Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics
Joint Authors
Dey, Sanku
Alotaibi, Refah Mohammed
Alomani, Ghadah A.
Saha, Mahendra
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-02-25
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance.
Usually, conventional PCIs perform well under normally distributed quality characteristics.
However, when these PCIs are employed to evaluate nonnormally distributed process, they often provide inaccurate results.
In this article, in order to estimate the PCI Spmk when the process follows power Lindley distribution, first, seven classical methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares methods of estimation, Cramèr–von Mises method of estimation, maximum product of spacings method of estimation, Anderson–Darling, and right-tail Anderson–Darling methods of estimation, are considered and the performance of these estimation methods based on their mean squared error is compared.
Next, three bootstrap confidence intervals (BCIs) of the PCI Spmk, namely, standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap, are considered and compared in terms of their average width, coverage probability, and relative coverage.
Besides, a new cost-effective PCI, namely, Spmkc is introduced by incorporating tolerance cost function in the index Spmk.
To evaluate the performance of the methods of estimation and BCIs, a simulation study is carried out.
Simulation results showed that the maximum likelihood method of estimation performs better than their counterparts in terms of mean squared error, while bias-corrected percentile bootstrap provides smaller confidence length (width) and higher relative coverage than standard bootstrap and percentile bootstrap across sample sizes.
Finally, two real data examples are provided to investigate the performance of the proposed procedures.
American Psychological Association (APA)
Alomani, Ghadah A.& Alotaibi, Refah Mohammed& Dey, Sanku& Saha, Mahendra. 2020. Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1201944
Modern Language Association (MLA)
Alomani, Ghadah A.…[et al.]. Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics. Mathematical Problems in Engineering No. 2020 (2020), pp.1-17.
https://search.emarefa.net/detail/BIM-1201944
American Medical Association (AMA)
Alomani, Ghadah A.& Alotaibi, Refah Mohammed& Dey, Sanku& Saha, Mahendra. Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-17.
https://search.emarefa.net/detail/BIM-1201944
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1201944