 Unknown entry age in a Weibull survival segment

Conditional survival for a segment of length $u$ entered at age $\tau$ is $\exp \{-{\lambda }^p[(\tau +u{)}^p-{\tau }^p]\}$ under inverse-scale parameter $\lambda$. It depends on the entry age unless $p=1$. Unknown ages require a specified entry-age model or recovered history; merely adding equally unspecified segments does not supply the missing likelihood information.