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Multi-vari analysis

Multi-vari analysis is a graphical technique for decomposing variation in a process output into families by where and when variation occurs. It is used in the Analyze phase, before investing in a full designed experiment, to identify which family of variation is dominant so the team focuses on the right Xs.

The three variation families

Family	Source	When it dominates	Process example
Positional (within-piece)	Variation within a single unit — different locations on the same part	Large variation across measurement points on the same unit	Film thickness thicker at edges than center; hardness varies across a tablet's face
Cyclical (piece-to-piece)	Variation from one unit to the next within a short window	Large variation from unit to unit in the same run	Every 5th tablet is softer; alternating units differ due to dual-tool setup
Temporal (time-to-time)	Variation across time — shifts, days, batches	Large variation from one time period to another	Yield is lower on Mondays; first-shift output differs from third-shift

How to construct a multi-vari chart

Select the sampling scheme: Sample multiple units at each time interval; within each unit, measure at multiple positions if applicable.
Collect data: For each time period, measure (e.g.) 3 consecutive units. For each unit, measure at multiple positions (e.g., top, center, bottom).
Plot: X-axis = time periods (groups). Y-axis = response value. Within each group, plot the individual measurements as a connected set (the "family"). The within-group spread shows within-piece and piece-to-piece variation; the shift of the families across the X-axis shows time-to-time variation.
Interpret: The largest spread = dominant variation family.

Reading the chart: If within a group the dots are far apart → positional or cyclical variation dominates If group averages shift dramatically across time → temporal variation dominates If both occur → both need to be addressed, starting with the largest

Worked example: tablet coating thickness

A coating process produces tablets with variable coating thickness. The team collects data on 3 tablets per 30-minute interval, measuring thickness at 5 positions on each tablet, over 8 consecutive 30-minute intervals (4 hours total).

Within-piece range (position-to-position on one tablet): avg 12 µm
Piece-to-piece range (tablet-to-tablet within same interval): avg 8 µm
Time-to-time range (interval-to-interval average shift): avg 3 µm

Conclusion: positional variation dominates. The hypothesis: tablets are not tumbling evenly through the spray zone, so edges and faces of the same tablet receive different amounts of coating. The team investigates pan speed, baffle design and spray nozzle position/atomization rather than batch-level variables (materials, supplier) or shift-level variables (operator, ambient conditions).

Multi-vari vs. control chart

A control chart monitors a single metric over time and detects when the process shifts or becomes unstable. A multi-vari chart captures multiple dimensions of variation simultaneously to identify which dimension matters most. They answer different questions:

Control chart: "Is the process in control?" (stability question)
Multi-vari: "Where is the variation coming from?" (stratification question)

Multi-vari is a passive observational study — no factors are actively changed. This makes it a fast way to narrow the hypothesis space before an active experiment (DOE).

Common exam traps

Multi-vari does not prove causation — it identifies the dominant variation family and focuses the investigation.
Cyclical variation is piece-to-piece within a short time window, not time-to-time. The exam distinguishes these.
The correct next step after identifying temporal variation as dominant: investigate what changes across time periods (shift, operator, material lot, ambient conditions), not change the within-unit measurement method.

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More: DMAIC overview · Project charter · VOC & CTQ · SIPOC · MSA in DMAIC · Process capability · Data collection planning · Graphical analysis · Root cause analysis · Multi-vari analysis · Hypothesis testing · Regression · DOE · FMEA · Define tollgate · Change management · Financial benefits · Team dynamics · Improve tollgate · Piloting & scaling · Poka-yoke (BB) · Solution selection · Control plan · SPC in DMAIC · Sustaining gains

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