XbarR (JMSL Numerical Library)

java.lang.Object
- com.imsl.chart.AbstractChartNode
- - com.imsl.chart.ChartNode
  - - com.imsl.chart.Data
    - - com.imsl.chart.qc.ShewhartControlChart
      - com.imsl.chart.qc.XbarR

All Implemented Interfaces:

Serializable, Cloneable
```
public class XbarR
extends ShewhartControlChart
```
XbarR is an X-bar chart for monitoring a process using sample ranges.
The control limits are at
$bar{bar x} + k frac{bar{R}}{d_{2,n}sqrt{n}}$
where is the grand mean of all of the observations, is the mean of the observed ranges, n is the sample size, and k is the value of the "ControlLimit" attribute for the limit. Additionally, $d_{2,n}=E[R]/sigma$ , where R is the range of data from a Gaussian distribution. Therefore $bar{R}/d_{2,n}$ is an estimate of the within sample standard deviation. By default, the chart contains an upper control limit with k=3, a lower control limit with k=-3, and a central line equal to . Additional control limits can be added. The method addWeco adds control limits with k = -2, -1, 1, 2.

See Also:
Example, NIST Engineering Statistics Handbook: Shewhart X-bar and R and S Control Charts, Serialized Form

Field Summary
- Fields inherited from class com.imsl.chart.qc.ShewhartControlChart
  d2, d3
- Fields inherited from class com.imsl.chart.ChartNode
  AXIS_X_TOP, AXIS_Y_RIGHT, BAR_TYPE_HORIZONTAL, BAR_TYPE_VERTICAL, DASH_PATTERN_DASH, DASH_PATTERN_DASH_DOT, DASH_PATTERN_DOT, DASH_PATTERN_SOLID, DATA_TYPE_FILL, DATA_TYPE_LINE, DATA_TYPE_MARKER, DATA_TYPE_PICTURE, DATA_TYPE_TUBE, DENDROGRAM_TYPE_HORIZONTAL, DENDROGRAM_TYPE_VERTICAL, FILL_TYPE_GRADIENT, FILL_TYPE_NONE, FILL_TYPE_PAINT, FILL_TYPE_SOLID, LABEL_TYPE_PERCENT, MARKER_TYPE_ASTERISK, MARKER_TYPE_CIRCLE_CIRCLE, MARKER_TYPE_CIRCLE_PLUS, MARKER_TYPE_CIRCLE_X, MARKER_TYPE_DIAMOND_PLUS, MARKER_TYPE_FILLED_CIRCLE, MARKER_TYPE_FILLED_DIAMOND, MARKER_TYPE_FILLED_SQUARE, MARKER_TYPE_FILLED_TRIANGLE, MARKER_TYPE_HOLLOW_CIRCLE, MARKER_TYPE_HOLLOW_DIAMOND, MARKER_TYPE_HOLLOW_SQUARE, MARKER_TYPE_HOLLOW_TRIANGLE, MARKER_TYPE_OCTAGON_PLUS, MARKER_TYPE_OCTAGON_X, MARKER_TYPE_PLUS, MARKER_TYPE_SQUARE_PLUS, MARKER_TYPE_SQUARE_X, MARKER_TYPE_X, TEXT_X_CENTER, TEXT_X_LEFT, TEXT_X_RIGHT, TEXT_Y_BOTTOM, TEXT_Y_CENTER, TEXT_Y_TOP
- Fields inherited from class com.imsl.chart.AbstractChartNode
  AUTOSCALE_DATA, AUTOSCALE_DENSITY, AUTOSCALE_NUMBER, AUTOSCALE_OFF, AUTOSCALE_WINDOW, AXIS_X, AXIS_Y, AXIS_Z, LABEL_TYPE_NONE, LABEL_TYPE_TITLE, LABEL_TYPE_X, LABEL_TYPE_Y, LABEL_TYPE_Z, TRANSFORM_CUSTOM, TRANSFORM_LINEAR, TRANSFORM_LOG

Constructor Summary

Constructors
Constructor and Description
`XbarR(AxisXY axis, double[][] x)` Creates an X-bar chart from sample data using sample ranges.
`XbarR(AxisXY axis, int[] sampleSize, double[] xbar, double[] range)` Creates an X-bar control chart given the means and ranges for a series of unequally sized samples.
`XbarR(AxisXY axis, int sampleSize, double[] xbar, double[] range)` Creates an X-bar control chart given the means and ranges for a series of equally sized samples.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`capabilityIndexCp(double lowerSpecificationLimit, double upperSpecificationLimit)` Returns the capability index $c_p=frac{mathrm{USL}-mathrm{LSL}}{6sigma}$
`double`	`capabilityIndexCpk(double lowerSpecificationLimit, double upperSpecificationLimit)` Returns the capability index $c_{pk}$ $c_{pk}=minleft[frac{mathrm{USL}-bar{x}}{3sigma},frac{bar{x}-mathrm{LSL}}{3sigma}right]$
`static ShewhartControlChart[]`	`createCharts(Chart chart, double[][] x)` Creates a combined `XbarR` chart and `RChart` from data.
`static ShewhartControlChart[]`	`createCharts(Chart chart, int[] sampleSize, double[] xbar, double[] range)` Creates a combined `XbarR` chart and `RChart` given the means and ranges for a series of unequally sized samples.
`static ShewhartControlChart[]`	`createCharts(Chart chart, int sampleSize, double[] xbar, double[] range)` Creates a combined `XbarR` chart and `RChart` given the means and ranges for a series of equally sized samples.
`double`	`getRbar()` Returns the value of the "Rbar" attribute, the mean of the ranges for a series of samples.
`void`	`prePaint()` Setup chart with current settings.
`void`	`setRbar(double rbar)` Sets the value of the "Rbar" attribute, the mean of the ranges for a series of samples.

