ON THE ASYMPTOTIC-DISTRIBUTION OF AN ESTIMATE OF THE CHANGE POINT IN A FAILURE RATE

The failure rate tau(t) is assumed to have the shape of the "first' part of the "bathtub" model, i.e., tau(t) is non-increasing for t < tau and is constant for t greater-than-or-equal-to tau. Asymptotic distribution of one of the estimates proposed earlier has been investigated in this paper. This leads to a test for the hypothesis H-0 : tau less-than-or-equal-to tau0 vs H-1 : tau > tau0 (where tau0 > 0). Asymptotic expression for the power of this test under Pitman alternatives is derived. Some simulations are reported.