Bias-Corrected Maximum Likelihood Estimation for the Process Performance Index using Inverse Gaussian Distribution  
Author Tzong-Ru Tsai


Co-Author(s) Hua Xin; Ya-Yen Fan; Yulong Lio


Abstract An analytical bias-corrected maximum likelihood estimation procedure and a bootstrap bias-corrected maximum likelihood estimation procedure are proposed for the inverse Gaussian distribution (IGD) to obtain more reliable maximum likelihood estimates (MLEs) of the model parameters and the generalized process capability index (PCI) proposed by Maiti et al. (2010) when the sample size is small. An approximate confidence interval (ACI) of the generalized PCI is obtained for the IGD via using the delta method and the obtained reliable MLEs of the model parameters. Monte Carlo simulations were conducted to evaluate the performance of two proposed estimation methods. Simulation results show that two proposed bias-correction methods outperform the typical maximum likelihood estimation method when the sample size is small in terms of the relative bias and relative mean squared error.


Keywords Bias correction; bootstrap methods; Fisher information matrix; inverse Gaussian distribution; maximum likelihood estimation
    Article #:  RQD27-55

Proceedings of 27th ISSAT International Conference on Reliability & Quality in Design
Virtual Event

August 4-6, 2022