 A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samplesPalaniappan Ramu and Harshal Kaushik International Journal of Reliability and Safety, 2020, vol. 14, issue 1, 14-38 Abstract: Normal transformations are often used in reliability analysis. A Third order Polynomial Normal Transformation (TPNT) approach is used in this work. The underlying idea is to approximate the Cumulative Distribution Function (CDF) of the response in probit space using a third order polynomial while imposing monotonicity constraints. The current work proposes to apply log transformation to the ordinate of the transformed CDF and hence names the approach Log-TPNT. The log transformed data assists in improved fitting to the tails of the distribution resulting in better predictions of extreme values. Log-TPNT is demonstrated on a suite of statistical distributions covering all types of tails and analytical examples that cover aspects of high dimensions, non-linearity and system reliability. Results reveal that Log-TPNT can predict the response values corresponding to high reliability, with samples as scarce as 9. Finally, the variations associated with the response estimates are quantified using bootstrap. Keywords: reliability; cumulative distribution function; normal transformation; polynomial fit; bootstrap. (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ids:ijrsaf:v:14:y:2020:i:1:p:14-38 Access Statistics for this article More articles in International Journal of Reliability and Safety from Inderscience Enterprises Ltd |
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