A new capability index for non-normal distributions based on linex loss function

Abstract

Capability indices are the most common tools in process capability analysis, measuring how much the product meets the costumer expectations. One type of capability indices are loss-based indices that consider the cost of the difference between the product characteristic and its target value. In this work, we apply an asymmetric loss function to construct a new loss-based capability index for non-normal processes allowing a more customized way of considering the costs in capability analysis. The performance of the proposed capability index is studied by simulation results. Three real examples are given to show the utilization of the proposed index.

Keywords:

• asymmetric loss function
• bootstrap
• linex function
• process capability analysis
• process capability index

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Funding

The authors received no funding for this work.

Notes on contributors

Mahdiyeh Erfanian

Mahdiyeh Erfanian is a PhD candidate of Statistics at Ferdowsi university of Mashhad, Mashhad, Iran. She received her MSc in Mathematical Statistics at Ferdowsi University of Mashhad, Mashhad, Iran. She currently works on her PhD thesis about statistical profile monitoring.

Bahram Sadeghpour Gildeh

Bahram Sadeghpour Gildeh is a professor of Statistics at Ferdowsi University of Mashhad, Mashhad, Iran. He received his MSc in Mathematical Statistics at Ferdowsi University of Mashhad, Mashhad, Iran, and PhD in Informatics at the Blaise Pascal University, France. His research interests include statistical quality control, process capability analysis and fuzzy statistics.