Multi-Vari Studies

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

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.

1. Define Y. Prefer a continuous characteristic (dimension, weight, time, temperature). Attribute rates are harder to read on multi-vari charts.
2. Choose positions (positional factor). Use 2–5 locations per unit: edge/center/edge, cavities on one cycle, or other fixed layout positions.
3. Choose consecutive units (cyclical factor). Often 3–5 consecutive units per time period so unit-to-unit swing is visible.
4. Choose time periods (temporal factor). Sample across 3 or more natural blocks (shifts, days, runs) that cover the problem window.
5. Hold the measurement system steady. One gage and one appraiser when possible—or a validated MSA—so "positional" is not really gage noise.
6. 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:

1. 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.
2. Cyclical pattern — Compare consecutive units. Large unit-to-unit jumps with tight within-unit ranges point to feedstock, tooling cycle, or unit-level inputs.
3. Temporal pattern — Do whole blocks sit higher or lower? Does variance explode after a shift change? Look at setup, environment, staffing, and maintenance.
4. 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.