Estimation of the generalized process capability index C pyk based on bias-corrected maximum-likelihood estimators for the generalized inverse Lindley distribution and bootstrap confidence intervals

GEDİK BALAY İ.

Journal of Statistical Computation and Simulation, vol.91, no.10, pp.1960-1979, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 91 Issue: 10
  • Publication Date: 2021
  • Doi Number: 10.1080/00949655.2021.1879081
  • Journal Name: Journal of Statistical Computation and Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Business Source Elite, Business Source Premier, CAB Abstracts, Communication Abstracts, Metadex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1960-1979
  • Keywords: Process capability index, Bias correction, maximum-likelihood estimators, generalized inverse Lindley distribution, bootstrap confidence intervals
  • Ankara Yıldırım Beyazıt University Affiliated: Yes

Abstract

© 2021 Informa UK Limited, trading as Taylor & Francis Group.In this paper, we are interested in estimating the generalized process capability index ((Formula presented.)) proposed by Maiti et al. [On generalizing process capability indices. Qual Technol Quant Manag. 2010;7(3):279–300], when the underlying distribution is the generalized inverse Lindley (GIL) distribution. We estimate parameters of the GIL distribution using maximum likelihood (ML), bias-corrected maximum-likelihood (BCML) and bootstrap bias-corrected maximum-likelihood (BBCML) methodologies. (Formula presented.) are obtained using proposed estimators. Bootstrap confidence intervals called standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB) (Formula presented.) are constructed based on the estimators of (Formula presented.). We compare efficiencies of the parameter estimators and the performance of ML, BCML and BBCML based Cpyk via an extensive Monte Carlo simulation study. A simulation study is also described to compare the coverage probabilities (CP) and average lengths (AL) of SB, PB and BCPB confidence intervals for proposed (Formula presented.). Finally, two real datasets are analysed for illustrative purposes.