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Estimation and confidence intervals of $$C_{Np}(u,v)$$ C Np ( u , v ) for logistic-exponential distribution with application

Author

Listed:
  • Sanku Dey

    (St. Anthony’s College
    Chandigarh University)

  • Mahendra Saha

    (Central University of Rajasthan
    Chandigarh University)

  • M. Z. Anis

    (SQC & OR Unit, Indian Statistical Institute
    Chandigarh University)

  • Sudhansu S. Maiti

    (Visva-Bharati University
    Chandigarh University)

  • Sumit Kumar

    (Visva-Bharati University
    Chandigarh University)

Abstract

The process capability index (PCI) has been one of the most useful indicators for evaluating the capability of a manufacturing process. Since PCI is based on sample observations, it is essentially an estimated value. Hence, it is natural to think of a confidence interval (CI) of the PCI. In this paper, bootstrap confidence intervals and highest posterior density (HPD) credible intervals of non-normal PCIs, $$C_{Npmk}$$ C Npmk , $$C_{Npm}$$ C Npm , $$C_{Npk}$$ C Npk and $$C_{Np}$$ C Np are studied through simulation when the underlying distribution is two parameter logistic-exponential (LE). First, maximum likelihood method is used to estimate the model parameters and then three bootstrap confidence intervals (BCIs) are considered for obtaining CIs of non-normal PCIs, $$C_{Npmk}$$ C Npmk , $$C_{Npm}$$ C Npm , $$C_{Npk}$$ C Npk and $$C_{Np}$$ C Np . Next, the Bayesian estimation is studied with respect to symmetric (squared error) loss function using gamma priors for the model parameters. In order to assess the performance of BCIs and HPD credible intervals of $$C_{Npmk}$$ C Npmk , $$C_{Npm}$$ C Npm , $$C_{Npk}$$ C Npk and $$C_{Np}$$ C Np with respect to average width, coverage probabilities and relative coverage, Monte Carlo simulations are conducted. Finally, a real data set, related to weight of the rubber edge of the speaker driver has been analyzed for illustrative purpose.

Suggested Citation

  • Sanku Dey & Mahendra Saha & M. Z. Anis & Sudhansu S. Maiti & Sumit Kumar, 2023. "Estimation and confidence intervals of $$C_{Np}(u,v)$$ C Np ( u , v ) for logistic-exponential distribution with application," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 431-446, March.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:1:d:10.1007_s13198-023-01870-y
    DOI: 10.1007/s13198-023-01870-y
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    References listed on IDEAS

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