= 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 $\delta_i=\mathbf 1_{\{T_i\leq C_i\}}$, 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> $R$ is
$$
L\ \propto\ \prod_i f(Y_i)^{\delta_i}R(Y_i)^{1-\delta_i}.
$$
A 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.<NIST and SEMATECH e-Handbook of Statistical Methods>[Sections 8.1.3.1 and 8.4.1.2, censoring and likelihoods for reliability data]{ref}
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