Home / Statistical Tools / Control Charts / Z-MR (Z Score with Moving Range)
Z-MR (Z Score with Moving Range)¶
From Excel click...
QXL Stat Tools Tab > Control Charts > Short Run > Z-MR (Z Score with Moving Range)
A Z-MR chart is two stacked panels built from measurements that come from more than one part. The upper panel, Z Chart, plots a standardized value: each measurement with its own part's mean subtracted and the result divided by an estimated standard deviation. Its Y axis is labelled Z Score. The lower panel, Moving Range Chart, plots the moving range of those standardized values, not of the raw measurements, and its Y axis is labelled Moving Range of Z.
Because every point has been standardized, parts measured in different sizes, and parts with different average levels, all land on one common scale and can be charted together.
This chart is called three different things
The ribbon button reads Z-MR (Z Score with Moving Range). The dialog that opens is titled Z-MR Chart. The worksheet it writes is named ZMR, with no hyphen and no "Chart". All three refer to this one analysis.
Every option in the dialog is described on the Options page.
When to use it¶
- Your measurements are continuous and you have one measurement per row, each row belonging to a named part.
- No single part gives you enough points for a chart of its own. Ten parts with eight measurements each will not support ten separate Individuals charts, but standardizing removes the part-to-part difference in level and scale and leaves one chart of eighty points.
- The parts run in blocks: you make a batch of one part, then a batch of the next. That is the pattern this chart is built around, and it is what the run dividers on the finished chart mark.
If every measurement comes from the same part, you do not need to standardize, and an I-MR chart plots the measurements in their own units instead. Z-MR has no Capability tab, so if you need a capability index or a histogram alongside the chart, use one of the charts that offers one.
How it works¶
You choose one Measurement Column and one Part Column on the Data tab. Rows keep their worksheet order, and Quantum XL divides them into runs: a run is a maximal block of consecutive rows carrying the same part name. If a part appears again later in the sheet, that later block is a new run, not a continuation of the earlier one. The run boundaries are drawn on the finished chart as vertical dividers with the part name beside them.
Each measurement is turned into a standardized value:
- The mean subtracted is always the part's own mean, pooled over every row of that part wherever it appears in the sheet, so both runs of a part are centered on the same number.
- The standard deviation divided by depends on the sigma mode you choose on the Limits & Estimation tab. Constant estimates one standard deviation for the whole chart. Relative to size does the same after taking the natural logarithm of the data first. By parts estimates one per part, and By runs estimates one per run.
The Z panel's lines never move: the center line is 0, the upper control limit is +3, and the lower control limit is -3, on every Z-MR chart. There is no sigma multiplier to change them and no Control Limits group in the dialog. A point outside the band is three standard deviations from its own part's mean.
The Moving Range panel is computed on the standardized values, and its window never crosses a run boundary, so the first point of each run is blank at the default moving range length. Its center line and limits are constants that depend only on the moving range length and on whether you chose the average or the median moving range, so two Z-MR charts of completely different products show the same moving range band.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet per chart, named ZMR. Under GroupBy the sheet name gains the group name. On it, from the top:
- A User Input block in the first two columns, holding the analysis title (Z-MR Chart), the measurement column, the part column, the X-axis label column and any GroupBy columns you selected, and whether the calculation type was Excel or GroupBy. Modify Existing Analysis reads it back.
- The Z Chart panel, plotting each standardized value with its fixed center line at 0 and its limits at plus and minus 3, plus the zone lines and any reference lines you asked for. Vertical dividers mark the part runs and carry the part names. Points that broke an enabled out-of-control test are drawn in a different color.
- The Moving Range Chart panel below it, aligned so its points line up vertically with the panel above.
- A summary table to the right, listing for each panel the center line, the control limits, the count of out-of-control points, and the count of points you marked as outliers.
There is no capability block and no histogram on a Z-MR worksheet. This chart has no Capability tab, and the capability output is switched off in the engine as well as hidden in the dialog.
When the analysis finishes, the Control Chart task pane opens on the right. See Options for what it can and cannot change on this chart.