XbarS (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.XbarS

All Implemented Interfaces:

Serializable, Cloneable
```
public class XbarS
extends ShewhartControlChart
```
XbarS is an X-bar chart for monitoring a process using sample standard deviations.
The control limits are at
$bar{bar{x}} + k frac{bar{s}}{c_{4,n}sqrt{n}}$
where is the grand mean of all of the observations, n is the sample size, and k is the value of the "ControlLimit" attribute for the limit. Additionally, $c_{4,n}$ is a factor such that $bar{s}/c_{4,n}$ is an unbiased estimator of the within sample standard deviation. By default, the chart contains an upper control limit line with k=3, a lower control limit line with k=-3, and a central line equal to . Additional control limit lines 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
`XbarS(AxisXY axis, double[][] x)` Creates an `XbarS` chart from sample data using within sample standard deviations.
`XbarS(AxisXY axis, int[] sampleSize, double[] xbar, double[] w)` Creates an `XbarS` chart given the means and standard deviations for a series of unequally sized samples.
`XbarS(AxisXY axis, int sampleSize, double[] xbar, double[] w)` Creates an `XbarS` chart given the means and standard deviations 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 `XbarS` chart and `SChart` from data.
`static ShewhartControlChart[]`	`createCharts(Chart chart, int[] sampleSize, double[] xbar, double[] w)` Creates a combined X-bar chart and S-chart given the means and in sample standard deviations for a series of unequally sized samples.
`static ShewhartControlChart[]`	`createCharts(Chart chart, int sampleSize, double[] xbar, double[] w)` Creates a combined `XbarS` chart and `SChart` given the means and in sample standard deviations for a series of equally sized samples.
`double`	`getWbar()` Returns the value of the "Wbar" attribute, the within sample variation for a series of samples.
`void`	`prePaint()` Setup chart with current settings.
`void`	`setWbar(double wbar)` Sets the value of the "Wbar" attribute, the within sample variation 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
  - XbarS
```
public XbarS(AxisXY axis,
     double[][] x)
```
    Creates an XbarS chart from sample data using within sample standard deviations.
    
    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 at least one entry.
  - XbarS
```
public XbarS(AxisXY axis,
     int[] sampleSize,
     double[] xbar,
     double[] w)
```
    Creates an XbarS chart given the means and standard deviations for a series of unequally sized samples.
    
    Parameters:
    axis - the AxisXY parent of this node
    sampleSize - is an array containing the number of observations in each sample. Each sample must have at least one observation.
    xbar - is an array containing the mean values for a series of samples.
    w - is an array containing the within sample variation for a series of samples.
    
    Throws:
    
    IllegalArgumentException - is thrown if the three input arrays do not all have the same length.
  - XbarS
```
public XbarS(AxisXY axis,
     int sampleSize,
     double[] xbar,
     double[] w)
```
    Creates an XbarS chart given the means and standard deviations 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 at least one.
    xbar - is an array containing the mean values for a series of samples.
    w - is an array containing the within sample variation for a series of samples.
    
    Throws:
    
    IllegalArgumentException - is thrown if the two input arrays do not have the same length.
- 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
    $sigma=frac{bar{s}}{c_{4,n}sqrt{n}}$
    .
    
    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
    $sigma=frac{bar{s}}{c_{4,n}sqrt{n}}$
    .
    
    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 XbarS chart and SChart from data. The viewport of the XbarS chart is [0.2, 0.9] by [0.1, 0.4]. The viewport of the SChart 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 row must have at least one entry.
    
    Returns:
    an array of length two containing the XBarS chart and the SChart.
  - createCharts
```
public static ShewhartControlChart[] createCharts(Chart chart,
                                  int[] sampleSize,
                                  double[] xbar,
                                  double[] w)
```
    Creates a combined X-bar chart and S-chart given the means and in sample standard deviations for a series of unequally sized samples.
    
    Parameters:
    chart - is the Chart object which is the parent of the two charts being created.
    xbar - is an array containing the mean values for a series of samples.
    sampleSize - is an array containing the number of observations in each sample. Each sample must have at least one observation.
    w - is an array containing the in sample standard deviations of the samples.
    
    Returns:
    an array of length two containing the XBarS chart and the SChart.
  - createCharts
```
public static ShewhartControlChart[] createCharts(Chart chart,
                                  int sampleSize,
                                  double[] xbar,
                                  double[] w)
```
    Creates a combined XbarS chart and SChart given the means and in sample standard deviations for a series of equally sized samples. The viewport of the XbarS chart is [0.2, 0.9] by [0.1, 0.4]. The viewport of the SChart 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.
    xbar - is an array containing the mean values for a series of samples.
    sampleSize - is the number of observations in each sample. It must be at least one.
    w - is an array containing the in sample standard deviations of the samples.
    
    Returns:
    an array of length two containing the XBarS chart and the SChart.
  - getWbar
```
public double getWbar()
```
    Returns the value of the "Wbar" attribute, the within sample variation for a series of samples. Its default value is set by the constructor to an estimate of the within sample variation
    
    Returns:
    the within sample variation for a series of samples.
  - prePaint
```
public void prePaint()
```
    Setup chart with current settings.
    
    Overrides:
    
    prePaint in class ChartNode
  - setWbar
```
public void setWbar(double wbar)
```
    Sets the value of the "Wbar" attribute, the within sample variation for a series of samples. Its default value is set by the constructor to an estimate of the within sample variation.
    
    Parameters:
    wbar - is the within sample variation for a series of samples.

Class XbarS

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

XbarS

XbarS

XbarS

Method Detail

capabilityIndexCp

capabilityIndexCpk

createCharts

createCharts

createCharts

getWbar

prePaint

setWbar