Select the method or formula of your choice.
Each data point, z_{i}, in a Z chart
Each data point, R_{i}, the moving range of the z values in each group. R_{i} is not plotted for i < w because it is undefined.
Term | Description |
---|---|
x_{i} | observation i |
μ | mean for the group |
σ | standard deviation for the group |
w | width of moving range |
Minitab provides four methods for estimating σ, the process standard deviations. You should choose an estimation method based on the properties of your particular process/product. You can also choose to enter a historical value. You need to make assumptions about the process variation.
Use the following information to help you choose a method:
This option pools all the data across runs and parts to obtain a common estimate of σ.
Use this option when all the output from your process has the same variance—regardless of the size of the measurement.
This option takes the natural log of the data, pools the transformed data across all runs and all parts, and obtains a common estimate of σ for the transformed data. The natural log transformation stabilizes the variation in cases where variation increases as the size of the measurement increases.
Use this option when the variance increases in a fairly constant manner as the size of the measurement increases.
This option combines all runs of the same part to estimate σ for that part.
Use this option when all runs of a particular part or product have the same variance.
Z-MR Chart estimates the mean for each different part or product separately. Z-MR Chart pools all the data for a common part, and obtains the average of the pooled data. The result is the estimate of μ for that part. The part name data define the groupings for estimating the process means. When you use the Relative to size (combine all observations, use ln) option for estimating σ, the means are also taken on the natural log of the data.
You can also center data using historical values. Using historical means allows you to compare your process with past performance. When you use known means to center the data, the chart reflects whether the process is functioning as it has in the past with respect to location. That is, the chart shows whether each part/product mean is the same as previously established. When the process is functioning the same in respect to location, the values are distributed (equally) around the center line.
You can also use nominal specifications—target values—for each part/product to center the data. Using nominal specifications to center the data allows you to compare your process to desired performance. The nominal specifications are established target values for the dimension of interest for each part/product. When you use nominal specifications to center the data, the chart reflects whether the process is producing parts/products that are on target, or whether the process is biased.