com.imsl.chart.qc
Class XbarS

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

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, is a factor such that 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

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

double	capabilityIndexCp(double lowerSpecificationLimit, double upperSpecificationLimit) Returns the capability index
double	capabilityIndexCpk(double lowerSpecificationLimit, double upperSpecificationLimit) Returns the capability index
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

where LSL and USL are the lower and upper specification limits and

.

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

where LSL and USL are the lower and upper specification limits, is the center line, and

.

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.