Quality Tool - Scatter Diagrams

<p><strong>Understanding Relationships</strong></p>

<p>Identifying the true cause of a problem is the key to effective quality improvement.</p>

<p>When we use Scatter Diagrams for the diagnosis of a problem, we are basically looking for a relationship between two measurable variables. We hope to discover an insight into the true cause of a problem.</p>

<p>Unfortunately, the true cause of a problem is usually not obvious. Therefore we must proceed very cautiously.</p>

<p><strong>Analysing Scatter Diagrams</strong></p>

<p>Analysing scatter diagrams is a four-step process:</p>

<ul>
<li>Develop a plausible and relevant theory about the suspected relationship between two variables of concern.</li>
<li>Collect appropriate paired data (Quality Capsule # 014) and construct a scatter diagram.</li>
<li>Identify and classify the pattern of correlation.</li>
<li>Question your original theory and consider other explanations for the observed pattern of correlation.</li>
</ul>

<p><strong>Potential Pitfalls and Problems in Interpretation</strong></p>

<p><img alt="" src="http://sureshlulla.com/blog/wp-content/uploads/2020/10/Quality-Capsule_-Inside-Article-Diagram-017.png" /></p>

<p><em>Range of Data</em></p>

<p>It is critically important that a team restrict its interpretation of the scatter diagram to the range of the observations. The actual relationship between two variables X and Y is shown in the top left diagram.</p>

<p>But suppose the team had gathered data on X for the range 0 to 40, their scatter diagram would resemble the top right diagram labelled &lsquo;A&rsquo;. On the basis of a strong positive correlation displayed in the diagram, the team would be tempted to assume that a large value of X, say X = 80, would yield a correspondingly large value of Y. Obviously, this conclusion about the relationship between X and Y, which goes outside the range of the data shown in &lsquo;A&rsquo;, would be incorrect.</p>

<p><em>Range of Operations</em></p>

<p>Suppose the process operates within the range X = 30 to 70. The scatter diagram in this region of actual operations is shown in the bottom left diagram labelled &lsquo;B&rsquo;.</p>

<p>In the region of actual operation there is no correlation. Control of one variable will not help us control the other.</p>

<p><em>Effect of Scale</em></p>

<p>The diagram at the bottom right labelled &lsquo;C&rsquo; shows the same data, but here the team has decided to make the X and Y axes the same.</p>

<p>This simple change of scale makes it appear that the value of Y is almost constant, regardless of X.</p>

<p><em>Correlation without Physical Understanding</em></p>

<p>Scatter diagrams only show relationships. They do not prove cause and effect (<a href="http://sureshlulla.com/2020/09/23/quality-tool-cause-effect-diagram/">Quality Capsule #012</a>).</p>

<p>One must have plausible, physical explanation to establish cause and effect.</p>

<p><strong>Next</strong></p>

<p>In my next edu-blog, on Wednesday 4 November, I will share an appropriate Quality Fable:&nbsp;<em>Indian Curry and British Satisfaction</em>. This fable will stimulate your thinking on application of Quality Tools.</p>