Improved process capability assessment through semiparametric piecewise modeling

Abstract

Piecewise models have gained popularity as a useful tool in reliability and quality control/monitoring, particularly when the process data deviates from a normal distribution. In this study, we develop maximum likelihood estimators (MLEs) for the process capability indices, denoted as $C_{\mathrm{pk}}$, $C_{\mathrm{pm}}$, $C_{\mathrm{pm}}^{\ast }$ and $C_{\mathrm{pmk}}$, using a semiparametric model. To remove the bias in the MLEs with small sample sizes, we propose a bias-correction approach to obtain improved estimates. Furthermore, we extend the proposed method to situations where the change-points in the density function are unknown. To estimate the model parameters efficiently, we employ the profiled maximum likelihood approach. Our simulation study reveals that the suggested method yields accurate estimates with low bias and mean squared error. Finally, we provide real-world data applications to demonstrate the superiority of the proposed procedure over existing ones.

Keywords:

• Bias-correction method
• change-point model
• piecewise exponential model
• process capability index

Acknowledgments

The authors are thankful to the Editorial Board and to the reviewers for their valuable comments and suggestions that led to the last version.

Code Availability

All the functions and procedures concerning implementation included in the article have been implemented in R Core Team. The codes will be available at https://github.com/njerezlillo/improvedprocesscapability/tree/main.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Nixon Jerez-Lillo was funded by the National Agency for Research and Development (ANID)/Scholarship Program/Doctorado Nacional/2021-21210981. Paulo H. Ferreira acknowledges support from the Brazilian National Council for Scientific and Technological Development (CNPq, grant no. 307221/2022-9).