Multi-Vari Chart: Find Out Which Family of Variation Is Driving Your Process

A Multi-Vari Chart answers one question before you spend money answering others. Where does the variation live? Not which cause, but which family of causes. Does the output drift from day to day? Does it shift from batch to batch within a day? Does it change by position in the flow? Or does it wobble between two repeated measurements of the same thing?

You use it early in the Analyse phase of RDMAICS. You have confirmed your measure. You have a problem statement. You have a long list of suspected causes and no sensible way to rank them. A Multi-Vari study narrows that list by eliminating whole categories at once. If almost nothing moves between repeated measurements, your measurement system and your short-term noise are not the story. If almost everything moves between days, you stop studying positions and start studying days.

In Ci Flow the tool asks for a balanced worksheet with Response, Time, Cycle, Position and Replicate. It validates the study structure, calculates the variation families deterministically, and displays separate time panels so the three patterns do not overlap on one axis.

Everything below is built on the sample study that ships with the tool. The case is fictional. It exists so you can see the mechanics before you load your own numbers.

The study looks at a response measurement taken across a service flow with three positions: Intake, Resolver queue and Closure. It was sampled across two time periods, Day 1 and Day 2. Within each day there were three cycles, Cycle 1 to Cycle 3. At every position in every cycle in every day, two repeated measurements were taken, labelled Replicate 1 and Replicate 2. That gives 2 times by 3 cycles by 3 positions by 2 replicates, which is 36 measurements.

The process or group column carries Team A on Day 1 and Team B on Day 2. That is worth noticing now and we return to it in the limits section, because it changes what the time result actually means.

The lowest value in the worksheet is 52.2 at Intake, Cycle 1, Day 1. The highest is 81.8 at Closure, Cycle 3, Day 2. So the response climbs as you move through positions, climbs again across cycles, and sits higher overall on Day 2.

The worksheet has four required columns and two optional ones. Response measurement is the number you care about. Position or location, Cycle or batch, and Time period are the three nesting levels. Process or group and Notes are optional. In the sample data the Notes column is used to label the replicate within each cell, which is a tidy habit worth copying.

Balance matters more than volume here. Each time period must contain the same cycles. Each cycle must contain the same positions. Each position must carry the same number of replicates. The sample data is fully balanced at 36 rows. If you load something ragged, the structure check will tell you before you read anything into the chart.

Two practical points on collection. First, take your replicates as genuine repeats of the same unit at the same position, not as two different units. They are measuring repeat-measurement variation, so anything else contaminates that family. Second, decide your time periods and cycles before you collect, not afterwards. Reclassifying rows later turns a designed study into a story.

The output opens with Multi-Vari Profiles. There are two panels, one for Day 1 and one for Day 2. Each panel plots position on the horizontal axis and draws one line per cycle. Keeping time in separate panels is the point. It stops the day effect from flattening the cycle and position patterns into a single confusing graph. Under the panels, the tool states the study structure shown as 2 time periods by 3 cycles by 3 positions, and notes that replicates are averaged within each cell.

The statistical results table reports the decomposition. N is 36 and total corrected sum of squares is 2,103.04. Temporal sum of squares is 1,296 on 1 degree of freedom, which is 61.63 per cent of the total. Cyclical is 488 on 4 degrees of freedom, or 23.2 per cent. Positional is 296 on 12 degrees of freedom, or 14.07 per cent. Within-position is 23.04 on 18 degrees of freedom, or 1.1 per cent.

Key Findings labels temporal variation as dominant and both cyclical and positional as secondary. The decision-ready conclusion states that temporal variation is the dominant process family at 61.63 per cent of observed total variation, with within-position variation at 1.1 per cent.

The assumption and data checks are easy to skim past and should not be. Study structure is marked Valid, with 2 times, 6 time by cycle cells and 18 time by cycle by position cells, and a note that every nested level has replication. Decomposition reconciliation is marked Valid, with a component gap of 9.095e-13, which is rounding. Inference is marked as no p-values claimed, described as a descriptive variance-family decomposition, with a pointer to a designed mixed-effects study for formal variance-component inference. The tool also offers an AI review that talks through the result in plain language.

The result changes your investigation plan in three concrete ways.

First, you stop worrying about measurement repeatability for now. Within-position variation is 1.1 per cent of the total. Whatever is wrong, repeated measurement of the same thing is not adding much noise. That frees you from a measurement system study at this stage.

Second, you point your effort at whatever changes between the two time periods. The tool's own next actions say to investigate time-dependent changes such as shift, day, environment or material lot. In this study the time periods also differ by group, Team A on Day 1 and Team B on Day 2, so the honest next step is to separate those two explanations rather than assume either one.

Third, you keep position and cycle on the list but below time. Together they carry 37.27 per cent. Positional variation of 14.07 per cent is consistent with the visible climb from Intake to Closure in both panels, and it is real, but it is not the biggest lever.

Most Multi-Vari problems are design problems, not reading problems. They happen before the data reaches the tool.

Collapsing the structure is the most common. People record three positions and one cycle and call it a Multi-Vari study. With no cycle level you cannot separate cyclical from positional variation, and the decomposition has nothing to split.

Using different units as replicates is the next. Replicates must be repeat measurements of the same unit at the same position. If they are different units, the within-position share stops being repeat-measurement variation and starts absorbing unit-to-unit differences, which flatters your measurement system.

Reading share as significance is the third. A 61.63 per cent share is a share of the observed sum of squares in this one study. It is not a test result. The tool says so directly under Inference.

The Multi-Vari Chart ranks families of variation. It does not identify causes. A temporal share of 61.63 per cent tells you to look at what changes between Day 1 and Day 2. It does not tell you whether that is the team, the workload, the environment or the material. That work is yours.

It does not perform inference. The tool states plainly that no p-values are claimed and that this is a descriptive variance-family decomposition. There are no confidence intervals and no significance tests. If you need formal variance-component inference, the stated next action is to use a mixed-effects model.

It does not fix a confounded design. In this sample study, time and group move together. The tool reports the temporal family correctly as calculated, and it cannot separate day from team, because the data was not collected in a way that allows it. The second next action, confirming the nested sampling plan before generalising beyond the observed study, is a warning about exactly this.

It does not generalise. Two days, three cycles and three positions describe two days, three cycles and three positions. A dominant temporal family here does not promise a dominant temporal family next month. And it does not forecast, cost or prioritise improvements. It gives you a defensible ranking of where to look first, with a reconciled decomposition and a structure check behind it. Use it for that, then move on to the tools that test causes.