Overview of the Control Chart Platform
A control chart is a graphical way to filter out routine variation in a process. Filtering out routine variation helps manufacturers and other businesses determine whether a process is stable and predictable. If the variation is more than routine, the process can be adjusted to create higher quality output at a lower cost.
All processes exhibit variation as the process is measured over time. There are two types of variation in process measurements:
• Routine or common-cause variation. Even measurements from a stable process exhibit these random ups and downs. When process measurements exhibit only common-cause variation, the measurements stay within acceptable limits.
• Abnormal or special-cause variation. Examples of special-cause variation include a change in the process mean, points above or below the control limits, or measurements that trend up or down. These changes can be caused by factors such as a broken tool or machine, equipment degradation, and changes to raw materials. A change or defect in the process is often identifiable by abnormal variation in the process measurements.
Control charts quantify the routine variation in a process, so that special causes can be identified. One way control charts filter out routine variation is by applying control limits. Control limits define the range of process measurements for a process that is exhibiting only routine variation. Measurements between the control limits indicate a stable and predictable process. Measurements outside the limits indicate a special cause, and action should be taken to restore the process to a state of control.
Control chart performance is dependent on the sampling scheme used. The sampling plan should be rational, that is, the subgroups are representative of the process. Rational subgrouping means that you sample from the process by selecting subgroups in such a way that special causes are more likely to occur between subgroups rather than within subgroups.
Shewhart control charts are broadly classified into control charts for variables and control charts for attributes. Control charts for variables include moving average and CUSUM charts. CUSUM charts are also a type of attribute chart. For details, see “Moving Average Charts” and the “Cumulative Sum Control Charts” chapter.
Example of the Control Chart Platform
The following example uses the Coating.jmp sample data table in the Quality Control sample data folder (taken from the ASTM Manual on Presentation of Data and Control Chart Analysis). The quality characteristic of interest is the Weight column. A subgroup sample of four is chosen.
1. Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2. Select Analyze > Quality And Process > Control Chart > XBar.
Note the selected chart types of XBar and R.
3. Select Weight and click Process.
4. Select Sample and click Sample Label.
5. Click OK.
Figure 4.2 Variables Charts for Coating Data
An X-chart and an R-chart for the process are shown in Figure 4.2. Sample six indicates that the process is not in statistical control. To check the sample values, click the sample six summary point on either control chart. The corresponding rows highlight in the data table.
Note: If an S chart is chosen with the X-chart, then the limits for the X-chart are based on the standard deviation. Otherwise, the limits for the X-chart are based on the range.
Shewhart Control Chart Types
Shewhart control charts are broadly classified into control charts for variables and control charts for attributes.
Control Charts for Variables
Control charts for variables are classified according to the subgroup summary statistic plotted on the chart:
• Run charts display data as a connected series of points
• X-charts display subgroup means (averages)
• R-charts display subgroup ranges (maximum – minimum)
• S-charts display subgroup standard deviations
• Presummarize charts display subgroup means and standard deviations
The IR selection gives additional chart types:
• Individual Measurement charts display individual measurements
• Moving Range charts display moving ranges of two or more successive measurements
Run Charts
Run charts display a column of data as a connected series of points. Run charts can also plot the group means when the Sample Label role is used, either on the window or through a script.
XBar-, R-, and S- Charts
For quality characteristics measured on a continuous scale, a typical analysis shows both the process mean and its variability with a mean chart aligned above its corresponding R- or S-chart.
Individual Measurement Charts
Individual Measurement charts displays individual measurements. Individual Measurement charts are appropriate when only one measurement is available for each subgroup sample.
Moving Range charts displays moving ranges of two or more successive measurements. Moving ranges are computed for the number of consecutive measurements that you enter in the Range Span box. The default range span is 2. Because moving ranges are correlated, these charts should be interpreted with care.
Moving Average Charts
The control charts previously discussed plot each point based on information from a single subgroup sample. The Moving Average chart is different from other types because each point combines information from the current sample and from past samples. As a result, the Moving Average chart is more sensitive to small shifts in the process average. On the other hand, it is more difficult to interpret patterns of points on a Moving Average chart because consecutive moving averages can be highly correlated (Nelson 1982).
In a Moving Average chart, the quantities that are averaged can be individual observations instead of subgroup means. However, a Moving Average chart for individual measurements is not the same as a control (Shewhart) chart for individual measurements or moving ranges with individual measurements plotted.
Uniformly Weighted Moving Average Charts
Each point on a Uniformly Weighted Moving Average (UWMA) chart, also called a Moving Average chart, is the average of the w most recent subgroup means, including the present subgroup mean. When you obtain a new subgroup sample, the next moving average is computed by dropping the oldest of the previous w subgroup means and including the newest subgroup mean. The constant, w, is called the span of the moving average, and indicates how many subgroups to include to form the moving average. The larger the span (w), the smoother the UWMA line, and the less it reflects the magnitude of shifts. This means that larger values of w guard against smaller shifts.
