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 The RELIABILITY Procedure

## PROBPLOT Statement

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

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.

See "Analysis of Right-Censored Data from a Single Population" and "Weibull Analysis Comparing Groups of Data" for examples creating probability plots using 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 component probability plot for each level of the group-variables using the values of the variable. The observations in a given level are referred to as 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 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-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. The "Summary of Options" section, which follows, lists all options by function.

### Summary of Options

Table 30.23: 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 | 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 <(CONFIDENCE| -Weibayes method 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 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 "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 Turnbull algorithm. See "Interval-Censored Data" 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. 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 PROBLIST=number-list specifies list of initial values for Turnbull algorithm. See "Interval-Censored Data" for details. PSTABLE=number specifies stable parameterization. The number must be between zero and one. See "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 survival function for values in number-list THRESHOLD=number specifies a fixed threshold parameter. See Table 30.37 for the distributions with a threshold parameter. TOLLIKE=number specifies criterion for convergence in the Turnbull algorithm. Default is 10-8. See "Interval-Censored Data" for details. TOLPROB=number specifies criterion for setting interval probability to zero in the Turnbull algorithm. Default is 10-6. See "Interval-Censored Data" for details.

Table 30.24: Probability Plot Layout Options
 Option Option Description CENBIN plots censored data as frequency counts rather than as individual points CENSYMBOL= specifies symbols for censored values. symbol | (symbol list) 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 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 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 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 NROWS=n 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 ROTATE requests probability plots with probability scale on horizontal axis 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 30.25: Reference Line Options
Option Option Description
HREF < (INTERSECT) >=value-listrequests 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=nspecifies 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=linetypespecifies line style for HREF=lines
LVREF=linetypespecifies line style for VREF= lines
VREF < (INTERSECT) >=value-listspecifies 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=nspecifies 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 30.26: 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 30.27: Axis Options
 Option Option Description LAXIS=value1 to value2 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 30.28: 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 for fit line and confidence curves 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

Table 30.29: 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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