The RELIABILITY Procedure

RELATIONPLOT Statement

Subsections:

Summary of Options

<label:>RELATIONPLOT variable < $*$ censor-variable(values)> <=group-variable>
</ options> ;

<label:>RELATIONPLOT (variable1 variable2) <=group-variable> </ options> ;

You use the RELATIONPLOT statement to create life-stress relation plots. A life-stress relation plot is a graphical tool for the analysis of data from accelerated life tests. The plot is a display of the relationship between life and stress, such as temperature or voltage. You can also use the RELATIONPLOT statement to display a probability plot alongside the relation plot. See Figure 16.9 for an example of a relation plot.

You can specify the keyword RPLOT as an alias for RELATIONPLOT. You can use any number of RELATIONPLOT statements after a PROC RELIABILITY statement. You can specify an optional label to distinguish between multiple RELATIONPLOT statements in the output.

See the section Analysis of Accelerated Life Test Data for an example that uses the RELATIONPLOT statement.

To create a life-stress relation plot, you must specify one variable. If your data are right censored, you must specify a censor-variable and, in parentheses, the values of the censor-variable that correspond to censored data values. You must specify one group-variable to represent the values of stress. The group-variable must be a numeric variable.

The RELATIONPLOT statement plots the uncensored values of your data given by variable versus the values of the group-variable. You can optionally display a boxplot of the values of the data. You can also plot percentiles of the distribution fitted to the data. The RELATIONPLOT statement produces the same tabular output as the PROBPLOT statement, and all the analysis options are the same as for the PROBPLOT statement.

The elements of the RELATIONPLOT statement are described as follows.

variable

represents the data for which a plot is to be produced. The variable must be a numeric variable in the input data set.

censor-variable(values)

indicates which observations in the input data set are right censored. You specify the values of censor-variable that represent censored observations by placing those values in parentheses after the variable name. If your data are not right censored, then you omit the specification of censor-variable; otherwise, censor-variable must be a numeric variable in the input data set.

(variable1 variable2)

is another method of specifying the data for which a life-stress plot is to be produced. You can use this syntax in a situation where uncensored, interval-censored, left-censored, and right-censored values occur in the same set of data. Table 16.31 shows how you use this syntax to specify different types of censoring by using combinations of missing and nonmissing values. See the section Lognormal Analysis with Arbitrary Censoring for an example that uses this syntax to create a probability plot.

group-variable

is a group variable. The group-variable must be a numeric variable in the input data set.

options

control the features of the relation plot. All options are specified after the slash (/) in the RELATIONPLOT statement. The “Summary of Options” section, which follows, lists all options by function.

The only type of relation plot currently available for interval data is the type in which percentiles of the fitted distribution are plotted at each stress level.

Summary of Options

Table 16.46: Analysis Options

Option

Option Description

CONFIDENCE=number

Specifies the confidence coefficient for all confidence intervals. The number must be between 0 and 1. The default value is 0.95.

CONVERGE=number

Specifies the convergence criterion for maximum likelihood fit. See the section Maximum Likelihood Estimation for details.

CONVH=number

Specifies the convergence criterion for the relative Hessian convergence criterion. See the section Maximum Likelihood Estimation for details.

CORRB

Requests the parameter correlation matrix.

COVB

Requests the parameter covariance matrix.

FITTYPE | FIT= fit-specification

Specifies the method of estimating distribution parameters. The available fit-specifications and their meanings are shown in the following table.

Fit Specification	Definition
LSYX	Least squares fit to the probability plot. The probability axis is the dependent variable.
LSXY	Least squares fit to the probability plot. The lifetime axis is the dependent variable.
MLE	Maximum likelihood (default).
MODEL	Use the fit from the preceding MODEL statement
NONE	No fit is computed.
REGRESSION<(variable=number-list)>	Use the fit from the preceding MODEL statement. Nonlinear relations and percentiles from models that use two independent variables can be plotted. variable is a second independent variable in the MODEL statement, and number-list is a list of values of the second independent variable for which to plot the percentiles as a function of the first independent variable.
WEIBAYES
<(CONFIDENCE \| CONF=number)>
	Weibayes fit. number is the confidence coefficient for the Weibayes fit and is between 0 and 1. The default is 0.95.

