PROC RELIABILITY: PROBPLOT Statement

The RELIABILITY Procedure

PROBPLOT Statement

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

<label:>PROBPLOT (variable1 variable2) <=group-variables> </options> ;

You use the PROBPLOT statement to create a probability plot from complete, left-censored, right-censored, or interval-censored data.

You can specify the keyword PPLOT as an alias for PROBPLOT. You can specify any number of PROBPLOT statements after a PROC RELIABILITY statement. Each PROBPLOT statement creates a probability plot and an associated analysis. The probability distribution used in creating the probability plot and performing the analysis is determined by the DISTRIBUTION statement. You can specify an optional label to distinguish between multiple PROBPLOT statements in the output.

See the section Analysis of Right-Censored Data from a Single Population and the section Weibull Analysis Comparing Groups of Data for examples that create probability plots with the PROBPLOT statement.

To create a probability 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 can optionally specify one or two group-variables (also referred to as classification variables). The PROBPLOT statement displays a probability plot for each level of the group-variables. The observations in a given level are called a cell.

The elements of the PROBPLOT statement are described as follows.

variable

represents the data for which a probability 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 can 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 probability 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-variables

are one or two group variables. If no group variables are specified, a single probability plot is produced. The group-variables can be numeric or character variables in the input data set.

Note that the parentheses surrounding the group-variables are needed only if two group variables are specified.

options

control the features of the probability plot. All options are specified after the slash (/) in the PROBPLOT statement. See the section Summary of Options, which follows, for a list of all options by function.

Summary of Options

Table 12.29 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 (default)
\| MODEL	-use the fit from the preceding MODEL statement
\| NONE	-no fit is computed
\| WEIBAYES	-Weibayes method
<(CONFIDENCE\|CONF=number)>	number is the confidence coefficient for the Weibayes fit and is between 0 and 1. The default value is 0.95.
ITPRINT	requests iteration history for maximum likelihood fit
ITPRINTEM	requests iteration history for the Turnbull algorithm
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
MAXITEM=number1 <,number2>	number1 specifies maximum number of iterations allowed for Turnbull algorithm. Iteration history will be printed in increments of number2 if requested with ITPRINTEM. See the section Interval-Censored Data for details.
NOPCTILES	suppresses computation of percentiles for standard list of percentage points
NOPOLISH	suppress setting small interval probabilities to zero in the Turnbull algorithm. See the section Interval-Censored Data for details.
NPINTERVALS=	specifies type of nonparametric confidence interval displayed in a probability plot
POINTWISE \| POINT	-pointwise confidence intervals for the CDF
\| SIMULTANEOUS
\| SIMUL<number1, number2>	-simultaneous confidence intervals for the CDF. See the section Simultaneous Confidence Intervals for details.
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.
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. See the section Reliability Function for details.
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
PRINTPROBS	print intervals and associated probabilities for the Turnbull algorithm
PROBLIST=number-list	specifies list of initial values for Turnbull algorithm. See the section Interval-Censored Data for details.
PSTABLE=number	specifies stable parameterization. The number must be between zero and one. See the section Stable Parameters for further information.
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 the survival function, cumulative distribution function, and confidence limits 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.
TOLLIKE=number	specifies criterion for convergence in the Turnbull algorithm. Default is $\text{[math]}$ . See the section Interval-Censored Data for details.
TOLPROB=number	specifies criterion for setting interval probability to zero in the Turnbull algorithm. Default is $\text{[math]}$ . See the section Interval-Censored Data for details.

Table 12.30 lists plot layout options available when you use traditional graphics.

