AbstractWhen accelerated life tests can be applied to simulate the normal product operating conditions, engineers usually terminate the test upon successfully running to a multiple of a prespecified bogey without any failure to demonstrate a required minimum reliability level. This testing philosophy is called ‘bogey test’ (or extended test) in the automotive industry and is a subset of type I censored tests in standard reliability literature. Sometimes engineers encounter the difficulty of using this reliability demonstration approach when incidents do occur during the test. The incident might be a legitimate failure or a withdrawal caused by external forces such as a broken fixture of a non‐functional power supply. This paper derives a two‐stage sampling plan for possible back‐up solution on planning and running a bogey test with possible occurrence of incidents. A Weibull distribution with a given shape parameter is assumed for the underlying life chara