Statistical Process Control (SPC) is a vital tool in Lean Six Sigma that helps in monitoring and controlling a process to ensure that it operates at its full potential. Among the various tools used in SPC, control charts stand out as a powerful method for visually tracking process performance over time, detecting any signs of uncontrolled variation, and thereby facilitating the maintenance of process quality. In this article, we will delve into the theory behind control charts and outline the steps involved in constructing them.

Control Charts: An Overview

Control charts, also known as Shewhart charts or process-behavior charts, are graphical representations that show process variation over time. They consist of a center line that represents the average of the data points (typically the process mean), and two control limits that define the boundaries of acceptable variation. These limits are calculated based on the process data and are not arbitrary; they usually represent the process mean ± 3 standard deviations, covering approximately 99.73% of the data if the process follows a normal distribution.

Theory Behind Control Charts

The foundational theory behind control charts is based on the distinction between common cause variation and special cause variation. Common cause variation is inherent to the process and is predictable, while special cause variation results from external factors and indicates that the process is out of control. By distinguishing between these two types of variation, control charts help identify when a process is behaving normally and when there is an anomaly that requires investigation and corrective action.

Constructing a Control Chart

To construct a control chart, follow these steps:

Step 1: Determine the Type of Data

Decide whether the data is continuous (e.g., weight, length) or discrete (e.g., defect count). This determination will influence the choice of control chart, such as an X-bar and R chart for continuous data or a p-chart for discrete data.

Step 2: Collect Data

Collect a sufficient amount of data from the process. Typically, this involves selecting samples over a period of time to gather a representative snapshot of the process performance.

Step 3: Calculate the Center Line

For continuous data, calculate the average of each sample group and then the overall average of these averages for the center line. For discrete data, the calculation will depend on the specific type of chart used.

Step 4: Calculate Control Limits

Using the collected data, calculate the upper and lower control limits. For an X-bar chart, for example, this involves calculating the average range (R) of the samples, then determining the upper and lower control limits using predefined constants (A2, D3, D4) that vary based on sample size:

• Upper Control Limit (UCL) = Xˉ+A2×Rˉ

• Lower Control Limit (LCL) = Xˉ−A2×Rˉ

For other types of charts, the formula for control limits will vary accordingly.

Step 5: Plot the Data

Plot the data points, center line, and control limits on the chart. Each data point represents a sample or subgroup.

Step 6: Analyze the Chart

Examine the control chart for signs of control or out-of-control conditions. Patterns such as points outside the control limits, runs, or trends indicate special cause variation and warrant further investigation.

Conclusion

Control charts are a cornerstone of Statistical Process Control in Lean Six Sigma, providing a visual tool for monitoring process stability and identifying variations that require action. Constructing and analyzing control charts enable organizations to maintain high-quality processes, identify opportunities for improvement, and achieve operational excellence. By following the steps outlined above, practitioners can effectively implement control charts in their process improvement initiatives, driving towards sustained performance and quality enhancements.