# Multi-vari Charts Help Identify Sources of Process Variation

Posted by on Mar 15, 2020 in Multi-vari Chart, Quality Tools | 0 comments

A multi-vari chart is a useful tool to help you determine the sources of variation in a process.  The chart was first described by Leonard Sedar in 1950.  To develop a chart, the quality characteristic of interest is plotted across three horizontal panels that represent:

• Variability on a single piece
• Piece-to-piece variability
• Time-to-time variability

The problem solving team first develops a sampling plan based on families of variation.  Samples are then collected from the process and measured.  The sampling plan is not random sampling; rather samples are taken at prescribed times, from prescribed machines or equipment.  Three consecutive parts from each machine at each time are usually taken to determine “piece to piece” variation.

The individual measurements are then plotted on a chart like the one shown above.  The horizontal axis is divided by time, by machine, and by whatever other families of variation were identified.  Using this approach one can assess the following:

• Within piece variation, also known as positional variation, such as changes in shaft diameter from end to end and in the middle.
• Piece to piece variation, also known as cyclical variation, that is the variation seen measuring three consecutive pieces.
• Equipment to equipment variation, also known as locational variation, that is the variation seen from different equipment making the same part or multiple processing heads on the same machine, multi-cavity dies, etc.
• Time to time variation, also known as temporal variation, that is the variation observed from one time frame to another.

In the chart above, the quality characteristic of interest is hole eccentricity data taken from parts produced on three separate lines.  Three pieces from each line are taken every two hours, measured and entered into Minitab.  The response is the hole eccentricity data, factor 1 is piece, factor 2 is line, and factor 3 is time.  The order of the factors is important.  When determining the order one must remember to order them micro to macro, i.e., from the smallest variability to the largest variability factor.

Each point on the graph represents the value of the part measured, three parts at 8:00,  three at 10:00, and three at 12:00 for each line.  You can easily see that lines one and two are relatively close, where as line 3 is much higher at each of the different times.  As a result further investigation should center around why line 3 has such greater variation.

In planning a multi-vari investigation, keep the number of families to five or fewer so the sampling plan and analysis don’t become too complicated.  In addition, we need to ensure good traceability of parts to assess the variation within each family.  If we cannot trace parts through the process easily, then for time-based families, we need first-in, first-out discipline at each process operation so time sequence is not lost.

Sometimes the recommended analysis process fails because we don’t find a dominant family.  In this case, you can construct two-family multi-vari charts and look for interactions between the two.  In addition, you can always conduct a formal analysis of variance, ANOVA, to quantify the relative contributions of each family.