Try it while you read
Open the free Multi-Vari Chart and Box Plot tool and click Load sample: it reproduces the case study below.
Theory: divide and conquer the variation
A multi-vari study, introduced by Leonard Seder and used heavily in the Shainin method, observes the process without changing it and splits the total variation into nested families:
- Over time (temporal): differences between hours, shifts, days, batches.
- Part to part (cyclical): differences between consecutive parts made at the same time.
- Within the part (positional): differences between positions on one part, e.g. front, middle and rear of a shaft.
A nested analysis of variance gives each family its share of the total variation. The multi-vari chart shows the same visually: the length of the lines inside one part, the jumps between parts and the drift of the group means over time.
Key point
Step by step
- Plan the families and the sampling before you start; do not adjust the process during the study.
- Measure with a capable gauge, the same operator, and record time, part and position.
- Enter the data in the multi-vari tool, one row per measurement; rename the factor columns (e.g. Hour, Part, Position).
- Read the share per family, its p-value and the largest family; the box plot shows the spread per level.
- Follow the hint for the largest family, then confirm the suspected cause with a test or a designed experiment.
Case study: diameter of a turned shaft
A bearing seat Ø25 mm has too much spread. The Load sample: 3 consecutive shafts every hour from 08:00 to 12:00, diameter measured at the front, middle and rear of the seat, 45 values.
| Family | Share of variation | Significant? |
|---|---|---|
| Over time (hour) | 22.3 % | Yes (p < 0.001) |
| Part within hour | 0.8 % | No |
| Position within part | 76.9 % | Largest family |
The mean diameter rises from 24.9959 mm at the front through 25.0086 mm in the middle to 25.0197 mm at the rear: a taper of about 0.024 mm along the seat. Over the morning the mean drifts by about 0.015 mm (25.0003 mm at 08:00, 25.0153 mm at 12:00), the smaller second family. Consecutive parts are almost identical.
Result
Common mistakes
- Too short a study that misses the time family (one hour instead of a shift).
- Adjusting the machine during the study, which adds artificial variation.
- Measuring different positions on different parts, which mixes two families.
- Searching for causes in all directions instead of only the largest family.
Compare the families numerically with ANOVA, and check the resulting capability with the Cpk calculator.
Frequently asked questions
What is a family of variation?
A group of sources that act at the same level: over time (tool wear, temperature, batches), from part to part (clamping, cycle-to-cycle behaviour) or within one part (taper, ovality, flatness). Finding the largest family rules out most possible causes at once.
How many samples does a multi-vari study need?
Enough to capture the normal variation of the process, typically 3 to 5 consecutive parts at 4 to 6 times spread over a shift or a day, with 2 to 4 measurement positions per part. The study should cover at least 80 % of the usual process spread.
Should I check the gauge first?
Yes. If the measurement system adds a lot of noise, it can hide the families. Run a Gage R&R first, or at least a type 1 study.