Exponentially Weighted Moving Average Charts
Each point on an Exponentially Weighted Moving Average (EWMA) chart, also referred to as a Geometric Moving Average (GMA) chart, is the weighted average of all the previous subgroup means, including the mean of the present subgroup sample. The weights decrease exponentially going backward in time. The weight (0 < weight ≤ 1) assigned to the present subgroup sample mean is a parameter of the EWMA chart. Small values of weight are used to guard against small shifts.
Presummarize Charts
If your data consist of repeated measurements of the same process unit, you can combine these into one measurement for the unit. Pre-summarizing is not recommended unless the data have repeated measurements on each process or measurement unit.
Presummarize summarizes the process column into sample means and/or standard deviations, based either on the sample size or sample label chosen. Then it charts the summarized data based on the options chosen in the launch window. You can also append a capability analysis by checking the appropriate box in the launch window.
Control Charts for Attributes
In the previous types of charts, measurement data was the process variable. This data is often continuous, and the charts are based on theory for continuous data. Another type of data is count data, where the variable of interest is a discrete count of the number of defects or blemishes per subgroup. For discrete count data, attribute charts are applicable, as they are based on binomial and Poisson models. Because the counts are measured per subgroup, it is important when comparing charts to determine whether you have a similar number of items in the subgroups between the charts. Attribute charts, like variables charts, are classified according to the subgroup sample statistic plotted on the chart.
Determining Which Attribute Chart to Use
Each item is judged as either conforming or non-conforming:
p-chart
Shows the proportion of defective items.
np-chart
Shows the number of defective items.
The number of defects is counted for each item:
c-chart
Shows the number of defective items.
u-chart
Shows the average number of defective items.
For attribute charts, specify the column containing the defect count or defective proportion as the Process variable. The data are interpreted as counts, unless the column contains non-integer values between 0 and 1.
• p-charts display the proportion of nonconforming (defective) items in subgroup samples, which can vary in size. Since each subgroup for a p-chart consists of Ni items, and an item is judged as either conforming or nonconforming, the maximum number of nonconforming items in a subgroup is Ni.
• np-charts display the number of nonconforming (defective) items in subgroup samples. Because each subgroup for a np-chart consists of Ni items, and an item is judged as either conforming or nonconforming, the maximum number of nonconforming items in subgroup i is Ni.
Note: To use the Sigma column property for P- or NP- charts, the value needs to be equal to the proportion. JMP calculates the sigma as a function of the proportion and the sample sizes.
• c-charts display the number of nonconformities (defects) in a subgroup sample that usually, but does not necessarily, consists of one inspection unit.
Caution: For a c-chart, if you do not specify a Sample Size or Constant Size, then the Sample Label is used as the sample size.
• u-charts display the number of nonconformities (defects) per unit in subgroup samples that can have a varying number of inspection units.
Caution: For a u-chart, if you do not specify a Unit Size or Constant Size, then the Sample Label is used as the unit size.
Levey-Jennings Charts
Levey-Jennings charts show a process mean with control limits based on a long-term sigma. The control limits are placed at 3s distance from the center line. The standard deviation, s, for the Levey-Jennings chart is calculated the same way standard deviation is in the Distribution platform.
Launch the Control Chart Platform
When you launch the Control Chart platform by selecting Analyze > Quality And Process > Control Chart, you will see a Control Chart Launch window similar to Figure 4.3. The exact controls vary depending on which type of chart you select. Initially, the window shows the following types of information:
• Process information, for measurement variable selection
• Chart type information
• Limits specifications
• Specified statistics
Specific information shown for each section varies according to the type of chart that you select. Through interaction with the Launch window, you specify exactly how you want your charts to be created. The following sections describe the window elements.
Figure 4.3 XBar Control Chart Launch Window
Process Information
The Launch window displays a list of columns in the current data table. Here, you specify the variables to be analyzed and the subgroup sample size.
Process
The Process role selects variables for charting.
• For variables charts, specify measurements as the process.
• For attribute charts, specify the defect count or defective proportion as the process. The data are interpreted as counts, unless it contains non-integer values between 0 and 1.
Note: The rows of the table must be sorted in the order in which you want them to appear in the control chart. Even if there is a Sample Label variable specified, you still must sort the data accordingly.
Sample Label
The Sample Label role enables you to specify a variable whose values label the horizontal axis and can also identify unequal subgroup sizes. If no sample label variable is specified, the samples are identified by their subgroup sample number.
• If the sample subgroups are the same size, select the Sample Size Constant option and enter the size in the text box. If you entered a Sample Label variable, its values are used to label the horizontal axis. The sample size is used in the calculation of the limits regardless of whether the samples have missing values.
• If the sample subgroups have an unequal number of rows or have missing values and you have a column identifying each sample, select the Sample Grouped by Sample Label option and enter the sample identifying column as the sample label.
For attribute charts (p-, np-, c-, and u-charts), this variable is the subgroup sample size. Additional options appear on the launch window, including Sample Size, Constant Size, and/or Unit Size, depending on your selection. In variables charts, it identifies the sample. When the chart type is IR, a Range Span text box appears. The range span specifies the number of consecutive measurements from which the moving ranges are computed.