ITPRINT

Requests the iteration history for the maximum likelihood fit.

LRCL

Requests likelihood ratio confidence intervals for distribution parameters.

LRCLPER

Requests likelihood ratio confidence intervals for distribution percentiles.

LOCATION=number <LINIT>

Specifies a fixed or initial value of the location parameter.

MAXIT=number

Specifies the maximum number of iterations allowed for a maximum likelihood fit.

NOPCTILES

Suppresses computation of percentiles.

PCTLIST=number-list

Specifies a list of percentages for which to compute percentile estimates. The number-list must be a list of numbers separated by blanks or commas. Each number in the list must be between 0 and 100. If this option is not specified, percentiles are computed for a standard list of percentages.

PPOS=plotting-position

Specifies the plotting-position type used to compute nonparametric estimates of the probability distribution function. See the section Probability Plotting for details. The plotting position types available are shown in the following table.

Plotting Position	Type
EXPRANK	Expected ranks
MEDRANK	Median ranks
MEDRANK1	Median ranks (exact formula)
KM	Kaplan-Meier
MKM	Modified Kaplan-Meier (default)
NA \| NELSONAALEN	Nelson-Aalen

PPOUT

Requests a table of nonparametric cumulative probabilities in the printed output.

PSTABLE=number

Specifies a stable parameterization. The number must be between zero and one. See the section Stable Parameters for further information.

RELATION=transformation-keyword

Specifies the type of relationship between independent (stress) and dependent (lifetime) variables. The transformation specified is applied to the independent (stress) variable in the model. This determines the horizontal scale used in the relation plot. transformation-keyword can be any of the transformations listed in the following table. See Table 16.67 for definitions of the transformations.

Transformation Keyword	Type of Transformation
ARRHENIUS	Arrhenius (Nelson parameterization)
ARRHENIUS2	Arrhenius (activation energy)
POWER	Logarithmic
LINEAR	Linear
LOGISTIC	Logistic

READOUT

Specifies the data has the readout structure.

SCALE=number <SCINIT>

Specifies a fixed or initial value of scale parameter.

SHAPE=number <SHINIT>

Specifies a fixed or initial value of shape parameter.

SINGULAR=number

Specifies the singularity criterion for matrix inversion.

SURVTIME=number-list

Requests that survival function be computed for values in number-list. See the section Reliability Function for details.

THRESHOLD=number

Specifies a fixed threshold parameter. See Table 16.57 for the distributions with a threshold parameter.

variable=number-list

Enables creation of plots of percentiles from a regression model when two independent variables are used in a MODEL statement effect-list. The FIT=REGRESSION option must be used with this option. Percentile plots are created for each value of the independent variable in the number-list. number-list is a list of numeric values separated by blanks or commas, or in the form of a list $n_1$ to $n_2$ <by $n_3$ >.

Table 16.47 lists plot layout options that are available when you use traditional graphics.

Table 16.47: Plot Layout Options for Traditional Graphics

Option

Option Description

CENSYMBOL=symbol | (symbol-list)

Specifies symbols for censored values. The symbol is one of the symbol names (plus, star, square, diamond, triangle, hash, paw, point, dot, circle) or a letter (A–Z). If you are creating overlaid plots for groups of data, you can specify different symbols for the groups with a list of symbols or letters, separated by blanks, enclosed in parentheses. If no CENSYMBOL option is specified, the symbol used for censored values is the same as for failures.

HOFFSET=value

Specifies an offset for horizontal axis.

INBORDER

Requests a border around plots.

LBOXES=number

Specifies a line style for boxplots.

LFIT=linetype | (linetype-list))

Specifies line styles for fit lines and confidence curves in a probability plot. The linetype-list is a list of numbers from 1 to 46 representing different linetypes; the numbers can be separated by blanks or commas or can be a list in the form $n_1$ to $n_2$ <by $n_3$ >.

LPLOTFIT=linetype | (linetype-list))

Specifies line styles for percentile lines. linetype-list is a list of numbers that represent different linetypes; the numbers can be separated by blanks or commas or can be a list in the form $n_1$ to $n_2$ <by $n_3$ >.

