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Capability indices for Birnbaum-Saunders processes applied to electronic and food industries

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  • V�ctor Leiva
  • Carolina Marchant
  • Helton Saulo
  • Muhammad Aslam
  • Fernando Rojas

Abstract

Process capability indices (PCIs) are tools widely used by the industries to determine the quality of their products and the performance of their manufacturing processes. Classic versions of these indices were constructed for processes whose quality characteristics have a normal distribution. In practice, many of these characteristics do not follow this distribution. In such a case, the classic PCIs must be modified to take into account the non-normality. Ignoring the effect of this non-normality can lead to misinterpretation of the process capability and ill-advised business decisions. An asymmetric non-normal model that is receiving considerable attention due to its good properties is the Birnbaum-Saunders (BS) distribution. We propose, develop, implement and apply a methodology based on PCIs for BS processes considering estimation, parametric inference, bootstrap and optimization tools. This methodology is implemented in the statistical software {\tt R}. A simulation study is conducted to evaluate its performance. Real-world case studies with applications for three data sets are carried out to illustrate its potentiality. One of these data sets was already published and is associated with the electronic industry, whereas the other two are unpublished and associated with the food industry.

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  • 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.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:9:p:1881-1902
    DOI: 10.1080/02664763.2014.897690
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    References listed on IDEAS

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    1. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    2. Hsu, Ya-Chen & Pearn, W.L. & Wu, Pei-Ching, 2008. "Capability adjustment for gamma processes with mean shift consideration in implementing Six Sigma program," European Journal of Operational Research, Elsevier, vol. 191(2), pages 517-529, December.
    3. S. Balamurali & M. Kalyanasundaram, 2002. "Construction of a generalized robust Taguchi capability index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 967-971.
    4. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    5. V�ctor Leiva & Emilia Athayde & Cecilia Azevedo & Carolina Marchant, 2011. "Modeling wind energy flux by a Birnbaum--Saunders distribution with an unknown shift parameter," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2819-2838, February.
    6. W. L. Pearn, 1998. "New generalization of process capability index Cpk," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(6), pages 801-810.
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    Cited by:

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    2. 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.
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    5. 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.
    6. 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.
    7. Xu Guo & Hecheng Wu & Gaorong Li & Qiuyue Li, 2017. "Inference for the common mean of several Birnbaum–Saunders populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 941-954, April.
    8. 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.

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