Note: The rows of the table must be sorted in the order in which you want them to appear in the control chart. Even if there is a Sample Label variable specified, you still must sort the data accordingly.
The illustration in Figure 4.4 shows an X-chart for a process with unequal subgroup sample sizes, using the Coating.jmp sample data from the Quality Control sample data folder.
Figure 4.4 Variables Charts with Unequal Subgroup Sample Sizes
Phase
The Phase role enables you to specify a column identifying different phases, or sections. A phase is a group of consecutive observations in the data table. For example, phases might correspond to time periods during which a new process is brought into production and then put through successive changes. Phases generate, for each level of the specified Phase variable, a new sigma, set of limits, zones, and resulting tests.
On the window for X-, R-, S-, IR-, P-, NP-, C-, U-, Presummarize, and Levey-Jennings charts, a Phase variable button appears. If a phase variable is specified, the phase variable is examined, row by row, to identify to which phase each row belongs. Saving to a limits file reveals the sigma and specific limits calculated for each phase. See “Phase Example” for an example.
By
The By role identifies a variable to produce a separate analysis for each value that appears in the column.
Chart Type Information
Shewhart control charts are broadly classified as variables charts and attribute charts. Moving average charts and CUSUM charts can be thought of as special types of variables charts.
Figure 4.5 Window Options for Variables Control Charts
• XBar charts menu selection gives XBar, R, and S check boxes.
• The IR menu selection has check box options for the Individual Measurement, Moving Range, and Median Moving Range charts.
• The uniformly weighted moving average (UWMA) and exponentially weighted moving average (EWMA) selections are special charts for means.
• The CUSUM chart is a special chart for means or individual measurements.
• Presummarize enables you to specify information about pre-summarized statistics.
• P, NP, C, and U charts, Run Chart, and Levey-Jennings charts have no additional specifications.
The types of control charts are discussed in “Overview of the Control Chart Platform”.
Limits Specifications
You can specify computations for control limits by entering a value for k (K Sigma), or by entering a probability for α(Alpha), or by retrieving a limits value from the process columns' properties or a previously created Limits Table. Limits Tables and the Get Limits button are discussed in the section “Saving and Retrieving Limits”. There must be a specification of either K Sigma or Alpha. The window default for K Sigma is 3.
KSigma
The KSigma parameter option allows specification of control limits in terms of a multiple of the sample standard error. KSigma specifies control limits at k sample standard errors above and below the expected value, which shows as the center line. To specify k, the number of sigmas, click the radio button for KSigma and enter a positive k value into the text box. The usual choice for k is 3, which is three standard deviations. The examples shown in Figure 4.6 compare the X-chart for the Coating.jmp data with control lines drawn with KSigma = 3 and KSigma = 4.
Figure 4.6 K Sigma =3 (left) and K Sigma=4 (right) Control Limits
Alpha
The Alpha parameter option specifies control limits (also called probability limits) in terms of the probability α that a single subgroup statistic exceeds its control limits, assuming that the process is in control. To specify alpha, click the Alpha radio button and enter the probability that you want. Reasonable choices for α are 0.01 or 0.001. The Alpha value equivalent to a KSigma of 3 is 0.0027.
Specified Statistics
After specifying a process variable, if you click the Specify Stats (when available) button on the Control Chart Launch window, a tab with editable fields is appended to the bottom of the window. This lets you enter historical statistics (that is, statistics obtained from historical data) for the process variable. The Control Chart platform uses those entries to construct control charts. The example here shows 1 as the standard deviation of the process variable and 20 as the mean measurement.
Figure 4.7 Example of Specify Stats
Note: When the mean is user-specified, it is labeled in the plot as μ0.
If you check the Capability option on the Control Chart launch window (see Figure 4.3), a window appears as the platform is launched asking for specification limits. The standard deviation for the control chart selected is sent to the window and appears as a Specified Sigma value, which is the default option. After entering the specification limits and clicking OK, capability output appears in the same window next to the control chart. For information about how the capability indices are computed, see the Distributions chapter in the Basic Analysis book.
The Control Chart Report
The analysis produces a chart that can be used to determine whether a process is in a state of statistical control. The report varies depending on the type of chart that you select. Figure 4.8 displays the parts of a simple control chart. Control charts update dynamically as data is added or changed in the data table.
Figure 4.8 Example of a Control Chart
Note: Any rows that are excluded in the data table are also hidden in Run charts, P-charts, U-charts, and C-charts.
Control charts have the following characteristics:
• Each point plotted on the chart represents an individual process measurement or summary statistic. In Figure 4.8, the points represent the average for a sample of measurements.
Subgroups should be chosen rationally, that is, they should be chosen to maximize the probability of seeing a true process signal between subgroups.
• The vertical axis of a control chart is scaled in the same units as the summary statistic.
• The horizontal axis of a control chart identifies the subgroup samples and is time ordered. Observing the process over time is important in assessing if the process is changing.