NOCENPLOT

Suppresses plotting of censored data points.

NOCONF

Suppresses plotting of percentile confidence curves.

NOFIT

Suppresses plotting of fit line and percentile confidence curves.

NOFRAME

Suppresses the frame around the plotting area.

NOPPLEGEND

Suppresses the legend for overlaid probability plots.

NOPPOS

Suppresses plotting of symbols for failures in a probability plot.

NORPLEGEND

Suppresses the legend for the relation plot.

PINTERVALS=interval-type

Specifies the type of parametric pointwise confidence interval displayed in a probability plot. The available types of intervals are listed in the following table. The default type is PROBABILITY, pointwise confidence intervals on cumulative failure probability.

Interval Type	Definition
LIKELIHOOD \| LRCI	Likelihood ratio confidence intervals
PERCENTILES \| PER	Pointwise parametric confidence intervals for the percentiles of the fitted CDF
PROBABILITY \| CDF	Pointwise parametric confidence intervals for the cumulative failure probabilities. See the section Reliability Function for details.

PLOTDATA <DATA | MEDIANS | BOXES>

Requests that the data be plotted on the relationplot and specifies the representation of the data populations to be plotted.

PLOTFIT <number-list>

Specifies that percentiles of the fitted distribution be plotted on the relation plot. The optional number-list is a list of percentiles (between 0 and 100); if not specified, the 50th percentile (median) is plotted.

PPLEGEND = legend-statement-name

| NONE

Identifies a LEGENDn statement to specify legend for overlaid probability plots.

PPLOT

Places a probability plot on the same page as the relation plot.

RCENSYMBOL=symbol | (symbol-list)

Specifies symbols that represent right-censored and left-censored observations in a relation plot. The symbol is one of the symbol names (plus, star, square, diamond, triangle, hash, paw, point, dot, circle) or a letter (A–Z).

RPLEGEND = legend-statement-name

| NONE

Identifies a LEGENDn statement to specify legend for the relation plot.

SHOWMULTIPLES

Displays the count for multiple overlaying symbols.

TURNVLABELS

Vertically strings out characters in labels for vertical axis.

VOFFSET=value

Specifies length of offset at upper end of vertical axis.

WFIT=linetype

Specifies line width for fit line and confidence curves.

Table 16.48 lists plot layout options that are available when you use ODS graphics.

Table 16.48: Plot Layout Options for ODS Graphics

Option

Option Description

NOCENPLOT

Suppresses plotting of censored data points.

NOCONF

Suppresses plotting of percentile confidence curves.

NOFIT

Suppresses plotting of fit line and percentile confidence curves.

NOPPOS

Suppresses plotting of symbols for failures in a probability plot.

PINTERVALS=interval-type

Interval Type	Definition
LIKELIHOOD \| LRCI	Likelihood ratio confidence intervals
PERCENTILES \| PER	Pointwise parametric confidence intervals for the percentiles of the fitted CDF
PROBABILITY \| CDF	Pointwise parametric confidence intervals for the cumulative failure probabilities. See the section Reliability Function for details.

PLOTDATA

Requests that the data be plotted on the relationplot.

PLOTFIT <number-list>

PPLOT

Places a probability plot on the same page as the relation plot.

Table 16.49 lists reference line options that are available when you use traditional graphics.

Table 16.49: Reference Line Options for Traditional Graphics

Option

Option Description

HREF <(INTERSECT)>=value-list

Requests reference lines perpendicular to horizontal axis. If (INTERSECT) is specified, a second reference line perpendicular to the vertical axis is drawn that intersects the fit line at the same point as the horizontal axis reference line. If a horizontal axis reference line label is specified, the intersecting vertical axis reference line is labeled with the vertical axis value.

HREFLABELS=(’label1’ …’labeln’)

Specifies labels for HREF= lines.

HREFLABPOS=n

Specifies the vertical position of labels for HREF= lines. The valid values for n and the corresponding label placements are shown in the following table:

n	Label Placement
1	Top
2	Staggered from top
3	Bottom
4	Staggered from bottom
5	Alternating from top
6	Alternating from bottom

LHREF=linetype

Specifies a line style for HREF= lines.

