Suppose you work at a car assembly plant in a department that assembles engines. In an operating engine, parts of the crankshaft move up and down a certain distance from an ideal baseline position. AtoBDist is the distance (in mm) from the actual (A) position of a point on the crankshaft to the baseline (B) position.
To ensure production quality, you took five measurements each working day, from September 28 through October 15, and then ten per day from the 18th through the 25th. You want to draw an X-bar chart to track the process level through that time period, and test for the presence of special causes.
1 Open the worksheet CRANKSH.MTW.
2 Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar.
3 Choose All observations for a chart are in one column, then enter AtoBDist.
4 In Subgroup sizes, enter 5.
5 Click Xbar Options, then click the Tests tab.
6 Choose Perform all tests for special causes.
7 Click the S Limits tab.
8 Under Display control limits at, enter 1 2 3 in These multiples of the standard deviation. Click OK in each dialog box.
Session window output
Xbar Chart of AtoBDist
Test Results for Xbar Chart of AtoBDist
TEST 6. 4 out of 5 points more than 1 standard deviation from center line (on one side of CL).
Test Failed at points: 5
* WARNING * If graph is updated with new data, the results above may no * longer be correct.
Graph window output
Interpreting the results
Subgroup 5 failed Test 6, meaning it is the fourth point in a row in Zone B (1 to 2 standard deviations from the center line).
This suggests the presence of special causes.
R Chart
Variables Control Charts for Subgroups Overview
dataVariables control charts for subgroups plot statistics from measurement data, such as length or pressure, for subgroup data. Variables control charts for individuals, time-weighted charts, and multivariate charts also plot measurement data.
Attributes control charts plot count data, such as the number of defects or defective units.
For more information about control charts, see Control Charts Overview.
Choosing a variables control chart for subgroups Minitab offers five variables control charts:
• X-bar and R − an X-bar chart and R chart displayed in one window
• X-bar and S − an X-bar chart and S chart displayed in one window
• I-MR-R/S (Between/Within) − a three-way control chart that uses both between-subgroup and within-subgroup variation. An I-MR-R/S chart consists of an I chart, a MR chart, and a R or S chart.
• X-bar − a chart of subgroup means
• R − a chart of subgroup ranges
• S − a chart of subgroup standard deviations
• Zone − a chart of the cumulative scores based on each point's distance from the center line
The I-MR-R/S (Between/Within) chart requires that you have two or more observations in at least one subgroup.
Subgroups do not need to be the same size. Minitab calculates summary statistics for each subgroup, which are plotted on the chart and used to estimate process parameters.
R Chart
Stat > Control Charts > Variables Charts for Subgroups > R
A control chart of subgroup ranges. You can use R charts to track process variation and detect the presence of special causes. R charts are typically used to track process variation for samples of size 8 or less, while S charts are used for larger samples.
By default, an R chart bases the estimate of the process variation, σ, on the average of the subgroup ranges. You can also use a pooled standard deviation, or enter a historical value for s.
For more information, see Control Charts Overview and Variables Control Charts for Subgroups 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 subgroups are not equal, each control limit is not a single straight line but varies with the subgroup size. 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 R 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.
<Scale>
<Labels>
<Multiple Graphs>
<Data Options>
<R Options>
Data − Variables Control Chart
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.