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A function based nonlinear least squares estimation (FNLSE) method isproposed and investigated in parameter estimation of Jelinski-Moranda softwarereliability model. FNLSE extends the potential fitting functions of traditionalleast squares estimation (LSE), and takes the logarithm transformed nonlinearleast squares estimation (LogLSE) as a special case. A novel powertransformation function based nonlinear least squares estimation (powLSE) isproposed and applied to the parameter estimation of Jelinski-Moranda model.Solved with Newton-Raphson method, Both LogLSE and powLSE of Jelinski-Morandamodels are applied to the mean time between failures (MTBF) predications on sixstandard software failure time data sets. The experimental results demonstratethe effectiveness of powLSE with optimal power index compared to the classicalleast--squares estimation (LSE), maximum likelihood estimation (MLE) and LogLSEin terms of recursively relative error (RE) index and Braun statistic index.

Function Based Nonlinear Least Squares and Application to Jelinski--Moranda Software Reliability Model