Solving ML equations for 2-parameter Poisson-process models for ungrouped software-failure data

Existence conditions are given for maximum likelihood (ML) parameter estimates for several families of 2-parameter software-reliability Poisson-process models. For each such model, the ML equations can be expressed in terms of one equation in one unknown. Bounds are given on solutions to these one equation problems to serve as initial intervals for search algorithms like bisection. Uniqueness of the solutions is established in some cases. Solutions are also tabulated for certain simple cases. Results are given for ungrouped failure data (exact times are available for all failures). ML estimation problems for such a situation are treated as limiting cases of problems based on failure times grouped into intervals of decreasing mesh.