RELATIONPLOT Statement

Chapter Contents

The RELIABILITY Procedure

RELATIONPLOT Statement

RELATIONPLOT variable< $\ast$ censor-variable(values)> <=group-variable> </options>;
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 30.6 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.

See "Analysis of Accelerated Life Test Data" for an example using 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 30.20 shows how you use this syntax to specify different types of censoring by using combinations of missing and nonmissing values. See "Lognormal Analysis with Arbitrary Censoring" for an example of using 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 30.30: 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.
CONVH=number	specifies the convergence criterion for the relative Hessian convergence criterion
CORRB	requests parameter correlation matrix
COVB	requests parameter covariance matrix
FITTYPE=	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 (default)
\| MODEL	-use the fit from the preceding MODEL statement
\| NONE	-no fit is computed
\| 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.
EXPRANK	-expected ranks
\|MEDRANK	-median ranks
\|MEDRANK1	-median ranks (exact formula)
\|KM	-Kaplan-Meier
\|MKM	-modified Kaplan-Meier (default)
PPOUT	request table of cumulative probabilities
PSTABLE=number	specifies stable parameterization. The number must be between zero and one. See "Stable Parameters" for further information.
RELATION=ARRHENIUS \| ARRHENIUS2 \| LINEAR \| POWER	specifies type of relationship between life and stress. This determines the horizontal scale used in the relation plot. See Table 30.45 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
THRESHOLD=number	specifies a fixed threshold parameter. See Table 30.37 for the distributions with a threshold parameter.

Table 30.31: Plot Layout Options

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
JITTER=number	specifies amount to jitter overlaying plot symbols, in units of symbol width
LFIT=linetype	specifies a line style for fit line and confidence curves
LBOXES=number	specifies a line style for boxplots
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
NORPLEGEND	suppresses legend for relation plot
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
RPLEGEND = legend-statement-name \| NONE	identifies a LEGENDn statement to specify legend for the relation plot
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 30.32: Reference Line Options

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 vertical position of labels for HREF=lines. The valid values for n and the corresponding label placements are shown below.

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 below.

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 horizontal position of labels for VREF= lines. The valid values for n and the corresponding label placements are shown below.

n	label placement
1	left
2	right

Table 30.33: 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 30.34: Axis Options

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=n	specifies line thickness for axes and frame

Table 30.35: Graphics Catalog Options

Option	Option Description
DESCRIPTION=`string'	description for graphics catalog member
NAME=`string'	name for plot in graphics catalog

Table 30.36: 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 for fit line and confidence curves
CFRAME=color	color for frame
CGRID=color	color for grid lines
CHREF=color	color for HREF=lines
CPLOTFIT=color	color for percentile lines
CSREF=color	color for SREF= lines
CTEXT=color	color for text
CVREF=color	color for VREF= lines

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