Methods inherited from class com.imsl.chart.qc.ShewhartControlChart
addCenterLine, addControlLimit, addLowerControlLimit, addUpperControlLimit, addWecoLimits, dataRange, getCenter, getCenterLine, getControlData, getLowerControlLimit, getMeanSampleSize, getSampleSize, getUpperControlLimit, paint, removeControlLimit, setCenter, setData, setData, setSampleSize, setSampleSize, setX

Methods inherited from class com.imsl.chart.Data
formatLabel

Methods inherited from class com.imsl.chart.ChartNode
addPickListener, firePickListeners, getALT, getAxis, getBackground, getBarGap, getBarType, getBarWidth, getChart, getChartTitle, getChildren, getClipData, getComponent, getConcatenatedViewport, getDataType, getDoubleBuffering, getExplode, getFillOutlineColor, getFillOutlineType, getFillPaint, getFillType, getGradient, getHREF, getLegend, getLineDashPattern, getMarkerDashPattern, getMarkerThickness, getMarkerType, getParent, getReference, getScreenAxis, getScreenSize, getScreenViewport, getSize, getSkipWeekends, getTextAngle, getTextColor, getTitle, getToolTip, getViewport, isBitSet, removePickListener, setALT, setBarGap, setBarType, setBarWidth, setChartTitle, setClipData, setCustomTransform, setDataType, setDoubleBuffering, setExplode, setFillOutlineColor, setFillOutlineColor, setFillOutlineType, setFillPaint, setFillPaint, setFillPaint, setFillType, setGradient, setGradient, setGradient, setHREF, setImage, setLineDashPattern, setMarkerDashPattern, setMarkerThickness, setMarkerType, setReference, setScreenSize, setSize, setSkipWeekends, setTextAngle, setTextColor, setTextColor, setTitle, setTitle, setToolTip, setViewport, setViewport

Methods inherited from class com.imsl.chart.AbstractChartNode
clone, clone, clone, clone, getAbstractParent, getAttribute, getAutoscaleInput, getAutoscaleMinimumTimeInterval, getAutoscaleOutput, getBooleanAttribute, getChildList, getColorAttribute, getCustomTransform, getDensity, getDoubleAttribute, getFillColor, getFont, getFontName, getFontSize, getFontStyle, getImage, getIntegerAttribute, getLabelType, getLightColor, getLineColor, getLineWidth, getLocale, getMarkerColor, getMarkerSize, getName, getNumber, getPaint, getStringAttribute, getTextFormat, getTickLength, getTransform, getX, getY, isAncestorOf, isAttributeSet, isAttributeSetAtThisNode, parseColor, remove, setAttribute, setAutoscaleInput, setAutoscaleMinimumTimeInterval, setAutoscaleOutput, setDensity, setFillColor, setFillColor, setFont, setFontName, setFontSize, setFontStyle, setImage, setLabelType, setLightColor, setLightColor, setLineColor, setLineColor, setLineWidth, setLocale, setMarkerColor, setMarkerColor, setMarkerSize, setName, setNumber, setPaint, setTextFormat, setTextFormat, setTickLength, setTransform, setX, setY, toString

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - XbarR
```
public XbarR(AxisXY axis,
     double[][] x)
```
    Creates an X-bar chart from sample data using sample ranges.
    
    Parameters:
    axis - the AxisXY parent of this node.
    x - is an array of arrays containing sample data. The data of the i-th sample is in x[i]. Each row must have between 2 and 50 entries.
  - XbarR
```
public XbarR(AxisXY axis,
     int[] sampleSize,
     double[] xbar,
     double[] range)
```
    Creates an X-bar control chart given the means and ranges for a series of unequally sized samples.
    
    Parameters:
    axis - the AxisXY parent of this node
    sampleSize - is an array containing the nuumber of observations in each sample. Each sample must contain between 2 and 50 observations.
    xbar - is an array containing the mean values for a series of samples.
    range - is an array containing the ranges of the samples.
  - XbarR
```
public XbarR(AxisXY axis,
     int sampleSize,
     double[] xbar,
     double[] range)
```
    Creates an X-bar control chart given the means and ranges for a series of equally sized samples.
    
