Multi-Vari Study, Multi-Vari Charts

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 cannot 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.

Step to perform Multi-Vari chart

• Select the process that needs to be monitored and the characteristics to be inspected.
• Determine the sample size and time-frequency.
• Collect continuous data to ensure the output of process performance should be continuous.
• Define units: Output characteristic measurable multiple times.
• Collect the data (2 to 5 samples within a unit) and 3 to 5 consecutive units to ensure that the process is monitored long enough to understand.
• Multi-vari charts can be drawn by hand. Draw the chart on graph paper with time along the horizontal axis, then observe values on the vertical axis.
• Connect the observed values with appropriate lines.
  • Plot each measurement with a circle and then connect each measurement within each unit showing the variation’s magnitude. Compute the average within each unit and connect it with a line to the consecutive unit. We can also compute the range of each unit by subtracting the minimum value from the maximum value. Measure the overall average of all values and draw a horizontal line (for reference)
  • Each temporal set can be divided with a vertical line
  • Compute the overall average of each set and connect it with a line
• Finally, analyze the chart for variation both within the piece, from piece to piece, and from time to time.
• Repeat the same process of conducting Multi-vari study after the process improvements to confirm the results.

Creating a Multi-Vari Chart Manually

XYZ wants to assess the different machines and processes affecting the Quality Index.

Data Table

Draw the chart on graph paper with time along the horizontal axis and then Quality index values on the vertical axis.

Compute the average within each unit.

Compute the overall average of each set and connect it with a line (green line).

Interpret the results: Analyze the chart for variation both within the piece, from piece to piece, and from time to time.

From the data, the process averages are 5.00 (process 1), 4.75 (process 2) and 6.92 (process 3), against an overall average of 5.56. Process 3 is the only one above the overall average, so it is the best option. Machine 2 has the highest average within every process (6.50, 6.25 and 7.75). Note: the green triangle for process 3 is drawn too high, at about 7.6. Its true value is 6.92.

Creating a Multi-Vari Chart using Excel

• Time is on the horizontal (x) scale.
• Variable measurement is on the vertical (y) scale.

Creating a Multi-Vari Chart using Minitab

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

First, 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.
• The location on the cookie sheet.

Next I filled out this data table:

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 has my results (Response). Then I select my variables (Factors 1 to 3).

I click on OK.

Minitab created the chart for me.

Interpreting the Results

One thing immediately jumps out when I look at this chart: the center measurements are perfect. Every center cookie measures 4.10. The biggest family of variation is location on the sheet. Back cookies average 4.122 and left-middle cookies 4.113, while center, right-middle and front cookies average 4.097 to 4.100. Oven 2 stands out at two locations: back (4.133 against 4.120 and 4.113) and right middle (4.113 against 4.093 and 4.095). At the front and left middle it is within 0.01 of the other ovens.

Servicing Oven 2 should help at the back and right middle. The larger gain is likely to come from finding why cookies at the back and left middle of every sheet come out wider.

How to Solve a Multi-Vari Chart Question by Hand

When you don’t have access to tools like Minitab (like in the middle of a Six Sigma Black Belt Exam!), you can still analyze multivari data manually. Here’s how to determine which factor, like Tunnel Temperature or Shift, causes more variation in a process.

Additional Helpful Multi-Vari Videos

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

Also, see:

• Scatter Diagrams
• Charts
• Analysis

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 exercise, 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:

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: