
TOTAL TIME ON TEST PLOTName:
where \( X_0 \) is defined to be zero. The scaled total time to test is then defined as
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
where r is the index of the maximum uncensored failure time. Progressive censoring is not currently supported. The TOTAL TIME ON TEST PLOT is then a plot of \( TTT^{*}_{i} \) against \( i/n \) (or \( i/r \) for censored data). In addition, a reference line is plotted from (0,0) to (1,1). The primary purpose of this plot is to distinguish between a constant hazard function, an increasing hazard function or a decreasing hazard function. If the plot shows the data being nearly concave and mostly above the 45 degree line, this indicates the data is from a distribution with an increasing hazard function. If the plot shows the data being nearly convex and mostly below the 45 degree line, this indicates the data is from a distribution with a decreasing hazard function. If the plot shows the data randomly around the 45 degree line, this indicates the data is from a distribution with a constant hazard function (i.e., an exponential distribution).
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable containing failure times; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for uncensored data.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable containing failure times; <tag> is a tag variable indicating whether the times in <y> are failure times or censoring times; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for censored data.
TOTAL TIME ON TEST PLOT Y CENSOR
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.
Epstein and Sobel (1953), "Life Testing," Journal of the American Statistical Association, 48, 486–502. Barlow and Campo (1975), "Time on Test Processes and Applications to Failure data analysis," in Barlow, Fusssell and Singpurwalla (eds.) "Reliability and Fault Tree Analysis," SIAM, Philadelphia, 451–481.
SKIP 25 READ HAHN.DAT MILES TAG LET CENSOR = TAG LET CENSOR = 0 SUBSET TAG = 2 . TITLE CASE ASIS TITLE Total Time on Test Plot for HAHN.DAT LABEL CASE ASIS Y1LABEL TTT*(i) X1LABEL i/n . TOTAL TIME ON TEST PLOT MILES CENSORProgram 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 . . Step 2: Plot the data . case asis title case asis label case asis title offset 2 tic offset units screen tic mark offset 3 3 . ylimits 0 1 major y1tic mark number 6 minor y1tic mark number 3 y1label TTT(i) . xlimits 0 1 major x1tic mark number 6 minor x1tic mark number 3 x1label i/n x2label Circle: Gamma = 0.5, Square: Gamma = 1.0, Triangle: Gamma = 2.0 . title Scaled Total Time On Test Plot . character circle blank character fill on character hw 1.0 0.75 line solid dotted . title Total Time on Test Plot for Weibull Distributions total time on test plot y1 . preerase off frame off tic mark off tic mark labels off title label . character square total time on test plot y2 . character triangle total time on test plot y3  
Date created: 07/02/2020 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 