# How to Do Statistical Process Control

by Shane Hall; Updated September 26, 2017Statistical Process Control (SPC) is a process improvement and quality control strategy that uses statistics-based techniques to monitor processes and identify areas for improvement. Dr. Walter Shewhart pioneered the techniques of SPC in the 1920s. Originally used to evaluate manufacturing processes, SPC has applications in other industry settings, as well as education, health care and government services. Relying on graphical displays, SPC offers a way to empirically examine processes and does not require in-depth statistical knowledge.

#### Items you will need

- Data
- Paper
- Pencil
- Calculator

## Constructing a Control Chart

Draw a control chart, starting with a horizontal line, labeling it with points of time in which the measurements in your data were taken. For example, if a bakery wants to ensure that a machine puts a sufficient number of blueberries in each muffin, a baker could take measurements of the machine’s performance at intervals of time, such as every 15 minutes, every 30 minutes or every hour.

Draw a vertical line, labeling it with sufficient scale to cover the data you’ve collected. If the values in your data range from 0 to 20, draw your vertical scale accordingly.

Plot the data on your graph in a time-ordered sequence. Then draw a solid line to connect the points. Doing this will display patterns of temporal variation.

## Calculations and Analysis

With your calculator, calculate the mean of the data and draw a horizontal line on your control chart that corresponds to the mean value on your vertical axis. If, for example, data from the bakery example reveals a mean of 10 blueberries per muffin, you would draw your horizontal line from the point labeled 10 on the vertical axis. This is your center line.

Calculate the standard deviation, which is the square root of the variance. To get the variance, divide the sum of the squared deviations by the number of observations minus one. Then take the square root of that figure to obtain your standard deviation.

Draw two horizontal lines – upper limit and lower limit – on your control chart. The value of the upper limit and lower limit may vary, but the norm is equal to 3 standard deviations (above and below the mean, illustrated by your center line).

Examine your completed control chart, checking to see if the data points fall within the upper and lower limits. If they stay within the limits, your process is most likely in control. Points beyond the upper or lower limit, however, suggest that something unusual, requiring your attention, is occurring in the process.

#### Tips

Using 3 standard deviations above and below the mean to set the upper and lower limits is a guideline, rather than a strict standard. Some processes, in which more exacting control is needed, such as narrower upper and lower limits, may be appropriate.