The RELIABILITY Procedure

MCFPLOT Statement

Subsections:

Summary of Options

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

<label:>MCFPLOT (<INTERVAL=>variable1 variable2 <RECURRENCES=> variable3 <CENSOR=> variable4 ) <=group-variables> </ options> ;

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

You can specify any number of MCFPLOT statements after a PROC RELIABILITY statement. Each MCFPLOT statement creates a separate MCF plot and associated analysis. See the section Analysis of Recurrence Data on Repairs, the section Comparison of Two Samples of Repair Data, and the section Analysis of Interval Age Recurrence Data for examples that use the MCFPLOT statement. You can specify an optional label to distinguish between multiple MCFPLOT statements in the output.

To create a plot of the mean cumulative function for cost or number of repairs with exact age data, you specify a variable that represents the times of repairs. You must also specify a cost/censor-variable and the values, in parentheses, of the cost/censor-variable that correspond to end-of-history data values (also referred to as censored data values).

To create a plot of the mean cumulative function for cost or number of repairs with interval age data, you specify variable1 variable2 that represents the age intervals. You must also specify either variable3 that represents the number of recurrences in the intervals and variable4 that represents the number censored in the intervals, or a FREQ statement that represents the number of recurrent events in the intervals and a NENTER statement that represents the number of units observed in the intervals.

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

For exact data, you must also specify a unit-identification variable in conjunction with the MCFPLOT statement to identify the individual unit name for each instance of repair or end of history on the unit. Specify the unit-identification variable in the UNITID statement.

Add the EVENTPLOT option to any MCFPLOT statement to obtain a horizontal plot of failure and censoring times for each system.

The elements of the MCFPLOT statement are described as follows.

variable

represents the time of repair. A variable must be a numeric variable in the input data set.

variable1 variable2

represents time intervals for grouped data. variable1 and variable2 must be numeric variables in the input data set.

variable3

represents the number of recurrences in an interval. A variable3 must be a numeric variable in the input data set.

variable4

represents the number censored in an interval. A variable4 must be a numeric variable in the input data set.

cost/censor-variable(values)

indicates the cost of each repair or the number of repairs. This variable also indicates which observations in the input data set are end-of-history (censored) data points. You specify the values of cost/censor-variable that represent censored observations by placing those values in parentheses after the variable name. A cost/censor-variable must be a numeric variable in the input data set.

group-variables

are one or two group variables. If no group variables are specified, a single plot is produced. The group-variables can be any numeric or character variables in the input data set. For exact data, if a single group variable is specified, and the group variable has two levels, then a statistical test for equality of the groups represented by the two levels is computed and displayed in the “Tests for Equality of Mean Functions” table. Refer to Comparison of Two Groups of Recurrent Events Data for more details.

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

options

control the features of the mean cumulative function plot. All options are specified after a slash (/) in the MCFPLOT statement. The “Summary of Options” section, which follows, lists all options by function.

Summary of Options

Table 16.21 lists available analysis options.

Table 16.21: Analysis Options

Option

Option Description

CONFIDENCE=number

Specifies the confidence coefficient for all confidence intervals. Specify a number between 0 and 1. The default value is 0.95.

EVENTPLOT <(SORT=sort-order)>

Specifies a separate horizontal plot of failure and censoring times for each systerm. The following sort orders are available:

Sort Order	Definition
ASCENDINGTIME	sorts by increasing censoring times (default)
DESCENDINGTIME	sorts by decreasing censoring times
ASCENDINGFORMATTED	sorts alphabetically by system name or label
DESCENDINGFORMATTED	sorts alphabetically in reverse by system name or label

INDINC

Requests variance estimates of the MCF using the Nelson (2002) estimator under the independent increments assumption.

LOGINTERVALS

Requests that confidence intervals be computed based on the asymptotic normality of $\log$ (MCF). This is appropriate only when the MCF estimate is positive, so does not apply to MCF differences or when negative costs are specified.

MCFDIFF

Requests a plot of differences of MCFS of two groups specified by a single group variable.

NOVARIANCE

Suppresses MCF variance computation.

VARIANCE=variance-specification

Specifies the method of variance calculation. The following methods are available.

