The RELIABILITY Procedure 
RELATIONPLOT Statement 
You use the RELATIONPLOT statement to create lifestress relation plots. A lifestress 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 lifestress relation plot, you must specify one variable. If your data are right censored, you must specify a censorvariable and, in parentheses, the values of the censorvariable that correspond to censored data values. You must specify one groupvariable to represent the values of stress. The groupvariable must be a numeric variable.
The RELATIONPLOT statement plots the uncensored values of your data given by variable versus the values of the groupvariable. 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.
represents the data for which a plot is to be produced. The variable must be a numeric variable in the input data set.
indicates which observations in the input data set are right censored. You specify the values of censorvariable 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 censorvariable; otherwise, censorvariable must be a numeric variable in the input data set.
is another method of specifying the data for which a lifestress plot is to be produced. You can use this syntax in a situation where uncensored, intervalcensored, leftcensored, and rightcensored 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.
is a group variable. The groupvariable must be a numeric variable in the input data set.
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.
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=numberlist)> 
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 numberlist 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=numberlist > 
Variable is a second independent variable in the MODEL statement, and numberlist 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 
<(CONFIDENCECONF=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=numberlist 
specifies list of percentages for which to compute percentile estimates. The numberlist 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 
KaplanMeier 
 MKM 
modified KaplanMeier (default) 
 (NA  NELSONAALEN) 
 NelsonAalen 
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  
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 
requests that survival function be computed for values in numberlist. 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 to <by >. 
Table 12.40 lists plot layout options available when you use 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 to <by >. 
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 to <by >. 
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 <numberlist> 
specifies that percentiles of the fitted distribution be plotted on the relation plot. The optional numberlist is a list of percentiles (between 0 and 100), and, if not specified, the 50th percentile (median) is plotted. 
PPLEGEND = legendstatementname  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 rightcensored and leftcensored 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 = legendstatementname  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.
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 <numberlist> 
specifies that percentiles of the fitted distribution be plotted on the relation plot. The optional numberlist 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.
Option 
Option Description 


HREF <(INTERSECT)>=valuelist 
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= 
specifies vertical position of labels for HREF= lines. The valid values for n and the corresponding label placements are shown in the following table:


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=valuelist 
specifies reference lines perpendicular to horizontal stress axis 

SREFLABELS=(’label1’ ...’labeln’) 
specifies labels for SREF= lines 

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


VREF <(INTERSECT)>=valuelist 
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= 
specifies horizontal position of labels for VREF= lines. The valid values for n and the corresponding label placements are shown in the following table:

Table 12.43 lists reference line options available when you use ODS graphics.
Option 
Option Description 

PREF <(INTERSECT)>=valuelist 
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=valuelist 
specifies reference lines perpendicular to horizontal stress axis 
SREFLABELS=(’label1’ ...’labeln’) 
specifies labels for SREF= lines 
LREF <(INTERSECT)>=valuelist 
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.
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.
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= 
specifies line thickness for axes and frame 
Table 12.46 lists options to control the appearance of the axes when you use 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.
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.
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, rightcensored, and leftcensored observations in a relation plot 
Copyright © SAS Institute, Inc. All Rights Reserved.