    Parameters:
    axis - the AxisXY parent of this node
    sampleSize - is the number of observations in each sample. It must be between 2 and 50.
    xbar - is an array containing the mean values for a series of samples.
    range - is an array containing the ranges of the samples. The arrays xbar and range must have the same lengths.
- Method Detail
  - capabilityIndexCp
```
public double capabilityIndexCp(double lowerSpecificationLimit,
                       double upperSpecificationLimit)
```
    Returns the capability index
    $c_p=frac{mathrm{USL}-mathrm{LSL}}{6sigma}$
    where LSL and USL are the lower and upper specification limits and
    $sigma=frac{bar{R}}{d_{2,n}sqrt{n}}$
    .
    
    Parameters:
    lowerSpecificationLimit - is the lower specification limit.
    upperSpecificationLimit - is the upper specification limit.
    
    Returns:
    the capability index.
  - capabilityIndexCpk
```
public double capabilityIndexCpk(double lowerSpecificationLimit,
                        double upperSpecificationLimit)
```
    Returns the capability index $c_{pk}$
    $c_{pk}=minleft[frac{mathrm{USL}-bar{x}}{3sigma},frac{bar{x}-mathrm{LSL}}{3sigma}right]$
    where LSL and USL are the lower and upper specification limits, is the center line, and
    $sigma=frac{bar{R}}{d_{2,n}sqrt{n}}$
    .
    
    Parameters:
    lowerSpecificationLimit - is the lower specification limit.
    upperSpecificationLimit - is the upper specification limit.
    
    Returns:
    the capability index.
  - createCharts
```
public static ShewhartControlChart[] createCharts(Chart chart,
                                  double[][] x)
```
    Creates a combined XbarR chart and RChart from data. The viewport of the XbarR chart is [0.2, 0.9] by [0.1, 0.4]. The viewport of the RChart chart is [0.2, 0.9] by [0.5, 0.8].
    
    Parameters:
    chart - is the Chart object which is the parent of the two charts being created.
    x - is an array of arrays containing sample data. The data of the i-th sample is in x[i]. Each sample must contain at least 2 and no more than 50 observations.
    
    Returns:
    an array of length two containing the XBarR chart and the RChart.
  - createCharts
```
public static ShewhartControlChart[] createCharts(Chart chart,
                                  int[] sampleSize,
                                  double[] xbar,
                                  double[] range)
```
    Creates a combined XbarR chart and RChart given the means and ranges for a series of unequally sized samples. The viewport of the XbarR chart is [0.2, 0.9] by [0.1, 0.4]. The viewport of the RChart chart is [0.2, 0.9] by [0.5, 0.8].
    
    Parameters:
    chart - is the Chart object which is the parent of the two charts being created.
    sampleSize - is an array containing the number of observations in each sample. Each sample must have between 2 and 50 observations.
    xbar - is an array containing the mean values for a series of samples.
    range - is an array containing the ranges of the samples.
    
    Returns:
    an array of length two containing the XBarR chart and the RChart.
  - createCharts
```
public static ShewhartControlChart[] createCharts(Chart chart,
                                  int sampleSize,
                                  double[] xbar,
                                  double[] range)
```
    Creates a combined XbarR chart and RChart given the means and ranges for a series of equally sized samples. The viewport of the XbarR chart is [0.2, 0.9] by [0.1, 0.4]. The viewport of the RChart chart is [0.2, 0.9] by [0.5, 0.8].
    
    Parameters:
    chart - is the Chart object which is the parent of the two charts being created.
    sampleSize - is the number of observations in each sample. It must be between 2 and 50.
    xbar - is an array containing the mean values for a series of samples.
    range - is an array containing the ranges of the samples.
    
    Returns:
    an array of length two containing the XBarR chart and the RChart.
  - getRbar
```
public double getRbar()
```
    Returns the value of the "Rbar" attribute, the mean of the ranges for a series of samples.
    
    Returns:
    the mean of the ranges for a series of samples
  - prePaint
```
public void prePaint()
```
    Setup chart with current settings.
    
    Overrides:
    
    prePaint in class ChartNode
  - setRbar
```
public void setRbar(double rbar)
```
    Sets the value of the "Rbar" attribute, the mean of the ranges for a series of samples.
    
    Parameters:
    rbar - is the mean of the ranges for a series of samples.

Class XbarR

Field Summary

Fields inherited from class com.imsl.chart.qc.ShewhartControlChart

Fields inherited from class com.imsl.chart.ChartNode

Fields inherited from class com.imsl.chart.AbstractChartNode

Constructor Summary

Method Summary

Methods inherited from class com.imsl.chart.qc.ShewhartControlChart

Methods inherited from class com.imsl.chart.Data

Methods inherited from class com.imsl.chart.ChartNode

Methods inherited from class com.imsl.chart.AbstractChartNode

Methods inherited from class java.lang.Object

Constructor Detail

XbarR

XbarR

XbarR

Method Detail

capabilityIndexCp

capabilityIndexCpk

createCharts

createCharts

createCharts

getRbar

prePaint

setRbar