Z-MR Control Chart: Standardized Monitoring Across Batches and Conditions
What is the Z-MR Control Chart?
When batch sample sizes or measurement conditions differ, raw values are not directly comparable and an ordinary I-MR chart misleads. Z-MR standardizes each observation within its own batch as z = (x − μ)/σ, then plots an I-MR chart of the z values, removing scale differences so every batch is monitored on one common scale. The standardized values have mean 0 and standard deviation 1, so the limits are fixed at ±3 and rule testing is uniform.
When to Use It
Use it for mixed data across shifts, machines, operators or material batches, changing sample sizes, and multi-line consolidated monitoring. Z-MR pulls multi-source data onto a single scale, making it an effective complement for cross-condition process control.
How to Use It (Step by Step)
Enter the observations with their batch identifiers, and the tool standardizes within each batch, plots the Z individuals and moving-range charts with ±3 limits, and marks violations. Remember that Z-MR flags anomalies relative to each batch's own level, not absolute levels — pair it with conventional charts to see batch-to-batch level shifts.
Key Formulas / Example
z_ij = (x_ij − x̄_j)/s_j within batch j; control limits at ±3, with the moving-range chart built from successive z values. Each batch needs enough observations (10 or more recommended) for stable mean and standard-deviation estimates.