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A New Asymmetric Loss-Based Process Capability Index and Its Applications to Industrial Data

Author

Listed:
  • Tahir Md.

    (Department of Statistics, 30114 Banaras Hindu University , Varanasi, India)

  • Yadav Abhimanyu S.

    (Department of Statistics, 30114 Banaras Hindu University , Varanasi, India)

  • Singh Sanjay K.

    (Department of Statistics, 30114 Banaras Hindu University , Varanasi, India)

Abstract

This paper introduces a new capability index ( C QT ) {(C_{\rm QT})} which is based on an asymmetric loss function named Quadratic-Type Squared Error Loss Function (QTSELF). To estimate the proposed index C QT {C_{\rm QT}} , we have used five different classical methods of estimation (namely maximum likelihood, least squares and weighted least squares, Cramér–von-Mises, Anderson–Darling and maximum product of spacing) and their performances are compared. Additionally, three bootstrap confidence intervals, namely standard bootstrap ( 𝒮 {\mathcal{S}} -boot), percentile bootstrap ( 𝒫 {\mathcal{P}} -boot) and Student’s t bootstrap ( 𝒯 {\mathcal{T}} -boot) are constructed. Their performances are compared in terms of average widths and coverage probabilities through a Monte-Carlo simulation study. Finally, two datasets are taken from electronic industries to demonstrate the practical utilities of the proposed estimation techniques and confidence intervals.

Suggested Citation

  • Tahir Md. & Yadav Abhimanyu S. & Singh Sanjay K., 2026. "A New Asymmetric Loss-Based Process Capability Index and Its Applications to Industrial Data," Stochastics and Quality Control, De Gruyter, vol. 41(1), pages 35-47.
    • Handle: RePEc:bpj:ecqcon:v:41:y:2026:i:1:p:35-47:n:1004
    DOI: 10.1515/eqc-2025-0044
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