• The green line is the center line, or the average of the data. The center line indicates the average (expected) value of the summary statistic when the process is in statistical control. Measurements should appear equally on both sides of the center line. If not, this is possible evidence that the process average is changing.
• The two red lines are the upper and lower control limits, labeled UCL and LCL. These limits give the range of variation to be expected in the summary statistic when the process is in statistical control. If the process is exhibiting only routine variation, then all the points should fall randomly in that range. In Figure 4.8, one measurement is above the upper control limit. This is evidence that the measurement could have been influenced by a special cause, or is possibly a defect.
• A point outside the control limits (or the V-mask of a CUSUM chart) signals the presence of a special cause of variation.
Options within each platform create control charts that can be updated dynamically as samples are received and recorded or added to the data table.
When a control chart signals abnormal variation, action should be taken to return the process to a state of statistical control if the process degraded. If the abnormal variation indicates an improvement in the process, the causes of the variation should be studied and implemented.
When you double-click the x or y axis, the appropriate Axis Specification window appears for you to specify the format, axis values, number of ticks, gridline, reference lines, and other options to display on the axis.
For example, the Pickles.jmp data lists measurements taken each day for three days. In Figure 4.9, by default, the x axis is labeled at every other tick. Sometimes this gives redundant labels, as shown to the left in Figure 4.9. If you specify a label at an increment of eight, the x axis is labeled once for each day, as shown in the chart on the right.
Figure 4.9 Example of Labeled x Axis Tick Marks
Tip: For information about warnings and rules, see “Tests” and “Westgard Rules” in the “Control Chart Builder” chapter of this guide.
Control Chart Platform Options
Control Charts have red triangle menus that affect various parts of the platform:
• The menu on the top-most title bar affects the whole platform window. Its items vary with the type of chart that you select.
• There is a menu of items on the chart type title bar with options that affect each chart individually.
Control Chart Window Options
The red triangle menu on the window title bar lists options that affect the report window. If you request XBar and R at the same time, you can check each chart type to show or hide it. The specific options that are available depend on the type of control chart you request. Unavailable options show as grayed menu items.
Show Limits Legend
Shows or hides the Avg, UCL, and LCL values to the right of the chart.
Connect Through Missing
Connects points when some samples have missing values. In Figure 4.10, the left chart has no missing points. The middle chart has samples 2, 11, 19, and 27 missing with the points not connected. The right chart appears if you select the Connect Through Missing option, which is the default.
Figure 4.10 Example of Connected through Missing Option
Use Median
For Run Charts, when you select the Show Center Line option in the individual Run Chart red triangle menu, a line is drawn through the center value of the column. The center line is determined by the Use Median setting of the main Run Chart red triangle menu. When Use Median is selected, the median is used as the center line. Otherwise, the mean is used. When saving limits to a file, both the overall mean and median are saved.
Capability
Performs a Capability Analysis for your data. A popup window is first shown, where you can enter the Lower Spec Limit, Target, and Upper Spec Limit values for the process variable.
Figure 4.11 Capability Analysis Window
An example of a capability analysis report is shown in Figure 4.12 for Coating.jmp when the Lower Spec Limit is set as 16.5, the Target is set to 21.5, and the Upper Spec Limit is set to 23.
Figure 4.12 Capability Analysis Report for Coating.jmp
For additional information about Capability Analysis, see the Distributions chapter in the Basic Analysis book.
Save Sigma
Saves the computed value of sigma as a column property in the process variable column in the JMP data table.
Save Limits > in Column
Saves the computed values of sigma, center line, and the upper and lower limits as column properties in the process variable column in the JMP data table.
Save Limits > in New Table
Saves all parameters for the particular chart type, including sigma and K Sigma, sample size, the center line, and the upper and lower control limits in a new JMP data table. Save this data table to use the limits later. On the Control Chart launch window, click Get Limits and then select the saved data table. See the section “Saving and Retrieving Limits” for more information.
Save Summaries
Creates a new data table that contains the sample label, sample sizes, the statistic being plotted, the center line, and the control limits. The specific statistics included in the table depend on the type of chart.
Alarm Script
Enables you to write and run a script that indicates when the data fail special causes tests. Results can be written to the log or spoken. See “Tests” in the “Control Chart Builder” chapter of this guide for more information. See the Scripting Guide for more information about writing custom Alarm Scripts.
See the JMP Reports chapter in the Using JMP book for more information about the following options:
Redo
Contains options that enable you to repeat or relaunch the analysis. In platforms that support the feature, the Automatic Recalc option immediately reflects the changes that you make to the data table in the corresponding report window.
Save Script
Contains options that enable you to save a script that reproduces the report to several destinations.
Save By-Group Script
Contains options that enable you to save a script that reproduces the platform report for all levels of a By variable to several destinations. Available only when a By variable is specified in the launch window.
Individual Control Chart Options
The red triangle menu of chart options appears when you click the icon next to the chart name. Some options are also available under Chart Options when you right-click the chart.