Table 12.30 Probability Plot Layout Options for Traditional Graphics
Option	Option Description
CENBIN	plots censored data as frequency counts rather than as individual points
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). For 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 offset for horizontal axis
INBORDER	requests a border around probability plots
INTERTILE=value	specifies distance between tiles
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 $\text{[math]}$ >.
MISSING1	requests that missing values of first GROUP= variable be treated as a level of the variable
MISSING2	requests that missing values of second GROUP= variable be treated as a level of the variable
NCOLS= $\text{[math]}$	specifies number of columns plotted on a page
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
NOINSET	suppresses inset
NOPPLEGEND	suppresses legend for overlaid probability plots
NOPPOS	suppresses plotting of symbols for failures in a probability plot
NROWS= $\text{[math]}$	specifies number of rows plotted on a page
ORDER1=DATA \| FORMATTED \| FREQ \| INTERNAL	specifies display order for values of the first GROUP= variable
ORDER2=DATA \| FORMATTED \| FREQ \| INTERNAL	specifies display order for values of the second GROUP= variable
OVERLAY	requests overlaid plots for group variables
PCONFPLT	plots confidence intervals on probabilities for readout data
PPLEGEND = legend-statement-name \| NONE	identifies LEGENDn statement to specify legend for overlaid probability plots
PPOSSYMBOL=symbol \| (symbol list)	symbols representing failures on a probability plot
ROTATE	requests probability plots with probability scale on horizontal axis
SHOWMULTIPLES	display the count for multiple overlaying symbols
TURNVLABELS	vertically strings out characters in labels for vertical axis
VOFFSET=value	length of offset at upper end of vertical axis
WFIT=linetype	line width for fit line and confidence curves

Table 12.31 lists plot layout options available when you use ODS graphics.

Table 12.31 Probability Plot Layout Options for ODS Graphics
Option	Option Description
MISSING1	requests that missing values of first GROUP= variable be treated as a level of the variable
MISSING2	requests that missing values of second GROUP= variable be treated as a level of the variable
NCOLS= $\text{[math]}$	specifies number of columns plotted on a page
NOCENPLOT	suppresses plotting of censored data points
NOCONF	suppresses plotting of percentile confidence curves
NOFIT	suppresses plotting of fit line and percentile confidence curves
NOINSET	suppresses inset
NOPPLEGEND	suppresses legend for overlaid probability plots
NOPPOS	suppresses plotting of symbols for failures in a probability plot
NROWS= $\text{[math]}$	specifies number of rows plotted on a page
ORDER1=DATA \| FORMATTED \| FREQ \| INTERNAL	specifies display order for values of the first GROUP= variable
ORDER2=DATA \| FORMATTED \| FREQ \| INTERNAL	specifies display order for values of the second GROUP= variable
OVERLAY	requests overlaid plots for group variables
PCONFPLT	plots confidence intervals on probabilities for readout data
ROTATE	requests probability plots with probability scale on horizontal axis

Table 12.32 lists reference line options available when you use traditional graphics.

Table 12.32 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 line style for HREF= lines

LVREF=linetype

specifies line style for VREF= lines

VREF <(INTERSECT)>=value-list

specifies 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 12.33 lists reference line options available when you use ODS graphics.

Table 12.33 Reference Line Options for ODS Graphics
Option	Option Description
HREF \|
LREF <(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 \|
LREFLABELS =(’label1’ ...’labeln’)	specifies labels for HREF= lines
VREF \|
PREF <(INTERSECT)>=value-list	specifies 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 \|
PREFLABELS=(’label1’ ...’labeln’)	specifies labels for VREF= 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 12.34 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 12.35 lists options to control the appearance of the axes when you use traditional graphics.

Table 12.35 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 the probability axis
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 probability axis scale
PCTUPPER \| PUPPER=number	specifies the upper limit on probability axis scale
PAXISLABEL=‘string’	specifies a label for the probability axis
WAXIS= $\text{[math]}$	specifies the line thickness for axes and frame

Table 12.36 lists options to control the appearance of the axes when you use ODS graphics.

Table 12.36 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.
MINORLOGGRID	adds a minor grid for log axes
NOGRID	suppresses grid lines
PCTLOWER \| PLOWER=number	specifies the lower limit on probability axis scale
PCTUPPER \| PUPPER=number	specifies the upper limit on probability axis scale
PAXISLABEL=‘string’	specifies a label for the probability axis

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 12.37 Color and Pattern Options
Option	Option Description
CAXIS=color	color for axis
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
CFRAMESIDE=color	color for filling frame for row labels
CFRAMETOP=color	color for filling frame for column labels
CGRID=color	color for grid lines
CHREF=color	color for HREF= lines
CTEXT=color	color for text
CVREF=color	color for VREF= lines
PPOSCOLOR=color \| (color list)	colors of symbols representing failures on a probability plot

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 12.38 Graphics Catalog Options
Option	Option Description
DESCRIPTION=‘string’	description for graphics catalog member
NAME=‘string’	name for plot in graphics catalog

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