Title: A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samples

Authors: Palaniappan Ramu; Harshal Kaushik

Addresses: Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600 036, India ' School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK-74078, USA

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.

DOI: 10.1504/IJRS.2020.105890

International Journal of Reliability and Safety, 2020 Vol.14 No.1, pp.14 - 38

Received: 07 Mar 2019
Accepted: 27 Aug 2019
Published online: 16 Mar 2020 *

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