CUMULATIVE HAZARD

CUMULATIVE HAZARD (LET)

Let Subcommand

Compute the cumulative hazard for a set of failure times.

The hazard is constructed as follows:
1. Sort and rank the N failure times from shortest to longest failure time. Note that the hazard can accomodate data where the time may be a censoring time rather than a failure time (i.e., the unit was taken out of service before it failed).

2. Calculate a hazard value at each of the failure times. Note that the hazard is only caclulated at failure times, not censoring times. The hazard is:
   100.0*(1/(N-K+1)

   where K is the rank of the failure time. This expresses the hazard as a percentage. You can express the hazard as a proportion by omitting the multiplication by 100.

3. The cumulative hazard is the cumulative sum of the hazard. That is, the cumulative hazard at the failure time with rank K is the sum of the hazards of all failure times with ranks less than or equal to K.

LET <y> = CUMULATIVE HAZARD <x> <tag>             <SUBSET/EXCEPT/FOR qualification>
where <x> is the variable containing the failure times;
            <tag> is a variable that indicates whether the corresponding element of <x> is a failure time or a censoring time;
            <y> is a variable (of length 1 less than <x1>) where the cumulative hazards are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

A value of 0 for <tag> is used to signify a censoring time and a value of 1 for <tag> is used to signify a failure time. Dataplot uses 0.5 as the cutoff. That is, any value greater than or equal to 0.5 is interpreted as a failure time.

LET Y = CUMULATIVE HAZARD X CENSOR
LET Y = CUMULATIVE HAZARD X CENSOR SUBSET CENSOR = 1

Hazards are only computed for failure times (i.e., where = 1), not censoring times. The saved cumulative hazards () are set to 0 for censoring times. If you just want to keep the cumulative hazards at failure times, do something like:
LET Y = CUMULATIVE HAZARD X CENSOR
RETAIN Y SUBSET CENSOR = 1


The censoring times do affect the value of the cumulative hazard since they are used in determining the rank. If you only want the failure times to be used in the calculation of the cumulative hazard, do something like the following:

LET Y = CUMULATIVE HAZARD X CENSOR SUBSET CENSOR = 1
RETAIN Y SUBSET CENSOR = 1

None

None

HAZARD	= Compute the hazard for a variable.
HAZARD PLOT	= Generate a hazard plot.
PROBABILITY PLOT	= Generate a probability plot.
WEIBULL PLOT	= Generate a Weibull plot.
INTERARRIVAL TIME	= Compute the interarrival times of a variable.

Reliability

1998/5

SKIP 25
READ HAHN.DAT Y TAG
LET TAG = 0 SUBSET TAG = 2
LET Z = CUMULATIVE HAZARD Y TAG