SC QUALITY GUILDMulti-vari chart
SCQUALITYGUILD.COM/TOOLS/MULTI-VARI-CHART.HTML
Enter readings by time period, piece and position to draw a multi-vari chart and estimate how much of the variation is within-piece, piece-to-piece and time-to-time.
ON THE EXAM · CSSGB IV.A.1 · FREE · NOTHING YOU TYPE LEAVES YOUR BROWSER
Q-BotClick for an explanation of this tool.For educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
What a multi-vari study does
A multi-vari study samples a running process in a nested pattern so that variation can be sorted into families before anyone guesses at causes. The classic three families are:
- Within-piece (positional): differences between locations on the same unit, such as taper along a shaft, out-of-round, or thickness across a sheet.
- Piece-to-piece (cyclical): differences between consecutive units made close together in time.
- Time-to-time (temporal): differences between groups of units made at different times, shifts or lots.
The study is passive: you do not change anything, you only measure. Its value is in ruling out whole families, which shrinks the list of suspects for the analysis that follows.
Reading the chart
Each vertical bar spans the readings on one piece, so long bars mean within-piece variation is large. Piece means that jump around inside a time period show piece-to-piece variation. Period means that drift or step from one period to the next show time-to-time variation. A position that is high on every piece, as in the taper of the worked example, is a systematic pattern with a fixed cause.
How the percentages are estimated
The tool runs a nested analysis of variance (pieces nested in time periods, readings nested in pieces) and converts the mean squares into variance components using their expected values. Each component is shown as a share of the total variance. Variances add; standard deviations do not, so percentages are always taken on the variance scale. When a mean square comes out smaller than the one below it, the formula gives a negative variance, which is reported as zero.
Common traps
- Sampling too few periods. The time-to-time estimate rests on the number of periods minus one, so three or four periods give a rough answer.
- Letting the measurement system hide inside within-piece variation. Check the gauge first.
- Treating the dominant family as the root cause. It points where to look; a designed experiment or a confirmation run proves the cause.
On the CSSGB exam
Expect to look at a multi-vari chart and name the dominant family of variation, or to match a description (taper, warm-up drift, cycle-to-cycle scatter) to the family it belongs to. Know that multi-vari is an Analyze-phase tool used to narrow the search before hypothesis tests and experiments.