3. Production Process Characterization
3.1. Introduction to Production Process Characterization
3.1.3. Terminology/Concepts

3.1.3.1.

Distribution (Location, Spread and Shape)

Distributions are characterized by location, spread and shape

A fundamental concept in representing any of the outputs from a production process is that of a distribution. Distributions arise because any manufacturing process output will not yield the same value every time it is measured. There will be a natural scattering of the measured values about some central tendency value. This scattering about a central value is known as a distribution. A distribution is characterized by three values:

Location

The location is the expected value of the output being measured. For a stable process, this is the value around which the process has stabilized.

Spread

The spread is the expected amount of variation associated with the output. This tells us the range of possible values that we would expect to see.

Shape

The shape shows how the variation is distributed about the location. This tells us if our variation is symmetric about the mean or if it is skewed or possibly multimodal.

A primary goal of PPC is to estimate the distributions of the process outputs

One of the primary goals of a PPC study is to characterize our process outputs in terms of these three measurements. If we can demonstrate that our process is stabilized about a constant location, with a constant variance and a known stable shape, then we have a process that is both predictable and controllable. This is required before we can set up control charts or conduct experiments.

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The table below shows the most common numerical and graphical measures of location, spread and shape.

Parameter	Numerical	Graphical
Location	mean median	scatter plot box plot histogram
Spread	variance range inter-quartile range	box plot histogram
Shape	skewness kurtosis	box plot histogram probability plot