EWMA Chart

Time-Weighted Control Charts Overview

With the exception of moving average charts, Minitab's time-weighted control charts are weighted either by previous subgroup means or a target value. The advantage of using time-weighted control charts is the ability to detect small shifts from the target value.

For more information about control charts, see Control Charts Overview.

Choosing a time-weighted control chart Minitab offers three time-weighted control charts:

• Moving Average − a chart of unweighted moving averages

• EWMA − a chart of exponentially weighted moving averages

• CUSUM − a chart of the cumulative sum of the deviations from a nominal specification

EWMA, Moving Average, and CUSUM produce control charts for either data in subgroups or individual observations.

Typically, you use these charts to evaluate the process level. However, you can also use EWMA and CUSUM charts to plot control charts for subgroup ranges or standard deviations to evaluate process variation. See [10] and [23] for a discussion.

EWMA Chart

Stat > Control Charts > Time-weighted Charts > EWMA

A chart of exponentially weighted moving averages. Each EWMA point incorporates information from all the previous subgroups or observations. EWMA charts can be custom tailored to detect any size shift in the process. Because of this, they are often used to monitor in-control processes for detecting small shifts away from the target.

The plot points can be based on either subgroup means or individual observations. When data are in subgroups, the mean of all the observations in each subgroup is calculated. Exponentially weighted moving averages are then formed from these means. By default, the process standard deviation, σ, is estimated using a pooled standard deviation. You can also base the estimate on the average of subgroup ranges or subgroup standard deviations, or enter a historical value for σ.

When you have individual observations, exponentially weighted moving averages are formed from the individual observations. By default, σ is estimated with MRbar / d2, the average of the moving range divided by an unbiasing constant. Moving ranges are artificial subgroups created from the individual measurements. The moving range is of length 2, since consecutive values have the greatest chance of being alike. You can also estimate σ using the median of the moving range, change the length of the moving range, or enter an historical value for σ.

For more information, see Control Charts Overview and Time-Weighted Control Charts Overview.

Dialog box items

All observations for a chart are in one column: Choose if data are in one or more columns, then enter the columns.

Subgroup sizes: Enter a number or a column of subscripts. If the subgroup sizes do not vary much, you may want to force the control limits to be constant by specifying a fixed subgroup size using EWMA Options > Estimate.

Observations for a subgroup are in one row of columns: Choose if subgroups are arranged in rows across several columns, then enter the columns.

Weight for EWMA: Enter the weight to be used in the exponentially weighted moving average. The value specified must be a number between 0 and 1. By changing the weight used and the number of standard deviations for the control limits, you can construct a chart with specific properties. You can choose combinations of these two parameters by using an ARL (Average Run Length) table. See [17] for an extensive table.

<Scale>

Organize the data for all variables control charts in the same way. Variables charts include:

• Variables charts for subgroups

• Variables charts for individuals

• Time-weighted charts

• Multivariate charts

Structure your data for these charts using the guidelines below.

Worksheet Structure

Structure your data down a column or across rows, using the following table as a guide. Multivariate data must be entered down columns, with one column for each variable.

Subgroups are equal size Subgroups are unequal size Univariate (one

variable)

Down columns or across rows Down columns with subgroup indicator column

Multivariate (more than one variable)

Down columns Down columns with subgroup indicator column

Structure subgroup data down a column or across rows. Here is the same data set, with subgroups of size 5, structured both ways. Note that the first five observations in the left data set (subgroup 1) are the first row of the right-side data set, the second 5 observations are the second row, and so on.

When subgroups are of unequal size, you must enter your data in one column, then create a second column of subscripts which serve as subgroup indicators. In the following example, C1 contains the process data and C2 contains subgroup indicators:

Each time a subscript changes in C2, a new subgroup begins in C1. In this example, subgroup 1 has three observations, subgroup 2 has six observations, and so on.

Nonnormal data

To properly interpret Minitab's control charts, you must enter data that approximate a normal distribution. If the data are highly skewed, you may want to use the Box-Cox transformation to induce normality.

You can access the Box-Cox transformation two ways: by using the Box-Cox transformation option provided with the control chart commands, or by using the stand alone Box-Cox command. Use the stand alone command as an

exploratory tool to help you determine the best lambda value for the transformation. Then, you can use the transformation option to transform the data at the same time you draw the control chart.

For information on the stand alone Box-Cox transformation command, see Box-Cox Transformation.

For information on the Box-Cox transformation option, see Options − Box-Cox.

Missing data

See Missing data in control charts for information on how to handle missing data for different types of control charts.