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.

## Multi-vari vs other chart types

Stem and leaf charts, histograms, 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.

## 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:

Oven | Time | Location | Width |
---|---|---|---|

Oven 1 | 1 | Back | 4.12 |

Oven 1 | 1 | Left middle | 4.11 |

Oven 1 | 1 | Center | 4.1 |

Oven 1 | 1 | Right middle | 4.1 |

Oven 1 | 1 | Front | 4.1 |

Oven 1 | 2 | Back | 4.11 |

Oven 1 | 2 | Left middle | 4.11 |

Oven 1 | 2 | Center | 4.1 |

Oven 1 | 2 | Right middle | 4.09 |

Oven 1 | 2 | Front | 4.09 |

Oven 1 | 3 | Back | 4.13 |

Oven 1 | 3 | Left middle | 4.12 |

Oven 1 | 3 | Center | 4.1 |

Oven 1 | 3 | Right middle | 4.09 |

Oven 1 | 3 | Front | 4.1 |

Oven 1 | 4 | Back | 4.12 |

Oven 1 | 4 | Left middle | 4.11 |

Oven 1 | 4 | Center | 4.1 |

Oven 1 | 4 | Right middle | 4.09 |

Oven 1 | 4 | Front | 4.1 |

Oven 2 | 1 | Back | 4.13 |

Oven 2 | 1 | Left middle | 4.11 |

Oven 2 | 1 | Center | 4.1 |

Oven 2 | 1 | Right middle | 4.11 |

Oven 2 | 1 | Front | 4.09 |

Oven 2 | 2 | Back | 4.13 |

Oven 2 | 2 | Left middle | 4.12 |

Oven 2 | 2 | Center | 4.1 |

Oven 2 | 2 | Right middle | 4.12 |

Oven 2 | 2 | Front | 4.09 |

Oven 2 | 3 | Back | 4.14 |

Oven 2 | 3 | Left middle | 4.12 |

Oven 2 | 3 | Center | 4.1 |

Oven 2 | 3 | Right middle | 4.13 |

Oven 2 | 3 | Front | 4.1 |

Oven 2 | 4 | Back | 4.13 |

Oven 2 | 4 | Left middle | 4.11 |

Oven 2 | 4 | Center | 4.1 |

Oven 2 | 4 | Right middle | 4.09 |

Oven 2 | 4 | Front | 4.09 |

Oven 3 | 1 | Back | 4.11 |

Oven 3 | 1 | Left middle | 4.11 |

Oven 3 | 1 | Center | 4.1 |

Oven 3 | 1 | Right middle | 4.1 |

Oven 3 | 1 | Front | 4.1 |

Oven 3 | 2 | Back | 4.1 |

Oven 3 | 2 | Left middle | 4.11 |

Oven 3 | 2 | Center | 4.1 |

Oven 3 | 2 | Right middle | 4.09 |

Oven 3 | 2 | Front | 4.09 |

Oven 3 | 3 | Back | 4.12 |

Oven 3 | 3 | Left middle | 4.12 |

Oven 3 | 3 | Center | 4.1 |

Oven 3 | 3 | Right middle | 4.1 |

Oven 3 | 3 | Front | 4.1 |

Oven 3 | 4 | Back | 4.12 |

Oven 3 | 4 | Left middle | 4.11 |

Oven 3 | 4 | Center | 4.1 |

Oven 3 | 4 | Right middle | 4.09 |

Oven 3 | 4 | Front | 4.11 |

### 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.

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

I click on **OK**.

Minitab creates the chart for me.

### 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.

## Additional Helpful Multi-Vari Videos

## 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

**Answer:** (A) Multi – Vari Chart. This is by definition. The Mulit-vari chart helps you isolate variation inside a subgroup. Also see Pareto chart, FMEA, and Shewhart analysis.

## 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

**Answer:** (B) Multi-vari charts. SPC or statistical process control (including run charts) help you monitor how an on-going process is performing, so options A and D are not correct. Cause and effect diagrams are concerned with root cause analysis, so option C is not correct

## Comments (6)

Hello,

The video for creating a Multi-Var table is no longer available. Can we get this updated?

Thanks, Mike.

I’ve replaced that video with another and also added another helpful video at the end.

Best, Ted.

Ted dear,

for IASSC exam am i allowed to use any tool like sigma or minitab, and originally is it common (if you any clue) that IASSC asks question that requires to plot the data using any tool ?

many thanks

Hi Ahmed,

My understanding is that IASSC only allows you to have the approved equation sheet on exam day.

Best, Ted

Why cant we use a box plot for this kind of scenario ? Since we have one common independent variable across all sub groups? Pictorial representation of box plot will give better clarity about the scenario.

Box plots are great (see here). Extending them to handle more than 2 dimensions gets tricky, quickly (reference). If you really want to try, here are some interesting graphical treatments.