The RELIABILITY Procedure

PROBPLOT Statement

Subsections:

Summary of Options

<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 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-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 16.35 lists analysis options that are available when you use either traditional graphics or ODS Graphics.

Table 16.35: 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.
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.

INEST | IN=SAS-data-set

Specifies a SAS data set that can contain initial values, equality constraints, upper bounds, or lower bounds for the scale, shape, and threshold parameters in a three-parameter Weibull model for lifetime data, and applies only to three-parameter Weibull models. See the section INEST Data Set for the Three-Parameter Weibull for details.

ITPRINT

Requests the iteration history for maximum likelihood fit.

ITPRINTEM

Requests the iteration history for the Turnbull algorithm.

LRCL

Requests likelihood ratio confidence intervals for distribution parameters.

LRCLPER

Requests likelihood ratio confidence intervals for distribution percentiles.

LRCLSURV

Requests likelihood ratio confidence intervals for survival and cumulative distribution functions at times specified with the SURVTIME=number-list option.

LOCATION=number <LINIT>

Specifies a fixed or initial value of location parameter.

MAKEHAM=number <MKINIT>

Specifies the fixed or initial value of the Makeham parameter for the three-parameter Gompertz distribution.

MAXIT=number

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

MAXITEM=number1 <,number2>

number1 Specifies the maximum number of iterations allowed for the Turnbull algorithm. Iteration history will be printed in increments of number2 if an iteration history is requested with ITPRINTEM. See the section Interval-Censored Data for details.

NOPCTILES

Suppresses computation of percentiles for standard list of percentage points.

NOPOLISH

Suppresses the setting of small interval probabilities to 0 in the Turnbull algorithm. See the section Interval-Censored Data for details.

NPINTERVALS=interval-type

Specifies the type of nonparametric confidence interval displayed in a probability plot. The available types of intervals are listed in the following table.

Interval Type	Definition
POINTWISE \| POINT	Pointwise confidence intervals for the CDF. See the section Pointwise Confidence Intervals for details.
SIMULTANEOUS \|
SIMUL<number1, number2>	Simultaneous confidence intervals for the CDF. number1 and number2 are constants that control the time interval for which simultaneous intervals are computed. The default time intervals are the lowest and highest times corresponding to failures in the case of right-censored data, or to the lowest and highest intervals for which probabilities are computed for interval-censored data. See the section Simultaneous Confidence Intervals for details.

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.

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.

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.

PRINTPROBS

Specifies that intervals and associated probabilities for the Turnbull algorithm be printed.

PROBLIST=number-list

Specifies a list of initial values for Turnbull algorithm. See the section Interval-Censored Data for details.

PSTABLE=number

Specifies a stable parameterization. The number must be between 0 and 1. See the section Stable Parameters for further information.

READOUT

Specifies the data have the readout structure.

SCALE=number <SCINIT>

Specifies a fixed or initial value of the scale parameter.

SHAPE=number <SHINIT>

Specifies a fixed or initial value of the shape parameter.

SINGULAR=number

Specifies the 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 16.57 for the distributions with a threshold parameter.

TOLLIKE=number

Specifies the criterion for convergence in the Turnbull algorithm. The default is $10^{-8}$ . See the section Interval-Censored Data for details.

TOLPROB=number

Specifies the criterion for setting interval probabilities to 0 in the Turnbull algorithm. The default is $10^{-6}$ . See the section Interval-Censored Data for details.

Table 16.36 lists analysis options that are available when ODS Graphics is enabled.

Table 16.36: Analysis Options for ODS Graphics

Option

Option Description

PROFILE<(options)>

Requests a profile log-likelihood plot of the threshold parameter for a three-parameter Weibull distribution. The options listed in the following table are available; they are specified by enclosing them in parentheses after the PROFILE option.

Profile Option	Option Description
NOCONF	Specifies that a reference line on the vertical, log-likelihood axis not be drawn. If this option is not specified, a reference line is drawn at a log-likelihood value that corresponds to the profile likelihood confidence limits on the horizontal axis.
NPROFILE=n	Specifies that the profile log likelihood be computed and plotted at n threshold points. If this option is not specified, the profile log likelihood is computed and plotted at 100 points.
RANGE=(value1, value2)	Specifies the range of threshold values for which the profile log likelihood is computed and plotted as (value1, value2). If this option is not specified, the range of threshold values for which the profile log likelihood is computed is from 0 to the minimum failure time.

