What is a Z-MR chart?

A Z-MR chart plots the standardized process mean (Z chart) and variation (MR chart) for short-run processes when little data are available. Short-run processes often do not have enough data in each run to produce good estimates of the process parameters.

For example, you may manufacture only 20 units of a part, then reset the machine to produce a different part in the next run.

The Z-MR chart standardizes the measurement data by subtracting the mean to center the data, then dividing by the standard deviation. Standardizing lets you evaluate data from different runs by interpreting a single control chart.

Example of a Z-MR chart

A manufacturer wants to assess the stability of its metal stamping process. Because the measurements were taken from only three runs, technicians use a Z-MR chart to monitor the mean and variation of the parts.

The standardized values for Run B seem to vary more than those for Run A and Run C. On the MR chart, one point is located beyond the upper control limit and the pattern of variation is nonrandom. The process may be influenced by special causes.

When should I use a Z-MR chart?

Use a Z-MR chart instead of an I-MR chart when there is not enough data in each run to produce good estimates of process parameters.

Standard control charting techniques rely on an adequate amount of data to reliably estimate process parameters, such as the process means (μ) and process standard deviations (σ). Short-run processes, such as processes that produce many different parts or products, often do not have enough data in each run to provide good estimates of the process parameters.

For example, you may manufacture only 20 units of a part, then reset the machine to manufacture a different part in the next run. Even if the runs are large enough to obtain estimates, you would need a separate control chart for each part made by the process, because it is likely that all parts would not have the same mean and standard deviation. Short-run charts provide a solution to these problems by pooling and standardizing the data.

Several methods are commonly used for short runs. The most general method assumes that each part or batch produced by a process has its own unique average and standard deviation. If the average and the standard deviation can be obtained, then the process data can be standardized by subtracting the mean and dividing the result by the standard deviation. The standardized data all come from a population with μ = 0 and σ = 1. Now you can use a single plot for the standardized data from different parts or products. The resulting control chart has a center line at 0, an upper limit at +3, and a lower limit at -3.

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