Box Plots
Superimposes box plots on the subgroup means plotted in a Mean chart. The box plot shows the subgroup maximum, minimum, 75th percentile, 25th percentile, and median. Markers for subgroup means show unless you deselect the Show Points option. The control limits displayed apply only to the subgroup mean. The Box Plots option is available only for 
-charts. It is most appropriate for larger subgroup sample sizes (more than 10 samples in a subgroup).
-charts. It is most appropriate for larger subgroup sample sizes (more than 10 samples in a subgroup).Needle
Connects plotted points to the center line with a vertical line segment.
Connect Points
Shows or hides the line that connects the data points.
Show Points
Shows or hides the points representing summary statistics. Initially, the points show. You can use this option to suppress the markers denoting subgroup means when the Box Plots option is in effect.
Connect Color
Displays the JMP color palette for you to choose the color of the line segments used to connect points.
Center Line Color
Displays the JMP color palette for you to choose the color of the line segments used to draw the center line.
Limits Color
Displays the JMP color palette for you to choose the color of the line segments used in the upper and lower limits lines.
Line Width
Allows you to select the width of the control lines. Options are Thin, Medium, or Thick.
Point Marker
Allows you to select the marker used on the chart.
Show Center Line
Initially displays the center line in green. Deselecting Show Center Line removes the center line and its legend from the chart.
Show Control Limits
Shows or hides the chart control limits and their legends.
Limits Precision
Sets the decimal limit for labels.
Tests
Shows a submenu that enables you to choose which tests to mark on the chart when the test is positive. Tests apply only for charts whose limits are 3σ limits. Tests 1 to 4 apply to Mean, Individual, and attribute charts. Tests 5 to 8 apply to Mean charts, Presummarize, and Individual Measurement charts only. If tests do not apply to a chart, the Tests option is dimmed. When sample sizes are unequal, the Test options are grayed out. If the samples change while the chart is open and they become equally sized, and the zone and/or test option is selected, the zones and/or tests are applied immediately and appear on the chart. These special tests are also referred to as the Western Electric Rules. For more information about special causes tests, see “Tests” in the “Control Chart Builder” chapter.
Westgard Rules
Westgard rules are control rules that help you decide whether a process is in or out of control. The different tests are abbreviated with the decision rule for the particular test. See the text and chart in “Westgard Rules” in the “Control Chart Builder” chapter.
Test Beyond Limits
Flags as a “*” any point that is beyond the limits. This test works on all charts with limits, regardless of the sample size being constant, and regardless of the size of k or the width of the limits. For example, if you had unequal sample sizes, and wanted to flag any points beyond the limits of an r-chart, you could use this command.
Show Zones
Shows or hides the zone lines. The zones are labeled A, B, and C as shown here in the Mean plot for weight in the Coating.jmp sample data. Control Chart tests use the zone lines as boundaries. The seven zone lines are set one sigma apart, centered on the center line.
Figure 4.13 Show Zones
Shade Zones
Shows or hides the default green, yellow, and red colors for the three zone areas and the area outside the zones. Green represents the area one sigma from the center line, yellow represents the area two and three sigmas from the center line, and red represents the area beyond three sigma. Shades can be shown with or without the zone lines.
Figure 4.14 Shade Zones
OC Curve
Gives Operating Characteristic (OC) curves for specific control charts. OC curves are defined in JMP only for X-, p-, np-, c-, and u-charts. The curve shows how the probability of accepting a lot changes with the quality of the sample. When you choose the OC Curve option from the control chart option list, JMP opens a new window containing the curve, using all the calculated values directly from the active control chart. Alternatively, you can run an OC curve directly from the Control category of the JMP Starter. Select the chart on which you want the curve based, then a window prompts you for Target, Lower Control Limit, Upper Control Limit, k, Sigma, and Sample Size. You can also perform both single and double acceptance sampling in the same manner. To engage this feature, choose View > JMP Starter > Control (under Click Category) > OC Curves. A pop-up window enables you to specify whether single or double acceptance sampling is desired. A second pop-up window is invoked, where you can specify acceptance failures, number inspected, and lot size (for single acceptance sampling). Clicking OK generates the desired OC curve.
Saving and Retrieving Limits
JMP can use previously established control limits for control charts:
• Upper and lower control limits, and a center line value.
• Parameters for computing limits such as a mean and standard deviation.
The control limits or limit parameter values must be either in a JMP data table, referred to as the Limits Table, or stored as a column property in the process column. When you specify the Control Chart command, you can retrieve the Limits Table with the Get Limits button on the Control Chart launch window.
The easiest way to create a Limits Table is to save results computed by the Control Chart platform. The Save Limits command in the red triangle menu for each control chart automatically saves limits from the sample values. The type of data saved in the table varies according to the type of control chart in the analysis window. You can also use values from any source and create your own Limits Table.
All Limits Tables must have:
• A column of special keywords that identify each row.
• A column for each of the variables whose values are the known standard parameters or limits. This column name must be the same as the corresponding process variable name in the data table to be analyzed by the Control Chart platform.
Table 3.10 describes the limit keywords and their associated control chart.
