Statistical Process Controls for Variable Data
In order to detect drift and variations in a process, statistical process controls should be implemented during manufacturing to help ensure the consistency of the final product. Specific parameters that will impact the final product should be monitored at key points in the manufacturing process and continuously evaluated. This data will be used to create control charts for the process, which will help create a visual for the stability or statistical control of that process. A control chart is comprised by grouping sample data over time and shows the center line of that data as well as allowable upper and lower limits for that process. This center line is calculated from the average of the data and is commonly denoted as x-bar. The upper and lower control limits are generally computed as ± 3 sigma levels of the average. Control limits represent the limit for acceptable amounts of variation in a process over time and are generally represented as UCL for Upper Control Limit and LCL for Lower Control Limit. However, it is important to note the difference between being in control and being within specifications. Control limits are generated by the process data, ± 3 sigma levels of the average, while specifications are selected based on the parts requirements.
For example, a company is producing bicycle springs with a key parameter being the length of the spring coil. There is a vision system installed in the production line to continuously monitor the length of the coil springs. The preventive maintenance schedule for the line has not been properly adhered to but the first batch of the day is still categorized as in control based on the data that has been collected. The in-control process is shown below, and the chart clearly shows no data points have drifted outside of the control limits showing that is batch experienced a normal level of variability. While this chart does show the process is in control it does not show if the process meets specifications as the data may be in control around the wrong baseline length.
As more batches of springs continue to be produced without preventive maintenance the process will naturally start to drift out of its regular operating range. The vision system will identify when a spring has been produced that does not meet the control limits and this will be shown in the control chart. As shown below, the spring that was produced out of control limit is easily identifiable on the control chart and highlights the issue with the process.
Depending on the data being monitored multiple forms of control charts can be used. Three commonly used control charts are the S-chart, the R-chart and the X-bar chart. Each chart has a different use case which is dependent on the size of the samples being collected as well as the type of variability being evaluated. Again, let’s go back to the bicycle spring manufacturing example. Assuming the production line did not have an automated vision-system sampling each bicycle springs length would be impractical as it would slow down the production speed of the line. Therefore, the team must manually sample springs from each batch throughout the day. There are two forms of variability that needs to be accounted for to ensure the process is in control. The within subgroup variability, also known as the variability of each individual sample group, and the between group variability which represents the variability between the sample groups taken. Depending on the subgroup size, also known as the sample size of each batch, a different control chart can be used. After within group variability has been calculated the X-bar can be used to find any potential process changes between the different sample groups or batches. The table below shows the three different control charts and their use case parameters.
| Chart Nomenclature | Chart Description | Variation Being Evaluated | Subgroup Size Required | How to Create the Graph |
| S-Chart | Standard Deviation Control Chart | Within Subgroups | More Than 8 | Create a time series plot for each subgroup’s standard deviation |
| R-Chart | Range Control Chart | Within Subgroups | 8 Or Less | Create a time series plot for each subgroup’s range |
| X-bar Chart | Mean Control Chart | Between Subgroups | N/A | Create a time series plot for the mean of each subgroup |
It is important to note that when looking at process controls the S-Chart and R-Chart should always be calculated before the X-bar chart. The limits of the X-bar chart are calculated with the assumption that within subgroup variation is stable. If this is not the case the variability between subgroups cannot be properly computed and may provide misleading results.