IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v14y2023i1d10.1007_s13198-023-01870-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-023-01870-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13198-023-01870-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yingjie Lan & Lawrence M. Leemis, 2008. "The logistic–exponential survival distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(3), pages 252-264, April.
    2. Mohammed Z. Anis, 2008. "Basic Process Capability Indices: An Expository Review," International Statistical Review, International Statistical Institute, vol. 76(3), pages 347-367, December.
    3. Sajid Ali & Muhammad Riaz, 2014. "On the generalized process capability under simple and mixture models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 832-852, April.
    4. Arnold, Barry C. & Press, S. James, 1983. "Bayesian inference for pareto populations," Journal of Econometrics, Elsevier, vol. 21(3), pages 287-306, April.
    5. Chien-Wei Wu & Tsai-Yu Lin, 2009. "A Bayesian procedure for assessing process performance based on the third-generation capability index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1205-1223.
    6. D. R. Anderson & K. P. Burnham & G. C. White, 1998. "Comparison of Akaike information criterion and consistent Akaike information criterion for model selection and statistical inference from capture-recapture studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 263-282.
    7. 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.
    8. Sanku Dey & Mahendra Saha, 2019. "Bootstrap confidence intervals of generalized process capability index Cpyk using different methods of estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(10), pages 1843-1869, July.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nirei, Makoto & Sushko, Vladyslav, 2011. "Jumps in foreign exchange rates and stochastic unwinding of carry trades," International Review of Economics & Finance, Elsevier, vol. 20(1), pages 110-127, January.
    2. Chanseok Park & Min Wang, 2024. "Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm," Mathematics, MDPI, vol. 12(11), pages 1-17, June.
    3. Hugo Horta & João M. Santos, 2016. "An instrument to measure individuals’ research agenda setting: the multi-dimensional research agendas inventory," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(3), pages 1243-1265, September.
    4. Azeem Ali & Sanku Dey & Haseeb Ur Rehman & Zeeshan Ali, 2019. "On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III 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. 10(5), pages 1052-1081, October.
    5. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    6. Marta Benková & Dagmar Bednárová & Gabriela Bogdanovská, 2024. "Process Capability Evaluation Using Capability Indices as a Part of Statistical Process Control," Mathematics, MDPI, vol. 12(11), pages 1-29, May.
    7. Sajid Ali & Muhammad Riaz, 2014. "On the generalized process capability under simple and mixture models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 832-852, April.
    8. José Alves & João Quental Gonçalves, 2022. "How Money relates to value? An empirical examination on Gold, Silver and Bitcoin," Working Papers REM 2022/0222, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    9. Ariane Manuela Amin, 2012. "What Drives Biodiversity Conservation Effort in the Developing World? An analysis for Sub-Saharan Africa," CERDI Working papers halshs-00722081, HAL.
    10. Majda Benzidia & Michel Lubrano, 2020. "A Bayesian look at American academic wages: From wage dispersion to wage compression," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(2), pages 213-238, June.
    11. Galbraith, John W. & Zinde-Walsh, Victoria, 2004. "Évaluation de critères d’information pour les modèles de séries chronologiques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 207-227, Juin-Sept.
    12. Aykroyd, Robert G. & Leiva, Víctor & Ruggeri, Fabrizio, 2019. "Recent developments of control charts, identification of big data sources and future trends of current research," Technological Forecasting and Social Change, Elsevier, vol. 144(C), pages 221-232.
    13. Jeevanand E. S. & Abdul-Sathar E. I., 2006. "Estimation of Pareto Survival Function in the Presence of Outlying Observations," Stochastics and Quality Control, De Gruyter, vol. 21(2), pages 199-208, January.
    14. Sanku Dey & Vikas Kumar Sharma & M. Z. Anis & Babita Yadav, 2017. "Assessing lifetime performance index of Weibull distributed products using progressive type II right censored samples," 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. 8(2), pages 318-333, June.
    15. Vasileios Alevizakos, 2023. "Process Capability and Performance Indices for Discrete Data," Mathematics, MDPI, vol. 11(16), pages 1-22, August.
    16. Zeinab Amin, 2008. "Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1203-1217.
    17. Ariane Manuela AMIN, 2012. "What Drives Biodiversity Conservation Effort in the Developing World? An analysis for Sub-Saharan Africa," Working Papers 201230, CERDI.
    18. Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    19. N. Balakrishnan & M. Doostparast & J. Ahmadi, 2009. "Reconstruction of past records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 89-109, June.
    20. Sanku Dey & Emrah Altun & Devendra Kumar & Indranil Ghosh, 2023. "The Reflected-Shifted-Truncated Lomax Distribution: Associated Inference with Applications," Annals of Data Science, Springer, vol. 10(3), pages 805-828, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:ijsaem:v:14:y:2023:i:1:d:10.1007_s13198-023-01870-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.