PROC RELIABILITY: MCFPLOT Statement

The RELIABILITY Procedure

MCFPLOT Statement

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

<label:>MCFPLOT ( <INTERVAL=>variable1 variable2 <RECURRENCES=> variable3 <CENSOR=> variable4 ) <=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, variable3 that represents the number of recurrences in the intervals, and variable4 that represents the number censored 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.

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 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.

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 12.16 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.
INDINC	requests variance estimates of the MCF using the Nelson estimator under an independent increments assumption
LOGINTERVALS	requests that confidence intervals be computed based on the asymptotic normality of $\text{[math]}$ (MCF). This is appropriate only when the MCF estimate is positive, so does not apply to MCF differences or costs if costs can be negative.
MCFDIFF	requests a plot of differences of MCFS of two groups specified by a single group variable
NOVARIANCE	suppresses MCF variance computation
VARIANCE=	alternate method of specifying variance calculation. Includes INDINC and VARMETHOD2 options.
INDINC	Nelson’s method assuming independent increments
\| LAWLESS	Lawless-Nadeau method
\| NELSON	Nelson’s method (the default method)
\| POISSON	Poisson process method
VARMETHOD2	requests that the method of Lawless and Nadeau (1995) be used to compute variance estimates of the MCF

Table 12.17 lists plot layout options available when you use traditional graphics.

Table 12.17 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 distance between tiles
MCFLEGEND=legend-statement-name \| NONE	identifies 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= $\text{[math]}$	specifies number of columns plotted on a page
NOCENPLOT	suppresses plotting of censored data points
NOCONF	suppresses plotting of confidence intervals
NOFRAME	suppresses frame around plotting area
NOINSET	suppresses inset
NOLEGEND	suppresses legend for overlaid MCF plots
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 that plots with group variables be overlaid on a single page
PLOTSYMBOL=symbol \| (symbol list)	symbols representing events in an MCF plot
PLOTCOLOR=color \| (color list)	colors of symbols representing 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 12.18 lists plot layout options available when you use ODS graphics.

Table 12.18 Plot Layout Options for ODS Graphics
Option	Option Description
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= $\text{[math]}$	specifies number of columns plotted on a page
NOCENPLOT	suppresses plotting of censored data points
NOCONF	suppresses plotting of confidence intervals
NOINSET	suppresses inset
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 that plots with group variables be overlaid on a single page

Table 12.19 lists reference line options available when you use traditional graphics.

Table 12.19 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= $\text{[math]}$

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=value-list

specifies reference lines perpendicular to vertical axis

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 12.20 lists reference line options available when you use ODS graphics.

Table 12.20 Reference Line Options for ODS Graphics
Option	Option Description
HREF=value-list	specifies reference lines perpendicular to horizontal axis
HREFLABELS=(’label1’ ...’labeln’)	specifies labels for HREF= lines
VREF=value-list	specifies reference lines perpendicular to vertical axis
VREFLABELS=(’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 12.21 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 12.22 lists options to control the appearance of the axes when you use traditional graphics.

Table 12.22 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 number of tick intervals for the horizontal axis. This option has no effect if the HAXIS= option is used.
NVTICK=number	specifies 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= $\text{[math]}$	specifies line thickness for axes and frame

Table 12.23 lists options to control the appearance of the axes when you use ODS graphics.

Table 12.23 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.

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 12.24 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

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 12.25 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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