PROC RELIABILITY: RELATIONPLOT Statement

The RELIABILITY Procedure

RELATIONPLOT Statement

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

<label:>RELATIONPLOT (variable1 variable2) <=group-variables> </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 12.9 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 12.26 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 12.39 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 parameter correlation matrix
COVB	requests parameter covariance matrix
FITTYPE \| FIT=	specifies method of estimating distribution parameters
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, independently for each level of a single group variable (default)
\| MODEL	-use the fit from the preceding MODEL statement. The MODEL statement can have no more than one independent variable.
\| 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.
<Variable=number-list >	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. This option only applies to FITTYPE=REGRESSION.
\| WEIBAYES	-Weibayes method
<(CONFIDENCE\|CONF=number)>	The number is the confidence coefficient for the Weibayes fit. The number is between 0 and 1, with a default value of 0.95.
ITPRINT	requests iteration history for 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 fixed or initial value of location parameter
MAXIT=number	specifies maximum number of iterations allowed for maximum likelihood fit
NOPCTILES	suppress computation of percentiles
PCTLIST=number-list	specifies 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.
PPOS=	specifies plotting position type. See the section Probability Plotting for details.
EXPRANK	-expected ranks
\| MEDRANK	-median ranks
\| MEDRANK1	-median ranks (exact formula)
\| KM	-Kaplan-Meier
\| MKM	-modified Kaplan-Meier (default)
\| (NA \| NELSONAALEN)	- Nelson-Aalen
PPOUT	request table of cumulative probabilities
PSTABLE=number	specifies stable parameterization. The number must be between zero and one. See the section Stable Parameters for further information.
RELATION=ARRHENIUS \| ARRHENIUS2 \| POWER \| LINEAR \| LOGISTIC	specifies type of relationship between life and stress. This determines the horizontal scale used in the relation plot. See Table 12.58 for definitions of the transformations.
READOUT	analyzes data with readout structure
SCALE=number <SCINIT>	specifies fixed or initial value of scale parameter
SHAPE=number <SHINIT>	specifies fixed or initial value of shape parameter
SINGULAR=number	specifies 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 12.49 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 $\text{[math]}$ to $\text{[math]}$ <by $\text{[math]}$ >.

Table 12.40 lists plot layout options available when you use traditional graphics.

Table 12.40 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))	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, and can be separated by blanks or commas or can be a list in the form $\text{[math]}$ to $\text{[math]}$ <by $\text{[math]}$ >.
LPLOTFIT=linetype \| (linetype list))	line styles for percentile lines. linetype list is a list of numbers representing different linetypes, and can be separated by blanks or commas or can be a list in the form $\text{[math]}$ to $\text{[math]}$ <by $\text{[math]}$ >.
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 frame around plotting area
NOPPLEGEND	suppresses legend for overlaid probability plots
NOPPOS	suppresses plotting of symbols for failures in a probability plot
NORPLEGEND	suppresses legend for relation plot
PINTERVALS=	type of parametric pointwise confidence interval displayed in a probability plot. The default type is PROBABILITY, pointwise confidence intervals on cumulative failure probability.
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
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), and, 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)	symbols representing 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	display 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 12.41 lists plot layout options available when you use ODS graphics.

Table 12.41 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=	type of parametric pointwise confidence interval displayed in a probability plot. The default type is PROBABILITY, pointwise confidence intervals on cumulative failure probability.
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
PLOTDATA	requests that the data be plotted on the relationplot
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), and, if not specified, the 50th percentile (median) is plotted.
PPLOT	places a probability plot on the same page as the relation plot

Table 12.42 lists reference line options available when you use traditional graphics.

Table 12.42 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= $\text{[math]}$

specifies 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= $\text{[math]}$

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= $\text{[math]}$

specifies 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 12.43 lists reference line options available when you use ODS graphics.

Table 12.43 Reference Line Options for ODS Graphics
Option	Option Description
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 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.
PREFLABELS=(’label1’ ...’labeln’)	specifies labels for PREF= lines
SREF=value-list	specifies reference lines perpendicular to horizontal stress axis
SREFLABELS=(’label1’ ...’labeln’)	specifies labels for SREF= lines
LREF <(INTERSECT)>=value-list	requests reference lines perpendicular to vertical (lifetime) 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.
LREFLABELS=(’label1’ ...’labeln’)	specifies labels for LREF= lines

The following options control the appearance of the text when you use traditional graphics. These options are not available if ODS Graphics is enabled.

Table 12.44 Text Enhancement Options
Option	Option Description
FONT=font	specifies a software font for text
HEIGHT=value	specifies height of text used outside framed areas
INFONT=font	specifies a software font for text inside framed areas
INHEIGHT=value	specifies height of text inside framed areas

Table 12.45 lists options to control the appearance of the axes when you use traditional graphics.

Table 12.45 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 label for life, or analysis variable, axis
NOLTICK	suppresses tick marks and tick mark labels for lifetime or analysis variable axis
NOPLABEL	suppresses label for probability axis
NOPTICK	suppresses tick marks and tick mark labels for probability axis
NOSLABEL	suppresses label for 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 lower limit on probability axis scale
PCTUPPER \| PUPPER=number	specifies upper limit on probability axis scale
STRESSLOWER \| SLOWER=number	specifies lower limit on stress axis scale
STRESSUPPER \| SUPPER=number	specifies upper limit on stress axis scale
PAXISLABEL=‘string’	specifies label for probability axis
WAXIS= $\text{[math]}$	specifies line thickness for axes and frame

Table 12.46 lists options to control the appearance of the axes when you use ODS graphics.

Table 12.46 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 limit on probability axis scale
PCTUPPER \| PUPPER=number	specifies upper limit on probability axis scale
STRESSLOWER \| SLOWER=number	specifies lower limit on stress axis scale
STRESSUPPER \| SUPPER=number	specifies upper limit on stress axis scale
PAXISLABEL=‘string’	specifies label for probability axis

The following options 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 12.47 Graphics Catalog Options
Option	Option Description
DESCRIPTION=‘string’	description for graphics catalog member
NAME=‘string’	name for plot in graphics catalog

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

Table 12.48 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

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