What If Subgroup Sizes Are Not Fixed?

In standard Statistical Process Control (SPC) textbooks, subgroup sizes are typically recommended to be fixed at 3–5 samples.
This recommendation is based on an ideal assumption: each production batch or time interval yields the same number of samples.

However, in real manufacturing environments, this assumption often does not hold.
Due to factors such as end-of-batch material shortages, sample loss, or varying time windows in high-frequency automated data collection, subgroup sizes (n) frequently fluctuate.

Limitations of Traditional SPC Tools

When faced with variable subgroup sizes, traditional Excel templates or entry-level SPC software usually fail—either producing errors or requiring manual data splitting and padding.

Such workarounds not only distort the authenticity of the data, but also obscure the true sources and structure of process variation.

How Simple SPC Handles Variable Subgroup Sizes

Simple SPC provides full support for SPC analysis with non-fixed subgroup sizes using statistically sound and production-ready methods.

Stepwise Control Limit Algorithm

Accurately Capturing the True Voice of the Process

From a statistical standpoint, variations in subgroup size (n) directly affect the standard deviation of the subgroup mean.
For this reason, Simple SPC dynamically calculates the Upper and Lower Control Limits (UCL/LCL for each individual data point, based on the actual subgroup size of that point.

As a result, the control chart displays scientifically derived stepwise control limits, ensuring that out-of-control detection for every subgroup is statistically rigorous, consistent, and reliable, even when subgroup sizes fluctuate.

Full Control Chart Support for Variable Subgroups

For processes with fluctuating subgroup sizes, the system provides a complete set of statistical tools:

• X-bar Chart
  Monitors the process mean and central tendency.

• R Chart / S Chart
  Monitors within-subgroup variation.
  When subgroup sizes vary significantly, the system recommends using the Xbar-S chart, as it utilizes all sample information more accurately to estimate process variation.

Process Capability Analysis

• CPK / PPK

• PPM

• Distribution plots

• Capability histograms

Example

The figure below shows an SPC analysis report for a process with variable subgroup sizes generated by Our SPC.

Using the same dataset, the results were recalculated using the Simple SPC CPK Tool for verification and comparison.

CPK Tool Support

The CPK Tool fully supports analysis based on variable subgroup sizes, ensuring consistency between SPC monitoring and capability evaluation.

Consistent with Minitab Results

Professional rigor is the bottom line for quality engineers.

To validate statistical accuracy, we input the same complex dataset with variable subgroup sizes into both Minitab and the Simple SPC 4.0 CPK Tool for parallel verification.

Validation Results

The results show that both systems produce completely identical outputs, including:

• Control limits (UCL / LCL)

• Mean values

• Sigma estimates

• Process capability indices (CPK, PPK)

This confirms that Simple SPC maintains industrial-grade statistical precision, while delivering a lightweight, fully digitalized experience through a browser-based (B/S) architecture with no client installation required.