Scale Testing in small samples with missing time-to-failure information

We provide the exact likelihood ratio testing procedure of the scale parameter of the Erlang and gamma distribution when there is a missing time-to-failure information. This is an important result because the asymptotical χ2-test is oversized an thus inappropriate especially for small merged samples. The small merged samples can arise also for a large sample sizes, e.g. when individual times-to-failure are not available. Data sets with missing time-to-failure data can arise from field data collection systems. Real data and simulated examples are provided to illustrate the methods discussed.