Evaluation of a novel loss-based process capacity index $${\mathcal {S}}^{\prime }_{pk}$$ S pk ′ and its applications

Mahendra Saha (), Anju Devi, Abhimanyu Singh Yadav and Sudhansu S. Maiti
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Mahendra Saha: University of Delhi
Anju Devi: Central University of Rajasthan
Abhimanyu Singh Yadav: Banaras Hindu University
Sudhansu S. Maiti: Visvs-Bharati University

International Journal of System Assurance Engineering and Management, 2024, vol. 15, issue 6, No 15, 2188-2201

Abstract: Abstract Process capability indices (PCIs) are often used to assess process performance. Higher PCIs do not mean lower rejection rates. Thus, loss-based PCIs are better for process capability measurement. This study introduces a new capability index, $$\mathcal S^{\prime }_{pk}$$ S pk ′ , based on a symmetric loss function for normal process, to include loss into capability analysis. We then estimate PCI $${\mathcal {S}}^{\prime }_{pk}$$ S pk ′ employing six standard techniques of estimation and compare their mean squared errors (MSEs) through simulation analysis. For the index $${\mathcal {S}}^{\prime }_{pk}$$ S pk ′ , asymptotic confidence intervals (ACI), generalized confidence intervals (GCI), and parametric bootstrap confidence intervals (BCIs) are used to construct confidence intervals . Monte Carlo simulation evaluates ACI, GCI, and BCIs average widths and coverage probabilities. Our experiments showed that MPSE produced the smallest width. $${\mathcal {B}}{\mathcal {C}}_p$$ B C p -boot outperformed its competitors. For most sample sizes and estimation methodologies, $$\mathcal {P}$$ P -boot has a greater CP. Two electronic industry data sets are evaluated to demonstrate the accuracy of the suggested estimating methodologies, ACI, GCI, and BCIs.

Keywords: Asymptotic confidence interval; Bootstrap confidence interval; Classical methods of estimation; Generalized confidence interval; Normal distribution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13198-023-02235-1

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