You can save limits in a new data table or as properties of the response column. When you save control limits using the in New Table command, the limit keywords written to the table depend on the current chart types displayed.
Figure 4.15 shows examples of control limits saved to a data table using Coating.jmp. The rows with values _Mean, _LCL, and _UCL are for the Individual Measurement chart. The values with the R suffix (_AvgR, _LCLR, and _UCLR) are for the Moving Range chart. If you create these charts again using this Limits Table, the Control Chart platform identifies the appropriate limits from keywords in the _LimitsKey column.
Figure 4.15 Example of Saving Limits in a Data Table
Note that values for _KSigma, _Alpha, and _Range Span can be specified in the Control Chart Launch window. JMP always looks at the values from the window first. Values specified in the window take precedence over those in an active Limits Table.
Rows with unknown keywords and rows marked with the excluded row state are ignored. Except for _Range Span, _KSigma, _Alpha, and _Sample Size, any needed values not specified are estimated from the data.
Excluded, Hidden, and Deleted Samples
The following table summarizes the effects of various conditions on samples and subgroups:
|
All rows of the sample are excluded before creating the chart.
|
Sample is not included in the calculation of the limits, but it appears on the graph.
|
|
Sample is excluded after creating the chart.
|
Sample is included in the calculation of the limits, and it appears in the graph. Nothing changes on the output by excluding a sample with the graph open.
|
|
Sample is hidden before creating the chart.
|
Sample is included in the calculation of the limits, but does not appear on the graph.
|
|
Sample is hidden after creating the chart.
|
Sample is included in the calculation of the limits, but does not appear on the graph. The sample marker disappears from the graph, the sample label still appears on the axis, but limits remain the same.
|
|
All rows of the sample are both excluded and hidden before creating the chart.
|
Sample is not included in the calculation of the limits, and it does not appear on the graph.
|
|
All rows of the sample are both excluded and hidden after creating the chart.
|
Sample is included in the calculation of the limits, but does not appear on the graph. The sample marker disappears from the graph, the sample label still appears on the axis, but limits remain the same.
|
|
Data set is subsetted with Sample deleted before creating chart.
|
Sample is not included in the calculation of the limits, the axis does not include a value for the sample, and the sample marker does not appear on the graph.
|
|
Data set is subsetted with Sample deleted after creating chart.
|
Sample is not included in the calculation of the limits, and does not appear on the graph. The sample marker disappears from the graph, the sample label is removed from the axis, the graph shifts, and the limits change.
|
Some additional notes:
• Hide and Exclude operate only on the row state of the first observation in the sample. For example, if the second observation in the sample is hidden, while the first observation is not hidden, the sample will still appear on the chart.
• An exception to the exclude/hide rule: Both hidden and excluded rows are included in the count of points for Tests for Special Causes. An excluded row can be labeled with a special cause flag. A hidden point cannot be labeled. If the flag for a Tests for Special Causes is on a hidden point, it will not appear in the chart.
• Because of the specific rules in place (see Table 4.1), the control charts do not support the Automatic Recalc script.
Additional Examples of the Control Chart Platform
This section contains additional examples using the Control Chart platform.
Run Chart Example
Run charts display a column of data as a connected series of points. The following example is a Run chart for the Weight variable from Coating.jmp in the Quality Control sample data folder (taken from the ASTM Manual on Presentation of Data and Control Chart Analysis).
1. Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2. Select Analyze > Quality and Process > Control Chart > Run Chart.
3. Select Weight and click Process.
4. Select Sample and click Sample Label.
5. Click OK.
Figure 4.16 Run Chart
X Bar- and R-charts Example
The following example uses the Coating.jmp data table. The quality characteristic of interest is the Weight column. A subgroup sample of four is chosen. An X-chart and an R-chart for the process are shown in Figure 4.17.
1. Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2. Select Analyze > Quality and Process > Control Chart > XBar.
Note the selected chart types of XBar and R.
3. Select Weight and click Process.
4. Select Sample and click Sample Label.
5. Click OK.
Sample six indicates that the process is not in statistical control. To check the sample values, click the sample six summary point on either control chart. The corresponding rows highlight in the data table.
Note: If an S chart is chosen with the X-chart, then the limits for the X-chart are based on the standard deviation. Otherwise, the limits for the X-chart are based on the range.
Figure 4.17 Variables Charts for Coating Data
You can use Fit Y by X for an alternative visualization of the data. First, change the modeling type of Sample to Nominal. Specify the interval variable Weight as Y, Response and the nominal variable Sample as X, Factor. Select the Quantiles option from the Oneway Analysis drop-down menu. The box plots in Figure 4.18 show that the sixth sample has a small range of high values.
Figure 4.18 Quantiles Option in Fit Y By X Platform
X-Bar- and S-charts with Varying Subgroup Sizes Example
The following example uses the Coating.jmp data table. This quality characteristic of interest is the Weight 2 column. An X-chart and an S chart for the process are shown in Figure 4.19.
1. Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2. Select Analyze > Quality and Process > Control Chart > XBar.
