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Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications

Author

Listed:
  • Mahendra Saha

    (Central University of Rajasthan)

  • Sanku Dey

    (St. Anthony’s College)

  • Sudhansu S. Maiti

    (Visva-Bharati University)

Abstract

Process capability index is an important statistical technique that measures the ability of a process and hence it is used in quality control to quantify the relation between the actual performance of the process and the preset specification of the product. In this article bootstrap confidence intervals (BCIs) of generalized process capability index (GPCI) $$C_{pTk}$$ C pTk proposed by Maiti et al. (J Qual Technol Quant Manag 7(3):279–300, 2010) are studied through simulation when the underlying distribution is logistic-exponential (LE). The model parameters are estimated by the maximum likelihood method of estimation. Three non-parametric (NPR) as well as parametric (PR) BCIs, namely, percentile bootstrap ( $$\mathcal P$$ P -boot), student’s t bootstrap ( $$\mathcal T$$ T -boot) and bias-corrected percentile bootstrap ( $$\mathcal BC_p$$ B C p -boot) are considered for obtaining confidence intervals (CIs) of GPCI $$C_{pTk}$$ C pTk . Through extensive Monte Carlo simulations, we examine the estimated coverage probabilities and average widths of the BCIs for two parameter LE distribution and in particular for exponential distribution. Simulation results show that the estimated coverage probabilities of the $$\mathcal P$$ P -boot CI perform better than their counterparts. Finally, three real data sets are analyzed for illustrative purposes.

Suggested Citation

  • Mahendra Saha & Sanku Dey & Sudhansu S. Maiti, 2019. "Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications," 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. 10(4), pages 623-631, August.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:4:d:10.1007_s13198-019-00789-7
    DOI: 10.1007/s13198-019-00789-7
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    References listed on IDEAS

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    1. V�ctor Leiva & Carolina Marchant & Helton Saulo & Muhammad Aslam & Fernando Rojas, 2014. "Capability indices for Birnbaum-Saunders processes applied to electronic and food industries," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1881-1902, September.
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    Cited by:

    1. 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.
    2. Ashish Kumar & Muskaan Arora & Monika Saini, 2023. "Influence of mathematics on the academic performance of mechanical engineering students: a PLS-SEM approach," 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 367-376, February.
    3. Sanku Dey & Liang Wang & Mahendra Saha, 2024. "Inference of $$S^{\prime }_{pmk}$$ S pmk ′ based on bias-corrected methods of estimation for generalized exponential distribution," 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. 15(11), pages 5265-5278, November.

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