Calculating Control (SPC/QC) Limits

Control Limits are used as to calculate the odds that a given value (measurement) is part of the same group of data used to construct the histogram.  With properly set control limits, we can identify when the process has shifted or become unstable.  With this knowledge, we can then study that particular situation, identify root cause, and come up with a plan to minimize or eliminate these occurrences. 

Shewhart found that control limits placed at three standard deviations from the mean in either direction provide an economical tradeoff between the risk of reacting to a false signal and the risk of not reacting to a true signal – regardless the shape of the underlying process distribution.

If the process has a normal distribution, 99.7% of the population is captured by the curve at three standard deviations from the mean. Stated another way, there is only a 0.3% chance of finding a value beyond 3 standard deviations. Therefore, a measurement value beyond 3 standard deviations indicates that the process has either shifted or become unstable (more variability).

Control limits are defined as follows:

• Upper Contol Limit (UCL) – Average + 3 * Standard Deviation
• Upper Warning Limit (UWL) – Average + 2 * Standard Deviation
• QC Mean – Average
• Lower Warning Limit (UWL) – Average - 2 * Standard Deviation
• Lower Contol Limit (LCL) – Average - 3 * Standard Deviation

WIMS offers several tools to calculate these limits.  See Variable Analysis Graphs, Time Series Stats Form, and QC Report.  Control limits are then used to detect QC Flags, i.e. "Special Causes" in the data.  See QC Flag Detection Rules