LSREF=linetype

Specifies a line style for SREF= lines.

LVREF=linetype

Specifies a line style for VREF= lines.

SREF=value-list

Specifies reference lines perpendicular to horizontal stress axis.

SREFLABELS=(’label1’ …’labeln’)

Specifies labels for SREF= lines

SREFLABPOS=n

Specifies horizontal position of labels for SREF= lines. The valid values for n and the corresponding label placements are shown in the following table:

n	Label Placement
1	Top
2	Staggered from top
3	Bottom
4	Staggered from bottom

VREF <(INTERSECT)>=value-list

Requests reference lines perpendicular to vertical axis. If (INTERSECT) is specified, a second reference line perpendicular to the horizontal axis is drawn that intersects the fit line at the same point as the vertical axis reference line. If a vertical axis reference line label is specified, the intersecting horizontal axis reference line is labeled with the horizontal axis value.

VREFLABELS=(’label1’ …’labeln’)

Specifies labels for VREF= lines.

VREFLABPOS=n

Specifies the horizontal position of labels for VREF= lines. The valid values for n and the corresponding label placements are shown in the following table:

n	Label Placement
1	Left
2	Right

Table 16.50 lists reference line options that are available when you use ODS graphics.

Table 16.50: Reference Line Options for ODS Graphics

Option	Option Description
LREF <(INTERSECT)>=value-list	Requests reference lines perpendicular to lifetime axis. If (INTERSECT) is specified, a second reference line is drawn perpendicular to the stress axis (and the probability axis if applicable), and it intersects the fit line at the same point as the lifetime axis reference line. If a lifetime axis reference line label is specified, the intersecting stress/probability axis reference line is labeled with the stress/probability axis value.
LREFLABELS=(’label1’ …’labeln’)	Specifies labels for LREF= lines.
PREF <(INTERSECT)>=value-list	Requests reference lines perpendicular to probability axis, if a probability plot is specified with the PPLOT option. If (INTERSECT) is specified, a second reference line is drawn perpendicular to the lifetime axis and intersects the fit line at the same point as the probability axis reference line. If a probability axis reference line label is specified, the intersecting lifetime axis reference line is labeled with the lifetime axis value.
PREFLABELS=(’label1’ …’labeln’)	Specifies labels for PREF= lines.
SREF <(INTERSECT)>=value-list	Specifies reference lines perpendicular to stress stress axis. If (INTERSECT) is specified, a second reference line is drawn perpendicular to the lifetime axis and intersects the fit line at the same point as the stress axis reference line. If a stress axis reference line label is specified, the intersecting lifetime axis reference line is labeled with the lifetime axis value.
SREFLABELS=(’label1’ …’labeln’)	Specifies labels for SREF= lines.

Table 16.51 lists options that control the appearance of the text when you use traditional graphics. These options are not available if ODS Graphics is enabled.

Table 16.51: Text Enhancement Options

Option	Option Description
FONT=font	Specifies a software font for text.
HEIGHT=value	Specifies the height of text used outside framed areas.
INFONT=font	Specifies a software font for text inside framed areas.
INHEIGHT=value	Specifies the height of text inside framed areas.

Table 16.52 lists options that control the appearance of the axes when you use traditional graphics.