3. Select the chart types of XBar and S.
4. Select Weight 2 and click Process.
5. Select Sample and click Sample Label.
The Sample Size option should automatically change to Sample Grouped by Sample Label.
6. Click OK.
Figure 4.19 X and S Charts for Varying Subgroup Sizes
Weight 2 has several missing values in the data, so you might notice the chart has uneven limits. Although, each sample has the same number of observations, samples 1, 3, 5, and 7 each have a missing value.
Note: When sample sizes are unequal, the Test options are grayed out. If the samples change while the chart is open and they become equally sized, and the zone and/or test option is selected, the zones and/or tests will be applied immediately and appear on the chart.
Individual Measurement and Moving Range Charts Example
The Pickles.jmp data in the Quality Control sample data folder contains the acid content for vats of pickles. Because the pickles are sensitive to acidity and produced in large vats, high acidity ruins an entire pickle vat. The acidity in four vats is measured each day at 1, 2, and 3 PM. The data table records day, time, and acidity measurements. You can create Individual Measurement and Moving Range charts with date labels on the horizontal axis.
1. Select Help > Sample Data Library and open Quality Control/Pickles.jmp.
2. Select Analyze > Quality and Process > Control Chart > IR.
3. Select both Individual Measurement and Moving Range chart types.
4. Select Acid and click Process.
5. Select Date and click Sample Label.
6. Click OK.
The individual measurement and moving range charts shown in Figure 4.20 monitor the acidity in each vat produced.
Note: A Median Moving Range chart can also be evaluated. If you choose a Median Moving Range chart and an Individual Measurement chart, the limits on the Individual Measurement chart use the Median Moving Range as the sigma, rather than the Average Moving Range.
Figure 4.20 Individual Measurement and Moving Range Charts for Pickles Data
p-chart Example
Note: When you generate a p-chart and select Capability, JMP launches the Binomial Fit in Distribution and gives a Binomial-specific capability analysis.
The Washers.jmp data in the Quality Control sample data folder contains defect counts of 15 lots of 400 galvanized washers. The washers were inspected for finish defects such as rough galvanization and exposed steel. If a washer contained a finish defect, it was deemed nonconforming or defective. Thus, the defect count represents how many washers were defective for each lot of size 400. Using the Washers.jmp data table, specify a sample size variable, which would allow for varying sample sizes. This data contains all constant sample sizes.
1. Select Help > Sample Data Library and open Quality Control/Washers.jmp.
2. Select Analyze > Quality and Process > Control Chart > P.
3. Select # defective and click Process.
4. Select Lot and click Sample Label.
5. Select Lot Size and click Sample Size.
6. Click OK.
Figure 4.21 displays a p-chart for the proportion of defects.
Figure 4.21 p-chart
Note that although the points on the chart look the same as the np-chart in Figure 4.22, the y axis, Avg and limits are all different since they are now based on proportions.
np-chart Example
Note: When you generate a np-chart and select Capability, JMP launches the Binomial Fit in Distribution and gives a Binomial-specific capability analysis.
The following example uses the Washers.jmp data table.
• Select Help > Sample Data Library and open Quality Control/Washers.jmp.
• Select Analyze > Quality and Process > Control Chart > NP.
• Select # defective and click Process.
• Change the Constant Size to 400.
• Click OK.
Figure 4.22 displays an np-chart for the number of defects. Points 4 and 9 are above the upper control limit.
Figure 4.22 np-chart
c-chart Example
c-charts are similar to U-charts in that they monitor the number of nonconformities in an entire subgroup, made up of one or more units. c-charts can also be used to monitor the average number of defects per inspection unit.
Note: When you generate a c-chart and select Capability, JMP launches the Poisson Fit in Distribution and gives a Poisson-specific capability analysis.
In this example, a clothing manufacturer ships shirts in boxes of ten. Prior to shipment, each shirt is inspected for flaws. Because the manufacturer is interested in the average number of flaws per shirt, the number of flaws found in each box is divided by ten and then recorded.
1. Select Help > Sample Data Library and open Quality Control/Shirts.jmp.
2. Select Analyze > Quality and Process > Control Chart > C.
3. Select # Defects and click Process.
4. Select Box and click Sample Label.
5. Select Box Size and click Sample Size.
6. Click OK.
Figure 4.23 c-chart
u-chart Example
The Braces.jmp data in the Quality Control sample data folder records the defect count in boxes of automobile support braces. A box of braces is one inspection unit. The number of boxes inspected (per day) is the subgroup sample size, which can vary. The u-chart in Figure 4.24 is monitoring the number of brace defects per subgroup sample size. The upper and lower bounds vary according to the number of units inspected.
Note: When you generate a u-chart, and select Capability, JMP launches the Poisson Fit in Distribution and gives a Poisson-specific capability analysis. To use the Capability feature, the unit sizes must be equal.
1. Select Help > Sample Data Library and open Quality Control/Braces.jmp.
2. Select Analyze > Quality and Process > Control Chart > U.
3. Select # defects and click Process.
4. Select Date and click Sample Label.
5. Select Unit size and click Unit Size.
6. Click OK.
Figure 4.24 u-chart
UWMA Chart Example
In sample data table, Clips1.jmp, the measure of interest is the gap between the ends of manufactured metal clips. To monitor the process for a change in average gap, subgroup samples of five clips are selected daily. A UWMA chart with a moving average span of three is examined.
