Shrinkage Defects Follow Mold Temperature? —— Five Practical Steps to Create a Scatter Diagram, Let the Variables Speak for Themselves
The quality manager of a plastic injection molding factory has been plagued by shrinkage defects in a particular casing component for two months: the proportion of undersized parts fluctuates between 3% and 15%, and despite adjustments to process parameters and repairs to the mold, the issue remains unresolved. It wasn't until someone plotted the "mold temperature—shrinkage rate" data from the past month on a chart that the problem became clear—higher mold temperatures correlate with more severe shrinkage, with dozens of data points almost forming a straight line. This chart is a scatter diagram, one of the seven QC tools.
1. What is a Scatter Diagram Used For?
A scatter diagram uses the distribution of points to show the relationship between two variables, answering three questions: Is there a relationship? What is the direction? How strong is the relationship? Many "unclear" disputes in quality work essentially stem from not clearly understanding the relationship between variables: which factors are truly affecting the defect rate? What range should the parameters be set to for stability? A scatter diagram is the most cost-effective tool for exploring these relationships.
It is suitable for three scenarios:
- Suspecting that a certain parameter is related to quality outcomes but unsure of the direction and strength of the relationship.
- Two quality metrics fluctuating, wanting to determine if they have the same root cause.
- Needing to use data to convince colleagues from other departments that "this is indeed related, let's stop arguing based on feelings."
The scatter diagram holds a unique position among the seven QC tools: check sheets and stratification ensure that data is collected and categorized correctly, Pareto charts prioritize the most significant issues, and scatter diagrams help identify the underlying relationships. It is often used in conjunction with stratification—first, stratify the data by material, machine, and shift, then plot a scatter diagram for each stratum, which can often reveal relationships that are not apparent when the data is mixed together.
It is important to note that a scatter diagram is responsible for "finding suspects" but not for "establishing causality." Correlation on the chart does not equate to causation in reality; confirming the relationship requires subsequent experimental validation.
2. Five Steps to Create a Reliable Scatter Diagram
Step 1: Collect Paired Data. Collect at least 30 pairs of data, where X and Y must come from the same observation and correspond one-to-one. Data should cover the full range of the variables, not just "normal conditions." Record conditions such as time, batch, and machine to facilitate the tracing of anomalies.
Step 2: Define the Axes. Place the cause variable (adjustable parameter) on the X-axis and the result variable (quality characteristic) on the Y-axis. If both are results, place the one of greater concern on the Y-axis. Reversing the axes does not affect the shape of the graph but can impact subsequent communication.
Step 3: Set the Scale. Determine the minimum and maximum values for both variables, leaving a 5% to 10% margin at each end. Use uniform intervals for the scale. Incorrect scale ranges can straighten a curved relationship or amplify noise into a "correlation."
Step 4: Plot the Points. Plot each pair of points. If multiple points overlap, draw concentric circles or annotate the number of points nearby to avoid the illusion of "only a few points."
Step 5: Label and Archive. Clearly label the title, sample size, time period, conditions, and responsible person on the chart. A scatter diagram without source information will be meaningless three months later.
3. Four Key Observations for Interpretation
1. Look at the Direction: If the point cluster slopes from the upper left to the lower right, it indicates a negative correlation, where one variable decreases as the other increases. If it slopes from the lower left to the upper right, it indicates a positive correlation, where both variables increase or decrease together. If the points are scattered randomly, there is no correlation. For quality professionals, the direction itself is a clue: a negative correlation often suggests that increasing the parameter might be beneficial, while a positive correlation indicates that an upper limit should be set for the parameter.
2. Look at the Strength: The narrower the point band, the stronger the relationship; the wider and more scattered the band, the weaker the relationship. If the band is narrow and almost forms a line, it suggests that this variable largely determines the outcome.
3. Look at the Shape: If the point cluster forms a curve (U-shaped or parabolic), it indicates the presence of an optimal range, where both extremes are undesirable. For example, welding temperature—this is where a scatter diagram outshines a simple "higher is better" judgment.
4. Look for Anomalies: Points that are isolated and far from the point band often correspond to special events such as material changes, machine stops, or operator changes. First, check the records to confirm the cause, then decide whether to exclude them; do not delete them arbitrarily.
4. Case Study Review
Returning to the initial case, the factory collected 35 pairs of "mold temperature—shrinkage rate" data and plotted a scatter diagram. The point band showed a clear positive correlation, with only one data point (mold temperature 78°C, low shrinkage rate) being an outlier. Checking the records revealed that a new batch of material had just been introduced on that day, causing an occasional point due to material differences. Based on this, the mold temperature was gradually reduced from 80°C to 65°C for trial production, reducing the shrinkage defect rate from around 8% to less than 1%. Subsequently, DOE was used to confirm the optimal range, and both mold temperature and material temperature were incorporated into the procedure document. The entire process did not require any additional testing equipment; a single scatter diagram locked in the direction.
5. Five Common Misconceptions
Misconception 1: Drawing conclusions with too little data. Plotting with fewer than 20 pairs can result in random fluctuations appearing as correlations; collect at least 30 pairs.
Misconception 2: Inappropriate scale range. Using a narrow range on the X-axis can make a curved relationship appear linear or amplify normal variations into strong correlations.
Misconception 3: Confusing correlation with causation. A scatter diagram only shows that variables change together; whether one causes the other must be verified through experiments (such as DOE).
Misconception 4: Plotting without stratification. Mixing data from two batches of materials or two machines can result in false correlations that are completely opposite; stratify the data before plotting.
Misconception 5: Relying solely on the chart. The chart provides intuition, but the strength of the relationship should be quantitatively verified using the correlation coefficient r. The closer |r| is to 1, the stronger the relationship. Including both the chart and the r value in reports enhances persuasiveness.
The essence of a scatter diagram is to transform "I think it's related" into "it's visible on the chart and calculable from the data." By following the five steps to create the chart, the four key observations for interpretation, and supplementing with experimental validation, you can uncover the overlooked line between parameters and defects—often, the problem is not too difficult but rather that no one has put the two together to examine them.
Five Practical Steps for Scatter Diagrams—First Find the Suspect, Then Verify the Causality, Let Variable Relationships No Longer Be a Guess.
Knowledge code: 5.2.4
Version: v20260901
Author: QTank QTank is dedicated to providing systematic knowledge, methodologies, and practical tools for quality management professionals, helping enterprises continuously improve their quality capabilities.