Multi-vari charts help you to identify sources of variation. Use these charts to see within piece, piece to piece, and time to time variations.

What is a Multi-Vari Chart? video from simplilearn

Multi-vari vs other chart types

Stem and leaf chartshistograms, and frequency distributions are all snapshots of process variation. They can’t help you to figure out the source of that variation. Multi-vari charts, though, can. 

Recap of variation sources

  • Within piece: variations within a single instance of a product. Also known as positional variation.
  • Piece to piece: variations that occur between different instances of the same product. Also known as cyclical variation.
  • Time to time: variations that occur at different production times. Also known as temporal variation.

Generate Clues with Multi-vari Charts. This technique is especially well suited for analyzing multiple sources of common-cause variation: within piece, piece to piece, time to time, and process stream to process stream.

Reducing Process Variation- Davis Bothe

Benefits of Using Multi-Vari Charts

A multi-vari chart can:

  • Show most of your variations.
  • Assist you in breaking down the components of variation.
  • Show all measurements recorded.

Guidelines for Creating Multi-Vari Charts

When creating multi-vari charts, keep these points in mind:

  • Numeric data: You need to be able to plot the effects of variations using mean values.
  • Factors: Use a maximum of six factors.
  • Levels: You need at least two levels for each factor.
  • Amount of data: Collect observations for the majority of factor combinations.

Creating a Multi-Vari Chart

  • Time is on the horizontal (x) scale.
  • Variable measurement is on the vertical (y) scale.
Complexity Made Simple – The multi-vari tutorial using SPC XL by Paul Allen

Example Chart

Let’s walk through creating a multi-vari chart using a basic baking problem.

Issue

I’m baking cookies using three different ovens. Some of my cookies seem a bit wider than others. I need to figure out why. They’re all made from the same ingredients and recipe. So I think the most likely factors are:

  • Placement on the cookie sheet. (within piece, treating each sheet of cookies as a ‘piece’)
  • Temperature variations between ovens. (piece to piece)
  • Temperature levels in the kitchen when the cookies are being mixed and added to sheets. (time to time)

Therefore, I’ll use these three factors in my chart.

Data table

Firstly, I need to take width measurements on every cookie. I also need to record:

  • The oven it was baked in.
  • The batch it was part of.
  • Its location on the cookie sheet.

So I fill out this data table:

OvenTimeLocationWidth
Oven 11Back4.12
Oven 11Left middle4.11
Oven 11Center4.1
Oven 11Right middle4.1
Oven 11Front4.1
Oven 12Back4.11
Oven 12Left middle4.11
Oven 12Center4.1
Oven 12Right middle4.09
Oven 12Front4.09
Oven 13Back4.13
Oven 13Left middle4.12
Oven 13Center4.1
Oven 13Right middle4.09
Oven 13Front4.1
Oven 14Back4.12
Oven 14Left middle4.11
Oven 14Center4.1
Oven 14Right middle4.09
Oven 14Front4.1
Oven 21Back4.13
Oven 21Left middle4.11
Oven 21Center4.1
Oven 21Right middle4.11
Oven 21Front4.09
Oven 22Back4.13
Oven 22Left middle4.12
Oven 22Center4.1
Oven 22Right middle4.12
Oven 22Front4.09
Oven 23Back4.14
Oven 23Left middle4.12
Oven 23Center4.1
Oven 23Right middle4.13
Oven 23Front4.1
Oven 24Back4.13
Oven 24Left middle4.11
Oven 24Center4.1
Oven 24Right middle4.09
Oven 24Front4.09
Oven 31Back4.11
Oven 31Left middle4.11
Oven 31Center4.1
Oven 31Right middle4.1
Oven 31Front4.1
Oven 32Back4.1
Oven 32Left middle4.11
Oven 32Center4.1
Oven 32Right middle4.09
Oven 32Front4.09
Oven 33Back4.12
Oven 33Left middle4.12
Oven 33Center4.1
Oven 33Right middle4.1
Oven 33Front4.1
Oven 34Back4.12
Oven 34Left middle4.11
Oven 34Center4.1
Oven 34Right middle4.09
Oven 34Front4.11

Chart

To turn the data table into a chart, I use Minitab.

I copy and paste my table into its spreadsheet. I then select Stat > Quality Tools > Multi-Vari Chart from the menu.

Screenshot of Multi-Vari Chart selection in Minitab

I tell Minitab which column contains my results (Response). Then I select my variables (Factors 1 to 3).

Screenshot of Multi-Vari Chart pop up window in Minitab, with columns selected

I click on OK.

Minitab creates the chart for me.

A multi-vari chart with Width on the y-axis and Time on the X-axis. It is broken into five vertical sections marked Back, Center, Front, Left-middle, and Right-middle.
Multi-vari chart for cookie width by oven and location in oven

Interpreting the Results

One thing immediately jumps out at me when I look at this chart: the center measurements are perfect. In every other oven location, though – back, front, left middle and right middle – the measurements for Oven 2 are substantially skewed from Oven 1 and 3.

I can probably remove a lot of variation by servicing or repairing Oven 2.

Complimentary information to Multi-Vari Study, Multi-Vari Charts

Also see:

Find further information and examples in this PDF: Multi-Vari Analysis.

Six Sigma Green Belt Certification Multi-Vari Study, Multi-Vari Charts Questions:

Question: In an “X” Sifting exercises a Belt will use a(n) _______________ to assist in isolating families of variation that may exist within a subgroup, between subgroups or vary over time.

(A) Multi – Vari Chart
(B) Pareto Chart
(C) FMEA
(D) Shewhart Analysis


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Six Sigma Black Belt Certification Multi-Vari Study, Multi-Vari Charts Questions:

Question: Positional, cyclical, and temporal variations are most commonly analyzed in: Taken from (ASQ sample Black Belt exam.)

(A) SPC charts
(B) multi-vari charts
(C) cause and effect diagrams
(D) run charts

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