Estimation Under Reliability Growth Assuming Gamma Failure Models

Engineers often make changes during the development of a system in order to correct design weaknesses. If done well, this results in reliability growth (an increase in reliability and mean life) as development continues. The lifetime distribution at each stage in development is assumed to be gamma. Approximate maximum likelihood estimates (MLEs) of the parameters are obtained subject to the conditions that no parameter decreases in the next stage. An iterative procedure involving two constrained nonlinear optimization problems is proposed for obtaining the approximate MLEs. The constrained optimization problems can be computed using isotonic regression; the iterations converge rather quickly. The computations can be performed using common mathematical subroutine packages such as the International Mathematical and Statistical Libraries.