How do you interpret the slope and intercept of a Q-Q plot for SPC?

1 Q-Q plot basics

A Q-Q plot is a scatter plot that shows the relationship between the ordered values of your sample data (y-axis) and the corresponding percentiles of a normal distribution (x-axis). If your data are normally distributed, the points should fall along a straight line with a slope of 1 and an intercept of 0. This means that your data have the same mean and standard deviation as the normal distribution. However, if your data are not normal, the points will deviate from the line in different ways, depending on the type and degree of non-normality.

2 Slope of Q-Q plot

The slope of the Q-Q plot reflects the ratio of the standard deviation of your data to the standard deviation of the normal distribution. If the slope is greater than 1, it means that your data are more spread out than the normal distribution, and vice versa. A slope that is significantly different from 1 indicates that your data have a different scale or variability than the normal distribution. This could be due to measurement errors, outliers, or heterogeneous subgroups in your data.

3 Intercept of Q-Q plot

The intercept of the Q-Q plot reflects the difference between the mean of your data and the mean of the normal distribution. If the intercept is positive, it means that your data have a higher mean than the normal distribution, and vice versa. An intercept that is significantly different from 0 indicates that your data have a different location or central tendency than the normal distribution. This could be due to a shift in the process mean, a bias in the measurement system, or a skewed distribution.

4 Non-normal patterns

Besides the slope and intercept, you can also look for other patterns in the Q-Q plot that indicate non-normality. For example, if the points curve upward at the ends, it means that your data have heavier tails than the normal distribution, which implies a higher probability of extreme values. This could be due to fat-tailed distributions, such as lognormal or Weibull, or a mixture of distributions. If the points curve downward at the ends, it means that your data have lighter tails than the normal distribution, which implies a lower probability of extreme values. This could be due to thin-tailed distributions, such as uniform or exponential.

5 How to use Q-Q plot for SPC

The Q-Q plot can help you diagnose and improve your process by identifying non-normality and possible causes. However, it is not enough to rely on the Q-Q plot alone, as it is a graphical tool that is subject to visual interpretation and judgment. You should also use other tools, such as histograms, box plots, normality tests, and control charts, to complement and confirm your analysis. Moreover, you should always investigate the source and nature of non-normality, and determine whether it is inherent to the process or due to special causes. Depending on the situation, you may need to take corrective actions, such as removing outliers, stabilizing variability, transforming data, or using non-normal control charts.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?