Multi-Vari chart: Find where variation lives.
A multi-vari chart splits the variation of a measured output into families — for example within-part, part-to-part and time-to-time — so you can see where the dominant cause lives before you run a single experiment.
Why multi-vari?
When a quality problem keeps coming back — scrap, rework, a dimension drifting out of tolerance — the usual reaction is a brainstorm: list every possible cause, then test the favorites one by one. With dozens of suspects, that can take months, and many of the tests change nothing.
A multi-vari study starts from two simple facts. Variation is rarely spread evenly: one cause usually dominates the rest. And every cause leaves a pattern in the data — for example, it acts within a part, from one part to the next, or over time.
So instead of testing causes one at a time, you measure parts the process is already making and rule out whole families of causes at once. If the variation lives between hours, nothing that acts inside a single part can be the main cause — and those suspects drop off the list without a single experiment.
- Dozens of possible causes on the list
- 1 family where the variation livesMulti-vari
- A few suspects inside that family
- 1 dominant cause, proven by a test
Where it fits in problem solving
A multi-vari study doesn’t solve the problem on its own — it tells you where to look. In a progressive search, each step narrows the field until one cause is left. Shainin calls that dominant cause the Red X®. In Six Sigma projects, the same study belongs to the Analyze phase of DMAIC.
Define the problem
Turn the complaint into one measurable output — Shainin calls it the Green Y® — and check that the gauge can see the difference.
Find where the variation lives Multi-vari
Run a multi-vari study and identify the family that carries most of the variation.
Narrow down
Inside that family, compare the best and the worst parts to see what differs.
Prove the cause
Confirm it with a test: switch the suspect on and off and watch the problem come and go.
Fix and hold the gain
Set the right tolerance or control for the cause and verify the improvement.
Common families of variation
The three most common families are below. Depending on the process, a study splits them further or adds others — for example machine to machine, cavity to cavity or operator to operator. A multi-vari chart shows them side by side, so the biggest one stands out.
Within-part
Changes across a single part — end to end, side to side, around the diameter.
Example: taper or out-of-round on a machined shaft.
Part-to-part
Differences between consecutive parts, or between cavities, fixtures or machines.
Example: one mold cavity running differently from the others.
Time-to-time
Shifts from hour to hour, shift to shift or lot to lot.
Example: a dimension drifting while the machine warms up.
How a multi-vari study works
No special equipment and no experiments — just a planned way of sampling the running process.
Pick one measured output
The characteristic that shows the problem, and a gauge that can see the differences.
Measure several positions on each part
On a few consecutive parts, so both within-part and part-to-part variation show up.
Repeat over time
Across hours, shifts or lots — without adjusting the process in between.
Plot and compare
Put every reading on one chart. The family with the largest spread is where the cause lives.
How to read a multi-vari chart
Compare the length of the lines, the jumps between parts and the shifts between hours. The biggest spread shows where the cause lives.
Within-partLong lines, with the same position on top every time — the cause acts across the part itself.
Part-to-partShort lines, but big jumps from one part to the next — the cause changes from cycle to cycle.
Time-to-timeEach hour sits at its own level — the cause changes over time, like a machine warming up.
Case study
A known shift, an unknown pattern
An engine manufacturer was scrapping camshafts because the cam lobes ended up out of position. A progressive multi-vari — lobe position measured at several points along the process — traced the big change to hardening. The plant already knew the lobes moved there. What nobody knew was that they moved in a predictable, nonrandom pattern: the same amount, in the same direction, every time. So the lobe grinders were reprogrammed to compensate. The multi-vari showed where the cause lived; the pattern showed how to cancel it out.
$560,000less scrap per year
$5,000to implement
Multi-vari chart FAQ
What is a multi-vari chart used for?
To see which family of variation — for example within-part, part-to-part or time-to-time — contributes most to a problem, so the investigation starts in the right place instead of with a long list of guesses.
When should I use a multi-vari study?
When a measured characteristic varies too much and the cause is unknown — especially chronic problems where many causes have been suspected and none confirmed. It works on a running process, so you don’t need to stop production or design experiments first.
Who invented the multi-vari chart?
Leonard Seder published it in 1950. Dorian Shainin made it an early step in his approach to finding the dominant cause of variation, which he called the Red X®.
How is it different from a designed experiment (DOE)?
A designed experiment changes factors on purpose to measure their effect, so you must already know which factors to test. A multi-vari study only observes the process as it runs and tells you which family of causes to look at. Run the multi-vari first: any experiment you still need becomes small and focused.
Is multi-vari part of Six Sigma?
Yes. In Six Sigma projects it is used in the Analyze phase of DMAIC, to narrow down the possible causes before any designed experiment. In Shainin’s Red X® approach it is one of the first steps: it shows which family of variation to search in.
Is it the same as multivariate analysis?
No. Despite the similar name, a multi-vari chart is a simple graphical study of one measured output. Multivariate analysis is a family of statistical methods for many variables at once.
Does a multi-vari chart show the root cause?
Not by itself. It shows where the cause lives — which family carries the variation. Narrowing down and a confirmation test then show what the cause is.
How much data do I need?
Enough to see the process at its best and at its worst. A common rule of thumb is 2–5 readings per part on 3–5 consecutive parts, repeated over several periods until the study covers most of the usual range.
Can I use pass/fail data?
A multi-vari chart needs a measured value — a dimension, a force, a flow, a temperature. For pass/fail defects, first find a measurable characteristic behind the defect, or use a different strategy.
What software can I use?
Shainin WRXT (Web Red X® Tracker), the web application that comes with Shainin’s Red X® training, has the multi-vari chart built in. Ask an expert about access. General statistics packages draw it too: Minitab (Stat > Quality Tools > Multi-Vari Chart) and JMP, where it is called a variability chart. A spreadsheet works for a small study. The software only draws the chart; the sampling plan is what finds the cause.
Sources: Leonard A. Seder, “Diagnosis with Diagrams”, Industrial Quality Control (1950); Multi-vari chart, Wikipedia.
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