Method	Definition
INDINC	The method of Nelson (2002) assuming independent increments
LAWLESS \| VARMETHOD2	The method of Lawless and Nadeau (1995) (the default method)
NELSON	The method of Nelson (2002)
POISSON	Poisson process method

Table 16.22 lists plot layout options that are available when you use traditional graphics.

Table 16.22: 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. 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 repairs.
HOFFSET=value	Specifies offset for horizontal axis.
INBORDER	Requests a border around MCF plots.
INTERPOLATE=JOIN \| STEP \| NONE	Requests that symbols in an MCF plot be connected with a straight line, step function, or not connected.
INTERTILE=value	Specifies the distance between tiles.
MCFLEGEND=legend-statement-name \| NONE	Identifies a legend statement to specify legend for overlaid MCF plots.
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 the number of columns plotted on a page.
NOCENPLOT	Suppresses plotting of censored data points.
NOCONF	Suppresses plotting of confidence intervals.
NOFRAME	Suppresses the frame around the plotting area.
NOINSET	Suppresses the inset.
NOLEGEND	Suppresses the legend for overlaid MCF plots.
NROWS=n	Specifies the 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 that plots with group variables be overlaid on a single page.
PLOTSYMBOL=symbol \| (symbol-list)	Specifies symbols that represent events in an MCF plot.
PLOTCOLOR=color \| (color-list)	Specifies colors of symbols that represent events in an MCF plot.
TURNVLABELS	Vertically strings out characters in labels for vertical axis.
VOFFSET=value	Specifies length of offset at upper end of vertical axis.

Table 16.23 lists plot layout options available when you use ODS Graphics.

Table 16.23: Plot Layout Options for ODS Graphics

Option	Option Description
DUANE	Requests that a Duane plot be created in addition to an MCF plot. If you specify the FIT=MODEL option, the fitted parametric model is included in the Duane plot. See the section Duane Plots for a description of Duane plots.
FIT=MODEL	Requests that a parametric cumulative mean function fit with a MODEL statement be plotted on the same plot with nonparametric estimates of the MCF. This option is valid only if the response specification in the MCFPLOT statement matches the response specification in the MODEL statement. If this option is specified, the fit parametric intensity function is plotted on a separate graph.
INTERPOLATE=JOIN \| STEP \| NONE	Requests that symbols in an MCF plot be connected with a straight line, step function, or not connected.
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 the number of columns plotted on a page.
NOCENPLOT	Suppresses plotting of censored data points.
NOCONF	Suppresses plotting of confidence intervals.
NOINSET	Suppresses the inset.
NROWS=n	Specifies the number of rows 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 that plots with group variables be overlaid on a single page.

Table 16.24 lists reference line options that are available when you use traditional graphics.

Table 16.24: Reference Line Options for Traditional Graphics

Option

Option Description

HREF=value-list

Specifies reference lines perpendicular to horizontal axis.

HREFLABELS=(’label1’ …’labeln’)

Specifies labels for HREF= lines.

HREFLABPOS=n

Specifies the 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=value-list

Specifies reference lines perpendicular to vertical axis.

VREFLABELS=(’label1’ …’labeln’)

Specifies labels for VREF= lines.

VREFLABPOS=n

Specifies the 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 16.25 lists reference line options that are available when you use ODS Graphics.

Table 16.25: Reference Line Options for ODS Graphics

Option	Option Description
LREF<(INTERSECT)>=value-list	Specifies reference lines perpendicular to the lifetime axis. If (INTERSECT) is specified, a second reference line is drawn perpendicular to the MCF 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 MCF axis reference line is labeled with the MCF axis value.
LREFLABELS=(’label1’ …’labeln’)	Specifies labels for LREF= lines.
MREF<(INTERSECT)>=value-list	Specifies reference lines perpendicular to the MCF 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 MCF axis reference line. If an MCF axis reference line label is specified, the intersecting lifetime axis reference line is labeled with the lifetime axis value.
MREFLABELS=(’label1’ …’labeln’)	Specifies labels for MREF= lines.

Table 16.26 lists the options that control the appearance of the text when you use traditional graphics. These options are not available if ODS Graphics is enabled.

