A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samples Online publication date: Mon, 16-Mar-2020
by Palaniappan Ramu; Harshal Kaushik
International Journal of Reliability and Safety (IJRS), Vol. 14, No. 1, 2020
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.
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