Multi-Vari Chart: Positional, Cyclical and Temporal Variation

A multi-vari chart is a graph that splits a process’s variation into families, usually positional (within one unit), cyclical (unit to unit) and temporal (time to time), so you can see which family is largest before running experiments. Data are collected in a structured sampling plan and plotted together, and the largest family shows where to look for the root cause.

Leonard A. Seder, a quality engineer, introduced the chart in the two-part article “Diagnosis with Diagrams” in Industrial Quality Control (January and March 1950). It was later made popular by Dorian Shainin as a first step in his problem-solving approach. In Lean Six Sigma it is an Analyze-phase tool: the ASQ Six Sigma Black Belt study outline reproduced in the ASQ free training guide asks learners to use and interpret multi-vari charts and to tell positional, cyclical and temporal variation apart.

What are the three families of variation?

Family	Also called	What varies	Typical causes to investigate
Positional	Within-piece, within-unit	Readings at different places on the same unit, or across cavities, spindles or fixtures at the same moment	Taper or out-of-round from tooling or setup; mold cavity differences; fixture or clamping; temperature gradients across a part
Cyclical	Piece-to-piece, unit-to-unit	Consecutive units made close together in time	Machine repeatability; material variation within a lot; operator technique from cycle to cycle
Temporal	Time-to-time	Average readings from one time period to the next (hour to hour, shift to shift, day to day)	Tool wear; warm-up; drift; change of shift, material lot or ambient temperature

You can add other families when they matter, such as machine-to-machine, operator-to-operator or lot-to-lot. Each one is a level in the sampling plan.

How do you run a multi-vari study?

Choose the output (Y). Pick one measurable characteristic that matters to the customer, such as a diameter, weight or fill volume.
Check the measurement system. If the gauge adds a lot of variation, every family looks large. Run a Gage R&R first.
Design the sampling plan. Decide the levels, for example 3 positions on each of 3 consecutive units, sampled at 4 times through the day. That is 3 × 3 × 4 = 36 readings. Do not change the process during the study; the aim is to watch normal variation, not to experiment.
Collect enough of the usual variation. Sample until the spread in the study is close to the spread normally seen in the process. If the study range is much smaller, the main source has not shown up yet; extend the study over more time or more lots.
Plot the chart. Draw each unit as a vertical line from its lowest to its highest reading, connect unit averages within each time period, and connect the period averages.
Find the largest family and follow up. Compare the size of each family. Then focus cause analysis on that family with a fishbone diagram, comparisons or a designed experiment.

Multi-vari chart example

The data below are illustrative, chosen to show the method; they are not from a real plant. A turning operation makes shafts with a nominal diameter of 10.015 mm and illustrative specification limits of 10.000 to 10.030 mm. Too many shafts are rejected late in the day. The team measures the diameter at 3 positions along each of 3 consecutive shafts, at 8:00, 10:00, 12:00 and 14:00.

Illustrative multi-vari chart: each vertical line is one shaft (3 positions), the thin line joins shaft averages in a period, and the dashed red line joins the period averages.

Time	Shaft 1 (pos. 1, 2, 3)	Shaft 2	Shaft 3	Period average
8:00	10.002, 10.006, 10.009	10.001, 10.005, 10.010	10.003, 10.006, 10.008	10.0056
10:00	10.010, 10.013, 10.017	10.009, 10.014, 10.016	10.011, 10.013, 10.018	10.0134
12:00	10.018, 10.021, 10.025	10.017, 10.022, 10.026	10.019, 10.023, 10.024	10.0217
14:00	10.026, 10.030, 10.033	10.025, 10.029, 10.034	10.027, 10.031, 10.032	10.0297

Comparing the three families:

Positional (within shaft): the average range across the three positions is 0.0070 mm, and position 3 is always the largest, a small taper.
Cyclical (shaft to shaft): within each time period the three shaft averages differ by only about 0.0007 mm on average. Consecutive shafts are almost identical.
Temporal (time to time): the period averages climb from 10.0056 to 10.0297 mm, a range of about 0.0241 mm. This is the dominant family: more than three times the within-shaft range, and most of the 0.033 mm total range in the study.

The steady climb through the day makes tool wear or thermal growth useful suspects, but time-linked material changes or operator changes could also explain it. By 14:00 several readings are above the illustrative 10.030 mm upper limit. The next steps would be to confirm the cause (for example, measure tool wear and machine temperature over the same period), then, if tool wear is confirmed, test a tool-change interval or tool-wear offset, and watch the result on a control chart. The taper is a secondary, smaller issue to look at afterwards.

Multi-vari chart vs ANOVA and DOE

A multi-vari chart is a graphical, exploratory tool. It observes the process as it runs and narrows the search to one family of causes; it does not prove a cause. Analysis of variance (ANOVA) can put numbers on the same families (for example a nested ANOVA with positions within shafts within times), and a designed experiment changes suspected inputs on purpose to prove cause and effect. A common sequence is multi-vari chart first, then hypothesis tests or ANOVA, then DOE on the few remaining suspects.

Tips and common mistakes

Sampling too short a time. If the study covers only an hour, temporal causes such as wear or shift changes cannot show up.
Mixing up the order. Record which position, unit and time each reading belongs to; without that structure the chart cannot separate the families.
Changing the process during the study. Adjustments hide the very variation you are trying to see.
Skipping the measurement check. Poor gauges inflate the positional and cyclical families.
Stopping at the chart. The chart tells you where to look; confirm the cause with data before changing the process.

Sources and further reading

Historical reference: Multi-Vari Charts, Encyclopedia of Statistics in Quality and Reliability, describing Seder’s 1950 articles. All numerical data and the chart on this page are original illustrative examples.

Frequently asked questions

What is a multi-vari chart used for?

It is used to find which family of variation, positional, cyclical or temporal, contributes most to a process’s total variation, so root cause analysis can focus there.

What is the difference between positional, cyclical and temporal variation?

Positional variation is within a single unit, cyclical variation is between consecutive units, and temporal variation is between time periods such as hours or shifts.

Who invented the multi-vari chart?

Leonard A. Seder described it in 1950 in “Diagnosis with Diagrams”, published in Industrial Quality Control. Dorian Shainin later made it widely known.

In which DMAIC phase is a multi-vari chart used?

Mainly in Analyze, after the measurement system has been checked in Measure and before experiments in Improve.

Last updated: November 14, 2026 · Published by Lean Six Sigma Training Guide (sixsigmatrainingfree.com) · How this guide is written