A statistical process control (SPC) chart is a very useful tool for maintaining the quality of an ongoing, repetitive process. There are several different types of SPC charts, but the most common is normally referred to simply as a control chart. A control chart plots the ongoing performance of a process against expected outcomes based on statistics; these being the process average and multiples of the process standard deviation. The control chart allows a quick visual analysis of trends in the process and can readily show when results are outside expected limits.
Perform a series of repetitive measurements on the outcome of interest originating from the process you want to control. For example, if the process is the manufacture of ball bearings with a 1-inch diameter, you would randomly select a number of bearings and measure them. This sample should consist of at least 30 items that are representative of the normal process output and are selected at random.
Calculate the mean, or average, of the measurements.
Calculate the standard deviation of the process measurements. This is normally given the term "sigma" and is a measure of how much variation there is in the process. Sigma can be thought of as being close to the average deviation of all of the measurements from the mean of those same measurements. Most scientific or statistical calculators will have the ability to find the standard deviation of a series of numbers.
Calculate twice and three times the value of sigma and then both add and subtract these values from the process mean. For example, if the mean of the ball bearing measurements was 1.04 inches and sigma was 0.02 inches, you would calculate the following four values: 1.04 + (2)(0.02), 1.04 + (3)(0.02), 1.04 - (2)(0.02) and 1.04 - (3)(0.02).
Construct a horizontal graph template using Excel or similar graphing software, or simply using pen and paper. The horizontal axis of this graph will have units of time (moving forward from left to right), and the vertical axis will use the same units as your process measurement and will be centered at your process mean. So in the case of the ball bearing example, the vertical axis would be centered on a value of 1.04 inches.
Overlay horizontal lines on this template. One line will go horizontally down the middle of the graph to mark the process mean obtained from your initial repeat measurements. Two lines will go above the mean to mark the location of the mean plus two and three sigma, and two lines will go below the mean to mark the mean minus two and three sigma.
Overlay additional horizontal lines on the graph template to mark the locations of upper and lower specification limits, if any exist. You now have a completed control chart template.
Measure the process outcome on a regular basis in the future. A measurement could be taken once an hour, once a day or at any other reasonable interval. Plot these measurement results on the control chart template, adding additional data points to the right as time moves on.
Observe the location of the ongoing data points as they are plotted horizontally along on the control chart from left to right. The points should stay relatively close to the expected process mean. Points that exceed the plus or minus two sigma lines (either too high or too low) are considered a warning that the process is showing substantial deviation, whereas points that exceed the plus or minus three sigma lines or the specification lines are a red alert that the process is likely out of control.
Observe any trends or patterns in the ongoing plot of data points. This is a very valuable aspect of control charts since it is often possible to see measurements trending up or down toward failure and to remedy a problem before it becomes too pronounced or before scrap product is made.
Remember that even a well-controlled process will occasionally produce points outside plus or minus three sigma from the mean because of normal random variation. This means that there will be "false alarms" once in a while.
The SPC chart is only as good as the original measurements used to find the expected average and sigma. Make sure that the sample you choose is truly representative of the process and is sufficiently large.
- Remember that even a well-controlled process will occasionally produce points outside plus or minus three sigma from the mean because of normal random variation. This means that there will be "false alarms" once in a while.
- The SPC chart is only as good as the original measurements used to find the expected average and sigma. Make sure that the sample you choose is truly representative of the process and is sufficiently large.
Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" (Canada's national newspaper) and the U.K. magazine "New Scientist." He holds a Master of Science from the University of Waterloo. Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor.