A Systems View of Variation and Quality

Visualizing the Relationship Between the Process and the Result

THE AIM for this post is to share some visualizations I’ve been working on for teaching the basics of the Taguchi Loss Function to managers and leadership who are new to the material. My plan is to get these into a more polished state so readers can use them in their own workshops and seminars without having to do all the work up-front.

Recap

In a popular newsletter from October 2021, I wrote a high-level review of the Taguchi Loss Function, comparing it to a traditional in-spec/out-of-spec step function, and how the canonical curve Taguchi suggested in his 1960 paper is more aligned with what happens in reality.

The Taguchi Loss Function

Some may recall the diagram below from that newsletter:

Basic use case for the curve is in how it correlates a process’ capability with the approach toward or departure away from an ideal target, which defines a “loss” which is more aligned with real-world experience than a step-function with arbitrary specification limits. It also marries up well with an understanding of how a process varies, creating a distribution of results over time.

In this diagram, I’ve overlaid a normal distribution curve with the average aligned over the target:

When a process is so-aligned, we have a profoundly different view of quality: not conformance to specifications, which can be beyond the capabilities of the process, but on target with minimum variance. Well, almost: there still a lot of variation in this distribution. Ideally, that curve needs to tighten up to the mean.

Per Dr. Wheeler in his text Understanding Statistical Process Control:

“On Target” will require that one know the Process Average, and sets the Process Aim in such a way to get the Process Average as close to the Target as possible…

(p. 146)

Thus, we have in one diagram an example of how variation and quality are correlated. But, I think we can be more impactful when we can show how the curve works in practice with some animation.

Four Scenarios

In the following video, I’ve strung together four slides with animations to elaborate on these diagrams and make it a little clearer how the curve works at a high level when under/over shooting a target, and mis/ideally-aiming the process average over the target.

Click the video below to see the animations, and read below for descriptions of each.