TOTAL TIME ON TEST
Name:
TOTAL TIME ON TEST (LET)
SCALED TOTAL TIME ON TEST (LET)
Type:
Purpose:
Compute the total time on test for a set of failure times.
Description:
For uncensored data, the total time on test statistic for uncensored
data is (where X is ascending sorted order):
\( TTT_i = \sum_{j=1}^{i}{(N-j+1) (X_{j} - X_{j-1})} \)
where \( X_0 \) is defined to be zero.
The scaled total time to test is then defined as
\( TTT^{*}_{i} = \frac{TTT_{i}} {TTT_{n}} \)
The scaled total time on test lies between 0 and 1.
For type I and type II censored data, the scaled total time on
test is defined as
\( TTT^{*}_{i} = \frac{TTT_{i}} {TTT_{r}} \)
where r is the index of the maximum uncensored failure time.
Progressive censoring is not currently supported.
Syntax 1:
Syntax 2:
LET <y> = SCALED TOTAL TIME ON TEST <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 where the total time on test values are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax returns the scaled values.
Examples:
LET Y = TOTAL TIME ON TEST X CENSOR
Note:
If any of the response values are negative, an error is returned.
Note:
For the censoring variable, a value of 0 indicates a censored value
and a value of 1 indicates an uncensored value.
Dataplot will check the number of distinct values in the censoring
variable. If there is only one distinct value, then all observations
are treated as uncensored. If there are two distinct values, then
the smaller value indicates censored data and the larger value
indicates uncensored data. If there are more than two distinct
values, an error is returned.
For uncensored data, you can do something like the following
LET N = SIZE X
LET CENSOR = 1 FOR I = 1 1 N
LET TTT = SCALED TOTAL TIME ON TEST X CENSOR
Default:
Synonyms:
Related Commands:
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HAZARD HAZARD = Compute the hazard for a variable.
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CUMULATIVE CUMULATIVE HAZARD = Compute the cumulative hazard for a variable.
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INTERARRIVAL INTERARRIVAL TIME = Compute the interarrival times of a variable.
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TOTAL TOTAL TIME ON TEST PLOT = Generate a total time on test plot.
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HAZARD HAZARD PLOT = Generate a hazard plot.
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PROBABILITY PROBABILITY PLOT = Generate a probability plot.
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WEIBULL WEIBULL PLOT = Generate a Weibull plot.
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Applications:
Implementation Date:
Program 1:
SKIP 25
READ HAHN.DAT Y TAG
LET TAG = 0 SUBSET TAG = 2
LET Z = SCALED TOTAL TIME ON TEST Y TAG
Program 2:
. Step 1: Define some data
.
let n = 100
let gamma = 0.5
let y1 = weibull rand numb for i = 1 1 n
let gamma = 1.0
let y2 = weibull rand numb for i = 1 1 n
let gamma = 2.0
let y3 = weibull rand numb for i = 1 1 n
let tag = 1 for i = 1 1 n
.
. Step 2: Compute the total time to failure values
.
let z1 = scaled total time on test y1 tag
let z2 = scaled total time on test y2 tag
let z3 = scaled total time on test y3 tag
.
set write decimals 3
print y1 y2 y3 z1 z2 z3
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Date created: 07/02/2020
Last updated: 07/02/2020
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