Multi-Vari Chart

Introduction: Multi-Vari Chart

A Multi-Vari Chart is a graphical tool used to display and analyse variation within a process. It helps identify patterns of variation over time, between parts, or among different sources. This makes it especially useful in the Analyse phase of the DMAIC cycle to detect where inconsistency occurs.

Background

Developed by Leonard Seder in the 1950s, the Multi-Vari Chart originated as part of statistical quality control methods used in manufacturing. It visualises data in a way that shows multiple sources of variation simultaneously—such as within-part, between-part, and over-time variation. It became a key diagnostic tool in Six Sigma and industrial problem-solving.

Key Elements / Features

• Purpose: To visualise and quantify process variation from different sources.
• Types of Variation:
  • Within-part variation — differences within the same part or sample.
  • Between-part variation — differences among different parts or samples.
  • Temporal variation — changes over time or production runs.
• Structure: Data are plotted in grouped line graphs showing patterns across factors.
• Interpretation: The chart’s visual trends indicate which factor contributes most to process instability.

Formula for Total Process Variation:

\(
\sigma^2_{\text{total}} = \sigma^2_{\text{within}} + \sigma^2_{\text{between}} + \sigma^2_{\text{time}}
\)

Where:

• \(
  \sigma^2_{\text{total}} = \text{total variance observed in the process}
  \)
• \(
  \sigma^2_{\text{within}} = \text{variation within individual parts}
  \)
• \(
  \sigma^2_{\text{between}} = \text{variation between parts or samples}
  \)
• \(
  \sigma^2_{\text{time}} = \text{variation over time or shifts}
  \)

Example
Suppose we measure part length (in mm) from 3 machines, across 3 shifts, with 3 parts each:

• Within-part variation: For M1, Shift 1 = range(10.1, 10.2, 10.0) = 0.2 mm.
• Between-part variation: Average of M1 vs M2 vs M3 in Shift 1 shows ≈ 0.1–0.2 mm difference.
• Temporal variation: Comparing M1 across shifts, mean rises from 10.1 → 10.3 → 10.5 mm.

Interpretation: Most variation comes from time (shifts), suggesting a temperature or calibration drift rather than differences between machines or parts.

Applications / Examples

• Manufacturing: Analysing variation in dimensions between mould cavities.
• Service processes: Tracking cycle time variation between shifts.
• Healthcare: Comparing lab test results across technicians or days.

Relevance / Impact

The Multi-Vari Chart is a cornerstone in root cause analysis, allowing teams to see where variation originates. It supports data-driven decisions, reduces trial-and-error in problem-solving, and provides a visual foundation for process improvement and capability studies.

See also

• Control Chart
• Process Capability (Cp, Cpk)
• Measurement System Analysis (MSA)
• ANOVA (Analysis of Variance)