Parameter Estimation of Jelinski-Moranda Model Based on Weighted Nonlinear Least Squares and Heteroscedasticity

TL;DR

This paper introduces a weighted nonlinear least squares approach for estimating parameters in the Jelinski-Moranda model, addressing heteroscedasticity and comparing it with traditional methods, showing improved accuracy in software reliability data.

Contribution

The paper develops a novel WNLSE method for JM parameter estimation, incorporating heteroscedasticity considerations and demonstrating its superiority over existing methods.

Findings

WNLSE outperforms LSE and MLE in relative error.

Effective strategies for heteroscedasticity decision and weighting.

Validated on NTDS and Musa datasets.

Abstract

Parameter estimation method of Jelinski-Moranda (JM) model based on weighted nonlinear least squares (WNLS) is proposed. The formulae of resolving the parameter WNLS estimation (WNLSE) are derived, and the empirical weight function and heteroscedasticity problem are discussed. The effects of optimization parameter estimation selection based on maximum likelihood estimation (MLE) method, least squares estimation (LSE) method and weighted nonlinear least squares estimation (WNLSE) method are also investigated. Two strategies of heteroscedasticity decision and weighting methods embedded in JM model prediction process are also investigated. The experimental results on standard software reliability analysis database-Naval Tactical Data System (NTDS) and three datasets used by J.D. Musa demonstrate that WNLSE method can be superior to LSE and MLE under the relative error (RE) criterion.