Table 16.37 lists plot layout options that are available when you use traditional graphics.

Table 16.37: Probability Plot Layout Options for Traditional Graphics

Option	Option Description
CENBIN	Specifies that censored data be plotted 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 the symbol used for failures.
HOFFSET=value	Specifies the offset for the horizontal axis.
INBORDER	Requests a border around probability plots.
INTERTILE=value	Specifies the distance between tiles.
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; they can be separated by blanks or commas or can be a list in the form $n_1$ to $n_2$ <by $n_3$ >.
MISSING1	Requests that missing values of the first GROUP= variable be treated as a level of the variable.
MISSING2	Requests that missing values of the second GROUP= variable be treated as a level of the variable.
NCOLS=n	Specifies that n columns be plotted on a page.
NOCENPLOT	Suppresses the plotting of censored data points.
NOCONF	Suppresses the plotting of percentile confidence curves.
NOFIT	Suppresses the plotting of fit line and percentile confidence curves.
NOFRAME	Suppresses the frame around the plotting area.
NOINSET	Suppresses the inset.
NOPPLEGEND	Suppresses the legend for overlaid probability plots
NOPPOS	Suppresses plotting of symbols for failures in a probability plot.
NROWS=n	Specifies that n rows be 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 the 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 a legend for overlaid probability plots.
PPOSSYMBOL=symbol \| (symbol-list)	Specifies symbols to represent failures on a probability plot.
ROTATE	Requests probability plots with the probability scale on the horizontal axis.
SHOWMULTIPLES	Requests that the count be displayed for multiple overlaying symbols.
TURNVLABELS	Vertically strings out characters in labels for the vertical axis.
VOFFSET=value	Specifies value as the length of the offset at the upper end of the vertical axis.
WFIT=n	Specifies the line width for the fit line and confidence curves.

Table 16.38 lists plot layout options that are available when you use ODS graphics.

Table 16.38: 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=n	Specifies that n columns be plotted on a page.
NOCENPLOT	Suppresses plotting of censored data points.
NOCONF	Suppresses plotting of percentile confidence curves.
NOFIT	Suppresses plotting of the fit line and percentile confidence curves.
NOINSET	Suppresses the inset.
NOPPLEGEND	Suppresses the legend for overlaid probability plots.
NOPPOS	Suppresses plotting of symbols for failures in a probability plot.
NROWS=n	Specifies that n rows be plotted on a page.
ORDER1=DATA \| FORMATTED \|
FREQ \| INTERNAL	Specifies the display order for values of the first GROUP= variable.
ORDER2=DATA \| FORMATTED \|
FREQ \| INTERNAL	Specifies the 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 the probability scale on the horizontal axis.

Table 16.39 lists reference line options that are available when you use traditional graphics.

Table 16.39: 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 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 the line style for HREF= lines.

LVREF=linetype

Specifies the 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=n

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

Table 16.40: Reference Line Options for ODS Graphics

Option	Option Description
LREF <(INTERSECT)>=value-list	Requests reference lines perpendicular to the lifetime axis. If (INTERSECT) is specified, a second reference line is drawn perpendicular to the probability axis and 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 probability axis reference line is labeled with the probability axis value.
LREFLABELS =(’label1’ …’labeln’)	Specifies labels for LREF= lines.
PREF <(INTERSECT)>=value-list	Specifies reference lines perpendicular to the probability 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 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.

Table 16.41 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 16.41: 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 16.42 lists options that control the appearance of the axes when you use traditional graphics.

Table 16.42: 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=n	Specifies the line thickness for axes and frame.

Table 16.43 lists options that control the appearance of the axes when you use ODS Graphics.

Table 16.43: Axis Options for ODS 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
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.

Table 16.44 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 16.44: 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 that represent failures on a probability plot

Table 16.45 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 16.45: Graphics Catalog Options

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