The formulas to calculate the control limits are:
\[ LCL = x - (l \cdot x \cdot s) \]
\[ UCL = x + (l \cdot x \cdot s) \]
Where:
The control limit is a statistical concept used in quality control to assess the variation and performance of data within a process. It represents the boundaries within which data points are expected to fall under normal circumstances. These limits are defined using statistical calculations based on historical data and are used to monitor and maintain the stability and predictability of a process.
Control limits are typically set at a fixed number of standard deviations from the mean of the data. The upper control limit (UCL) is calculated by adding a certain number of standard deviations to the mean, while the lower control limit (LCL) is obtained by subtracting the same number of standard deviations from the mean. This establishes a range within which data points are considered expected and acceptable.
The importance of control limits lies in their ability to help organizations identify variation beyond what is considered normal, known as special cause variation. When data points fall outside the control limits, the process may have experienced a significant change or a special cause that needs to be investigated. This indicates that the process is no longer stable and predictable, which may lead to defects, errors, or deviations from desired outcomes.
Let's assume the following values:
Using the formulas to calculate the control limits:
\[ LCL = 50 - (1.96 \cdot 50 \cdot 5) = 50 - 490 = -440 \]
\[ UCL = 50 + (1.96 \cdot 50 \cdot 5) = 50 + 490 = 540 \]
The Lower Control Limit (LCL) is -440 and the Upper Control Limit (UCL) is 540.