  A function based nonlinear least squares estimation (FNLSE) method is
proposed and investigated in parameter estimation of Jelinski-Moranda software
reliability model. FNLSE extends the potential fitting functions of traditional
least squares estimation (LSE), and takes the logarithm transformed nonlinear
least squares estimation (LogLSE) as a special case. A novel power
transformation function based nonlinear least squares estimation (powLSE) is
proposed and applied to the parameter estimation of Jelinski-Moranda model.
Solved with Newton-Raphson method, Both LogLSE and powLSE of Jelinski-Moranda
models are applied to the mean time between failures (MTBF) predications on six
standard software failure time data sets. The experimental results demonstrate
the effectiveness of powLSE with optimal power index compared to the classical
least--squares estimation (LSE), maximum likelihood estimation (MLE) and LogLSE
in terms of recursively relative error (RE) index and Braun statistic index.
