Statistical Process Control

What is statistical process control (SPC)?

A tool that uses statistical methods to monitor a process to improve quality and consistency¹
- Using quantitative techniques to interpret data
- Applied to a process involving people, equipment, materials, and environment working together to produce an identifiable, measurable output
- That behaves in a predictable, consistent manner
It is also referred to as statistical quality control

Unlike other topics in this course it is not considered an inference test
However, SPC determines if variability is consistent with the process
- The normal variability in a process is referred to as “common cause” variability and any other source of variability is referred to as “special cause”
- Common cause is due to random variation in the process, like the \(null\) hypothesis in statistical inference
- Special cause is due to variation caused by something other than the process, like the \(alternative\) hypothesis

SPC was first developed for the manufacturing industry to reduce defective or non-conforming products
Today it is used in many different applications for example
- To improve quality and consistency the practice in healthcare¹
- In service industry to improve customer satisfaction ²

To control a process data is collected from process samples
Both categorical and quantitative variables are used
- Numerical variables are called variable characteristics
- Categorical variables are attribute characteristics
Fixing the number of samples collected is important in SPC
- Too many samples can cost time and resources
- Too few samples gives too much variability in control data

If process variation is from common cause
- The process is considered in-control
But if process variation is due to special cause
- The process is considered out-of-control
To determine the state of a process
- We typically use a control chart

This control chart is called a p-chart because it is
- Based on the proportion of non-conforming parts

p-chart for silicon chip defects

The middle line on the chart is
- the long-run or population proportion
- p for the process when it is in control
The upper control line (UCL) and lower control line (LCL)
- Are 3 standard deviations (SD) above p
- And 3SD below p¹

The risk of getting an out-of-control response
- From an in-control process is very small
Our model for a proportion is the normal distribution
- The probability of getting a sample 3SD above or below the mean
- From common cause (random chance) is 0.0027 or 0.27%
So, 99.7% of the time an in-control process should give
- An in-control response or sample

We can view the data for the attribute characteristics
- As a histogram and evaluate normality assumption

histogram of defects

This example shows the size of aerosol particles
- View the data before creating a control chart
- We can see that the variability isn’t random

Chart for aerosol particle size

We can view the data for the variable characteristics
- As a histogram and evaluate normality assumption like before

histogram of particle size

With control levels based on the subset
- You can see that most of the samples are out-of-control
- Indicating special-cause variation

Shewhart control chart

The middle line on the chart is
- the long-run or population mean
- x-bar for the process when it is in control
The upper control line (UCL) and lower control line (LCL)
- Are 3 standard deviations (SD) above x-bar
- And 3SD below x-bar

Once special cause variability is found
- The source of the variability needs to be identified
There are several tools for this part of SPC¹
- Pareto chart
- Cause-and-effect (fishbone) diagram
- Flowchart
- And many others

Example Pareto chart on complaints

Fishbone diagram for part size error

Flowchart diagram for customer comment