Table 16.26: Text Enhancement Options

Option	Option Description
FONT=font	Software font for text.
HEIGHT=value	Height of text used outside framed areas.
INFONT=font	Software font for text inside framed areas.
INHEIGHT=value	Height of text inside framed areas.

Table 16.27 lists options to control the appearance of the axes when you use traditional graphics.

Table 16.27: Axis Options for Traditional Graphics

Option	Option Description
HAXIS=value1 TO value2<BY value3>	Specifies tick mark values for the horizontal 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 HAXIS= lists follow: haxis = 0 to 10 haxis = 2 to 10 by 2 haxis = 0 to 200 by 10
HLOWER=number	Specifies the lower limit on the horizontal axis scale. The HLOWER= option specifies number as the lower horizontal axis tick mark. The tick mark interval and the upper axis limit are determined automatically. This option has no effect if the HAXIS option is used.
HUPPER=number	Specifies the upper limit on the horizontal axis scale. The HUPPER= option specifies number as the upper horizontal axis tick mark. The tick mark interval and the lower axis limit are determined automatically. This option has no effect if the HAXIS= option is used.
LGRID=number	Specifies a line style for all grid lines. number is between 1 and 46 and specifies a linestyle for grids.
LOGLOG	Requests log scales on both axes.
MINORLOGGRID	Adds a minor grid for log axes.
NOGRID	Suppresses grid lines.
NOHLABEL	Suppresses label for horizontal axis.
NOVLABEL	Suppresses label for vertical axis.
NOVTICK	Suppresses tick marks and tick mark labels for vertical axis.
NOHTICK	Suppresses tick marks and tick mark labels for horizontal axis.
NHTICK=number	Specifies the number of tick intervals for the horizontal axis. This option has no effect if the HAXIS= option is used.
NVTICK=number	Specifies the number of tick intervals for the vertical axis. This option has no effect if the VAXIS= option is used.
VAXIS=value1 TO value2<BY value3>	Specifies tick mark values for the vertical 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. This method of specification of tick marks is not valid for logarithmic axes. If value3 is omitted, a value of 1 is used. vaxis = 0 to 10 vaxis = 0 to 2 by .1
VAXISLABEL=’string’	Specifies a label for the vertical axis
VLOWER=number	Specifies the lower limit on the vertical axis scale. The VLOWER= option specifies number as the lower vertical axis tick mark. The tick mark interval and the upper axis limit are determined automatically. This option has no effect if the VAXIS= option is used.
VUPPER=number	Specifies the upper limit on the vertical axis scale. The VUPPER= option specifies number as the upper vertical axis tick mark. The tick mark interval and the lower axis limit are determined automatically. This option has no effect if the VAXIS= option is used.
WAXIS=n	Specifies the line thickness for axes and frame.

Table 16.28 lists options that control the appearance of the axes when you use ODS Graphics.

Table 16.28: Axis Options for ODS Graphics

Option	Option Description
HLOWER=number	Specifies the lower limit on the horizontal axis scale. The HLOWER= option specifies number as the lower horizontal axis tick mark. The tick mark interval and the upper axis limit are determined automatically. This option has no effect if the HAXIS option is used.
HUPPER=number	Specifies the upper limit on the horizontal axis scale. The HUPPER= option specifies number as the upper horizontal axis tick mark. The tick mark interval and the lower axis limit are determined automatically. This option has no effect if the HAXIS= option is used.
LOGLOG	Requests log scales on both axes.
MINORLOGGRID	Adds a minor grid for log axes.
NOGRID	Suppresses grid lines.
VLOWER=number	Specifies the lower limit on the vertical axis scale. The VLOWER= option specifies number as the lower vertical axis tick mark. The tick mark interval and the upper axis limit are determined automatically. This option has no effect if the VAXIS= option is used.
VUPPER=number	Specifies the upper limit on the vertical axis scale. The VUPPER= option specifies number as the upper vertical axis tick mark. The tick mark interval and the lower axis limit are determined automatically. This option has no effect if the VAXIS= option is used.

Table 16.29 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 16.29: 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.
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 16.30 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 16.30: Graphics Catalog Options

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