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

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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, \(\mathcal S^{\prime }_{pk}\), based on a symmetric loss function for normal process, to include loss into capability analysis. We then estimate PCI \({\mathcal {S}}^{\prime }_{pk}\) employing six standard techniques of estimation and compare their mean squared errors (MSEs) through simulation analysis. For the index \({\mathcal {S}}^{\prime }_{pk}\), 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. \({\mathcal {B}}{\mathcal {C}}_p\)-boot outperformed its competitors. For most sample sizes and estimation methodologies, \(\mathcal {P}\)-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.

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Acknowledgements

The author appreciates the Managing Editor and Reviewers for their attentive reading and helpful suggestions that improved the earlier version of this essay.

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No outside or internal funding funded this research

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Authors and Affiliations

  1. Department of Statistics, University of Delhi, Delhi, India

    Mahendra Saha

  2. Department of Statistics, Central University of Rajasthan, Ajmer, India

    Mahendra Saha & Anju Devi

  3. Department of Statistics, Banaras Hindu University, Banaras, India

    Abhimanyu Singh Yadav

  4. Department of Statistics, Visvs-Bharati University, Santiniketan, India

    Sudhansu S. Maiti

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  1. Mahendra Saha
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  2. Anju Devi
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  3. Abhimanyu Singh Yadav
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  4. Sudhansu S. Maiti
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Correspondence to Mahendra Saha.

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Saha, M., Devi, A., Yadav, A.S. et al. Evaluation of a novel loss-based process capacity index \({\mathcal {S}}^{\prime }_{pk}\) and its applications. Int J Syst Assur Eng Manag (2024). https://doi.org/10.1007/s13198-023-02235-1

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  • DOI: https://doi.org/10.1007/s13198-023-02235-1

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