA | An exponentially weighted moving average of the readings, against limits that widen from the first point to a steady width. | Chart · How-To · GroupBy · Options · Task Pane · Math |
| CUSUM | Two running sums of the deviations from target, one for drift up and one for drift down, against a decision interval rather than a limit pair. | Chart · How-To · GroupBy · Options · Task Pane · Math |
Attribute Charts¶
Counts from inspection rather than measurements. These six charts are two dialogs, not six: the ribbon has one entry for P, NP, and Laney's P' and one for C, U, and Laney's U', each opening a dialog with a Variant: radio row. The p and u pages document their whole dialog; the other four cover only what changes on that variant.
| Chart | What it plots | Pages |
|---|---|---|
| p Chart | The proportion of units that failed inspection in each subgroup. | Chart · How-To · GroupBy · Options · Task Pane · Math |
| np Chart | The number of units that failed inspection in each subgroup. | Chart · Options · Task Pane · Math |
| Laney P' Chart | The p chart statistic, with the limits widened by the measured overdispersion. | Chart · How-To · Options · Task Pane · Math |
| c Chart | The number of defects found in each subgroup, where every subgroup covers the same amount of product. | Chart · How-To · Options · Task Pane · Math |
| u Chart | Defects per unit, where the amount inspected varies from subgroup to subgroup. | Chart · How-To · GroupBy · Options · Task Pane · Math |
| Laney U' Chart | The u chart statistic, with the limits widened by the measured overdispersion. | Chart · How-To · Options · Task Pane · Math |
Rare Event Charts¶
Both charts draw every line as a quantile of a fitted distribution, so the band is asymmetric. The G chart's lower limit is usually 0, which no count can fall below, but the T chart's lower limit is often a small positive time, and an interval shorter than that does fire Rule 1.
| Chart | What it plots | Pages |
|---|---|---|
| G Chart | The count of opportunities between one event and the next. | Chart · How-To · GroupBy · Options · Task Pane · Math |
| T Chart | The elapsed time between one event and the next. | Chart · How-To · GroupBy · Options · Task Pane · Math |
Multivariate¶
The only charts here that watch several measurements at once. Two or more variable columns are consumed jointly, and two statistics are computed from all of them: T² for the joint mean and the Generalized Variance for the joint spread. Three ribbon commands share one tool, and the command only decides which of the two panels is drawn.
| Chart | What it plots | Pages |
|---|---|---|
| T² and Generalized Variance | Both panels: the joint mean of two or more correlated variables, and their joint spread. Hotelling T² and Generalized Variance on the same menu draw one panel each from the same calculation. | Chart · How-To · Options · Task Pane · Math |
Pages That Apply to Every Chart¶
- Create Control Charts: the Data Selection window, how to lay your data out, how subgroups are formed three different ways, and what the finished worksheet contains.
- Data Sources: what each family of chart reads from your data, which column types it accepts, denominators on the attribute charts, and the optional X-axis label column.
- Out-of-Control Tests: the nine numbered tests and the six Westgard tests, which chart offers which, how to set the thresholds, and what the output does and does not tell you.
- Update Control Charts: rerunning a chart after adding data.
- Control Chart Wizard: a guided path through picking a chart type.
- Marking Outliers: the two Outliers commands, which mark a source cell so a chart still plots it but no longer estimates its limits from it.
Each chart's Task Pane page covers what can be changed after the run without rebuilding, including the display window that controls how many points are shown at once.
The Math¶
The formulas are shared across charts, so they live in one place rather than being repeated on every chart page. Each chart's Math Details page pulls in the pieces it uses.