Table 16.52: Axis Options for Traditional Graphics

Option	Option Description
LAXIS=value1 TO value2<BY value3>	Specifies tick mark values for the lifetime axis. value1, value2, and value3 must be numeric, and value1 must be less than value2. The lower tick mark is value1. Tick marks are drawn at increments of value3. The last tick mark is the greatest value that does not exceed value2. If value3 is omitted, a value of 1 is used. This method of specification of tick marks is not valid for logarithmic axes. Examples of LAXIS= lists are laxis = -1 to 10 laxis = 0 to 200 by 10
LGRID=number	Specifies a line style for all grid lines. The number is between 1 and 46 and specifies a linestyle for grids.
LIFELOWER \| LLOWER=number	Specifies the lower limit on the lifetime axis scale. The LLOWER option specifies number as the lower lifetime axis tick mark. The tick interval and the upper lifetime axis limit are determined automatically. This option has no effect if the LAXIS option is used.
LIFEUPPER \| LUPPER=number	Specifies the upper limit on the lifetime axis scale. The LUPPER option specifies number as the upper lifetime axis tick mark. The tick interval and the lower lifetime axis limit are determined automatically. This option has no effect if the LAXIS option is used.
MPGRID	Adds a minor grid for the probability axis.
MINORLOGGRID	Adds a minor grid for log axes.
NOGRID	Suppresses grid lines.
NOLLABEL	Suppresses the label for the lifetime axis.
NOLTICK	Suppresses tick marks and tick mark labels for lifetime or analysis variable axis.
NOPLABEL	Suppresses the label for the probability axis.
NOPTICK	Suppresses tick marks and tick mark labels for probability axis.
NOSLABEL	Suppresses the label for the stress axis.
NOSTICK	Suppresses tick marks and tick mark labels for stress axis.
NSTRESSTICK=number	Specifies the number of tick intervals for stress axis for relation plot.
NTICK=number	Specifies the number of tick intervals for the lifetime axis. This option has no effect if the LAXIS option is used.
PCTLOWER \| PLOWER=number	Specifies the lower limit on the probability axis scale.
PCTUPPER \| PUPPER=number	Specifies the upper limit on the probability axis scale.
STRESSLOWER \| SLOWER=number	Specifies the lower limit on the stress axis scale.
STRESSUPPER \| SUPPER=number	Specifies the upper limit on the stress axis scale.
PAXISLABEL=‘string’	Specifies a label for the probability axis.
WAXIS=n	Specifies the line thickness for axes and frame.

Table 16.53 lists options that control the appearance of the axes when you use ODS Graphics.

Table 16.53: Axis Options for ODS Graphics

Option	Option Description
LIFELOWER \| LLOWER=number	Specifies the lower limit on the lifetime axis scale. The LLOWER option specifies number as the lower lifetime axis tick mark. The tick interval and the upper lifetime axis limit are determined automatically. This option has no effect if the LAXIS option is used.
LIFEUPPER \| LUPPER=number	Specifies the upper limit on the lifetime axis scale. The LUPPER option specifies number as the upper lifetime axis tick mark. The tick interval and the lower lifetime axis limit are determined automatically. This option has no effect if the LAXIS option is used.
NOGRID	Suppresses grid lines.
PCTLOWER \| PLOWER=number	Specifies lower the limit on the probability axis scale.
PCTUPPER \| PUPPER=number	Specifies upper the limit on the probability axis scale.
STRESSLOWER \| SLOWER=number	Specifies the lower limit on the stress axis scale.
STRESSUPPER \| SUPPER=number	Specifies the upper limit on the stress axis scale.
PAXISLABEL=‘string’	Specifies a label for the probability axis.

Table 16.54 lists options that control the use of a graphics catalog to store graphs if you use traditional graphics. These options are not available if ODS Graphics is enabled.

Table 16.54: Graphics Catalog Options

Option	Option Description
DESCRIPTION=‘string’	Description for graphics catalog member
NAME=‘string’	Name for plot in graphics catalog

Table 16.55 lists options that control colors and patterns used in the graph when you use traditional graphics. These options are not available if ODS Graphics is enabled.

Table 16.55: Color and Pattern Options

Option	Option Description
CAXIS=color	Color for axis
CBOXES=color	Color for box frame for boxplots
CBOXFILL=color	Color for filling boxes for boxplots
CCENSOR=color	Color for filling censor plot area
CENCOLOR=color	Color for censor symbol
CFIT=color \| (color-list)	color for fit lines and confidence curves in a probability plot
CFRAME=color	Color for frame
CGRID=color	Color for grid lines
CHREF=color	Color for HREF= lines
CPLOTFIT=color \| (color-list)	colors for percentile lines
CSREF=color	Color for SREF= lines
CTEXT=color	Color for text
CVREF=color	Color for VREF= lines
RCENCOLOR=color \| (color-list)	Colors for the symbols representing uncensored, right-censored, and left-censored observations in a relation plot