1. Select Help > Sample Data Library and open Quality Control/Clips1.jmp.
1. Select Analyze > Quality and Process > Control Chart > UWMA.
2. Select Gap and click Process.
3. Select Sample and click Sample Label.
4. Change the Moving Average Span to 3.
5. Click OK.
The result is the chart in Figure 4.25. The point for the first day is the mean of the five subgroup sample values for that day. The plotted point for the second day is the average of subgroup sample means for the first and second days. The points for the remaining days are the average of subsample means for each day and the two previous days.
The average clip gap appears to be decreasing, but no sample point falls outside the 3σ limits.
Figure 4.25 UWMA Charts for the Clips1 data
EWMA Chart Example
The following example uses the Clips1.jmp data table.
1. Select Help > Sample Data Library and open Quality Control/Clips1.jmp.
2. Select Analyze > Quality and Process > Control Chart > EWMA.
3. Select Gap and click Process.
4. Select Sample and click Sample Label.
5. Change the Weight to 0.5.
6. Leave the Sample Size Constant as 5.
7. Click OK.
Figure 4.26 displays the EWMA chart for the same data seen in Figure 4.25. This EWMA chart was generated for weight = 0.5.
Figure 4.26 EWMA Chart
Presummarize Chart Example
The following example uses the Coating.jmp data table.
1. Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2. Select Analyze > Quality and Process > Control Chart > Presummarize.
3. Select Weight and click Process.
4. Select Sample and click Sample Label.
5. Select both Individual on Group Means and Moving Range on Group Means. The Sample Grouped by Sample Label button is automatically selected when you choose a Sample Label variable.
When using Presummarize charts, you can select either On Group Means options or On Group Std Devs options or both. Each option creates two charts (an Individual Measurement, also known as an X chart, and a Moving Range chart) if both IR chart types are selected.
The On Group Means options compute each sample mean and then plot the means and create an Individual Measurement and a Moving Range chart on the means.
The On Group Std Devs options compute each sample standard deviation and plot the standard deviations as individual points. Individual Measurement and Moving Range charts for the standard deviations then appear.
6. Click OK.
Figure 4.27 Example of Charting Presummarized Data
Although the points for X- and S-charts are the same as the Individual on Group Means and Individual on Group Std Devs charts, the limits are different because they are computed as Individual charts.
Another way to generate the presummarized charts, with the Coating.jmp data table:
1. Choose Tables > Summary.
2. Assign Sample as the Group variable, then Mean(Weight) and Std Dev(Weight) as Statistics.
3. Click OK.
4. Select Analyze > Quality and Process > Control Chart > IR.
5. Select Mean(Weight) and Std Dev(Weight) and click Process.
6. Click OK.
The resulting charts match the presummarized charts.
Phase Example
Open Diameter.jmp, found in the Quality Control sample data folder. This data set contains the diameters taken for each day, both with the first prototype (phase 1) and the second prototype (phase 2).
• Select Help > Sample Data Library and open Quality Control/Diameter.jmp.
• Select Analyze > Quality and Process > Control Chart > XBar.
• Select DIAMETER and click Process.
• Select DAY and click Sample Label.
• Select Phase and click Phase.
• Select S and XBar.
• Click OK.
The resulting chart has different limits for each phase.
Figure 4.28 Phase Control Chart
Statistical Details for the Control Chart Platform
This section contains statistical details for median moving range charts, UWMA charts, and EWMA charts. For details on any other types of charts (such as X- and R-charts, p- and np- charts, and more) see the “Statistical Details for the Control Chart Builder Platform” in the “Control Chart Builder” chapter.
Control Limits for Median Moving Range Charts
LCL for Median Moving Range Chart = max(0, MMR - (k*Std Dev*d3(n)))
UCL for Median Moving Range Chart = MMR + (k*Std Dev*d3(n))
The standard deviation for Median Moving Range charts is estimated by:
Std Dev = MMR/d4(n)
where:
MMR = Center Line (Avg) for Median Moving Range chart
d4(n) = expected value of the range of a normally distributed sample of size n.
Control Limits for UWMA Charts
Control limits for UWMA charts are computed as follows. For each subgroup i,
LCLi =
UCLi =
where:
w is the span parameter (number of terms in moving average)
ni is the sample size of the ith subgroup
k is the number of standard deviations
Xw is the weighted average of subgroup means
is the process standard deviationControl Limits for EWMA Charts
Control limits for EWMA charts are computed as:
LCL =
UCL =
where:
r is the EWMA weight parameter (0 < r ≤ 1)
xij is the jth measurement in the ith subgroup, with j = 1, 2, 3,..., ni
ni is the sample size of the ith subgroup
k is the number of standard deviations
Xw is the weighted average of subgroup means
is the process standard deviation..................Content has been hidden....................
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