Normal Test Plot
Normal Test Plots (also called Normal Probability Plots or
Normal Quartile Plots) are used to investigate whether process
data exhibit the standard normal "bell curve" or Gaussian
First, the x-axis is transformed so that a cumulative normal
density function will plot in a straight line. Then, using the
mean and standard deviation (sigma) which are calculated from the
data, the data is transformed to the standard normal values, i.e.
where the mean is zero and the standard deviation is one. Then
the data points are plotted along the fitted normal line.
The nice thing is that you don't have to understand all the
transformations. All you have to do is look at the plotted
points, and see how well they fit the normal line. If they fit
well, you can safely assume that your process data is normally
distributed. That gives you confidence in your process capability
indices, and in % of non-conforming parts projections.
If your plotted points don't fit the line well, but curve away
from it in places, you may have a non-normal distribution. That
may mean that you need to get some expert help in understanding
your process. At the very least, you should suspect your process
capability indices (don't even calculate them), and realize that
you may be making more out-of-spec parts than you thought.
Things to look for:
First, look for points that are widely separated from the
others. Could these be the result of measurement or entry error?
Or are they real points that should be part of the distribution?
Then, compare your plot to the plots shown below. Does it exhibit
one of these shapes?
|If your chart looks like
||It indicates that your
||Right Skew - If the plotted
points appear to bend up and to the left of the normal line that
indicates a long tail to the right.
||Left Skew - If the plotted points
bend down and to the right of the normal line that indicates a
long tail to the left.
||Short Tails - An S shaped-curve
indicates shorter than normal tails, i.e. less variance than
||Long Tails - A curve which starts
below the normal line, bends to follow it, and ends above it
indicates long tails. That is, you are seeing more variance than
you would expect in a normal distribution.
If you have a skewed distribution, or long tails, you may well
have points in the tail(s) which are beyond specification limits.
You will need to decide what to do about this…do you
change the process to eliminate the long tail, or do you use
inspection, or do you live with infrequent out-of-spec parts? The
answer will depend on your process and your product. One rule of
thumb, though, is that it is usually cheaper to fix problems
where they occur, than to inspect, rework, or have upset
Normal Test Plot statistics:
For the x data and the y data, the following statistics are
||The average of all the data points
in the series.
||The smallest value in the
||The biggest value in the
||An expression of how widely spread
the values are around the mean.
||Is the cumulative density function
symmetrical? If so, skewness is zero. If the left hand tail is
longer, skewness will be negative. If the right hand tail is
longer, skewness will be positive.
||Kurtosis is a measure of the
pointiness of a distribution. The standard normal curve has a
kurtosis of zero. The Matterhorn has negative kurtosis, while a
flatter curve would have positive kurtosis. Positive kurtosis is
usually more of a problem for quality control, since, with "big"
tails, the process may well be wider than the spec limits.
||This measures how well the points in
your data set fit the goodness of fit. If this value is greater
than .753, you can be 95% confident that your data comes from a
non-normal distribution. If the value is close to .75, you can't
be sure, and you should keep an eye on this statistic as you
collect more data.
Create Normal Test Plots using PathMaker's Data Analyst tool.