Multi-Vari Studies
Key Takeaways
- A multi-vari study is a structured sampling plan that graphs process data so you can see which family of variation dominates: positional, cyclical, or temporal.
- Positional variation occurs within a single unit or fixed location pattern (within-piece, cavity-to-cavity, left-to-right); cyclical is unit-to-unit or batch-to-batch; temporal is time-ordered (shift, day, week).
- Design the sampling plan before collecting data: fix how many positions per unit, how many consecutive units, and how many time periods so the three families can be compared on one chart.
- Interpret the chart by comparing vertical spreads and patterns—the largest, most consistent family of spread points to the first root-cause hunt in Analyze.
- Multi-vari is an exploratory Create-level tool: it prioritizes where variation lives; it does not replace hypothesis tests, DOE, or MSA when you need statistical confirmation.
Multi-Vari Studies
Quick Answer: A multi-vari study is a planned data-collection and charting method that compares three families of process variation—positional (within a unit or fixed location pattern), cyclical (unit-to-unit or batch-to-batch), and temporal (over time such as shift or day)—so the Analyze phase starts with the family that actually drives the problem.
Why Multi-Vari Belongs in Analyze
After Measure gives you a baseline Y and candidate X's, you still need a practical map of where variation lives. Jumping to regression or DOE without that map wastes samples. Multi-vari is a Create-level BoK skill (IV.A.1): design a sampling plan, collect a modest structured sample, and read a chart that ranks variation families by visual magnitude. It is exploratory—not a substitute for p-values—but it is high leverage for focusing root-cause work.
Think of multi-vari as a stratified snapshot: instead of one undifferentiated pile of numbers, you sample so within-piece, piece-to-piece, and time-to-time differences appear side by side.
The Three Families of Variation
| Family | Meaning | Typical sources | Chart cue |
|---|---|---|---|
| Positional | Spread within one unit or across fixed locations on the same unit/setup | Thickness left/center/right; cavity A vs B; top vs bottom | Large vertical range inside one piece's marks |
| Cyclical | Differences from unit to unit (or lot to lot) in sequence | Tool wear within a lot; consecutive parts from different cavities | Large jumps between consecutive units; positions within a unit stay tight |
| Temporal | Changes over longer time | Shift A vs B; day-of-week; after maintenance; humidity drift | Whole time blocks sit higher/lower or change variance |
These families are not mutually exclusive. Multi-vari asks: which family is largest, and is that pattern stable across the study window?
Sampling Plans for Multi-Vari Charts
Design the plan before you walk the floor.
- Define Y. Prefer a continuous characteristic (dimension, weight, time, temperature). Attribute rates are harder to read on multi-vari charts.
- Choose positions (positional factor). Use 2–5 locations per unit: edge/center/edge, cavities on one cycle, or other fixed layout positions.
- Choose consecutive units (cyclical factor). Often 3–5 consecutive units per time period so unit-to-unit swing is visible.
- Choose time periods (temporal factor). Sample across 3 or more natural blocks (shifts, days, runs) that cover the problem window.
- Hold the measurement system steady. One gage and one appraiser when possible—or a validated MSA—so "positional" is not really gage noise.
- Keep the process as-is. Do not "fix" the process during the study; multi-vari pictures current noise.
Rule of thumb: 3–5 positions × 3–5 consecutive units × 3+ time periods. Adjust for cost and line speed, but do not collapse all three factors into one random sample.
Building and Reading the Chart
Classic multi-vari charts put the measured value on the vertical axis and arrange points so:
- The same unit's positions are clustered or connected (positional spread)
- Units follow production order within a time block (cyclical)
- Time blocks are separated along the horizontal axis (temporal)
Interpretation sequence:
- Positional ranges — For each unit, how large is high–low across positions? Large within-unit ranges point to fixture, fill pattern, or heat/profile across the part.
- Cyclical pattern — Compare consecutive units. Large unit-to-unit jumps with tight within-unit ranges point to feedstock, tooling cycle, or unit-level inputs.
- Temporal pattern — Do whole blocks sit higher or lower? Does variance explode after a shift change? Look at setup, environment, staffing, and maintenance.
- Name the dominant family and list 3–5 technical hypotheses inside that family before DOE.
Worked Scenario 1 — Injection-Molded Clip Thickness
Three positions (left, center, right), four consecutive shots per period, three shifts.
Pattern: Within each shot, left–center–right differs by about 0.12 mm. Consecutive shots differ by about 0.03 mm. Shift averages sit within 0.02 mm.
Interpretation: Positional dominates. Prioritize mold balance, gate location, cooling uniformity, and cavity fill—not shift handoffs first.
Worked Scenario 2 — Call Handle Time
Three consecutive calls per block across four times of day.
Pattern: Call-to-call spread is moderate. Late afternoon blocks sit about 4 minutes higher than morning blocks across days.
Interpretation: Temporal (time-of-day) dominates. Hypotheses focus on queue load, staffing, and escalation mix by hour.
Worked Scenario 3 — Shaft Diameter
Two diameters (front/rear) on five consecutive parts per lot, three lots in a day.
Pattern: Front vs rear differs by 0.01 mm. Consecutive parts swing by 0.08 mm. Lot means are similar.
Interpretation: Cyclical (part-to-part) dominates. Investigate stock hardness, tool wear within the lot, bar feeder consistency, and coolant—not primarily within-shaft geometry.
Pitfalls and Exam Focus
- Too few time periods → one-day anomalies look like "the process."
- Confounding position with appraiser → "positional" may be MSA error.
- Stopping at the family name → "It's positional" is a searchlight, not a root cause.
- Using multi-vari as proof of improvement → re-confirm with control charts or capability after changes.
CSSGB items usually test matching a described pattern to positional, cyclical, or temporal and knowing multi-vari is a planned sampling + graphical Analyze tool—not a formal hypothesis test. Create a defensible plan, rank the dominant family, then go deeper with the right next tool.
A multi-vari chart of coating thickness shows large high–low spreads among the four measurement locations on each panel, while consecutive panels within a shift and shift-to-shift averages look relatively tight. Which family of variation dominates, and what is the best next Analyze focus?
A Green Belt designs a multi-vari study for a filling process. Which sampling plan best supports separating positional, cyclical, and temporal variation?