Burn-in testing is used to screen out units or systems with short lifetimes. Units or systems that survived a burn-in test may give rise to left truncated data that is either right or interval censored.
Left truncated and right censored data
Tobias and Trindade reported in their 2012 book Applied Reliability on field failure times of units that survived a burn-in test of 5000 hours (Example 4.6, p. 109). These field failure times represent an example of left truncation in combination with right censoring.
Left truncated and interval censored data
Meeker and Escobar described in their 1998 book Statistical Methods for Reliability Data a field-tracking study of units that survived a 1000 hours burn-in test (Example 11.11, pp. 269-270). The data in Meeker and Escobar’s study is an example of left truncation in combination with interval censoring.
Model fitting using maximum likelihood optimization
The R code fits a Weibull (or lognormal) model to left truncated data that is either right or interval censored. The fitting of these models is done by log-likelihood optimization (using the optim function in R).