Life testing

Life testing observes failure times under a specified test protocol to estimate a lifetime probability distribution or check a reliability theory model. A test can end before every unit fails. Under right censoring, one records $Y_i=\min (T_i,C_i)$ and ${\delta }_i=1_{\{T_i\le C_i\}}$, where $T_i$ is the failure time and $C_i$ is the observation limit.

For independent censoring, the part of the likelihood function involving a continuous lifetime model with probability density function $f$ and survival function $R$ isA unit that fails at 45 hours contributes $f(45)$; one still working when observation ends at 60 hours contributes $R(60)$. Treating the latter as a failure at 60 hours invents an event that was not observed. The test protocol and any dependence between failure and observation limits therefore affect what can be inferred.^[ref]