A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samples Article Swipe
Palaniappan Ramu
,
Harshal D. Kaushik
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1504/ijrs.2020.10027561
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1504/ijrs.2020.10027561
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.
Related Topics
Concepts
Transformation (genetics)
Mathematics
Monotonic function
Polynomial
Reliability (semiconductor)
Order statistic
Statistics
Function (biology)
Cumulative distribution function
Probit
Applied mathematics
Probability density function
Mathematical analysis
Gene
Biochemistry
Quantum mechanics
Evolutionary biology
Chemistry
Physics
Power (physics)
Biology
Metadata
- Type
- article
- Language
- en
- Landing Page
- http://doi.org/10.1504/ijrs.2020.10027561
- https://doi.org/10.1504/ijrs.2020.10027561
- OA Status
- bronze
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3010750242
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3010750242Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1504/ijrs.2020.10027561Digital Object Identifier
- Title
-
A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samplesWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-01-01Full publication date if available
- Authors
-
Palaniappan Ramu, Harshal D. KaushikList of authors in order
- Landing page
-
https://doi.org/10.1504/ijrs.2020.10027561Publisher landing page
- PDF URL
-
https://doi.org/10.1504/ijrs.2020.10027561Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
bronzeOpen access status per OpenAlex
- OA URL
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https://doi.org/10.1504/ijrs.2020.10027561Direct OA link when available
- Concepts
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Transformation (genetics), Mathematics, Monotonic function, Polynomial, Reliability (semiconductor), Order statistic, Statistics, Function (biology), Cumulative distribution function, Probit, Applied mathematics, Probability density function, Mathematical analysis, Gene, Biochemistry, Quantum mechanics, Evolutionary biology, Chemistry, Physics, Power (physics), BiologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.approach | 15, 66 |
| abstract_inverted_index.covering | 98 |
| abstract_inverted_index.examples | 105 |
| abstract_inverted_index.imposing | 44 |
| abstract_inverted_index.improved | 74 |
| abstract_inverted_index.ordinate | 57 |
| abstract_inverted_index.proposes | 50 |
| abstract_inverted_index.response | 34, 123, 141 |
| abstract_inverted_index.Log-TPNT. | 67 |
| abstract_inverted_index.analysis. | 7 |
| abstract_inverted_index.estimates | 142 |
| abstract_inverted_index.resulting | 82 |
| abstract_inverted_index.Cumulative | 28 |
| abstract_inverted_index.Polynomial | 11 |
| abstract_inverted_index.analytical | 104 |
| abstract_inverted_index.associated | 138 |
| abstract_inverted_index.bootstrap. | 146 |
| abstract_inverted_index.polynomial | 42 |
| abstract_inverted_index.quantified | 144 |
| abstract_inverted_index.underlying | 22 |
| abstract_inverted_index.variations | 137 |
| abstract_inverted_index.approximate | 26 |
| abstract_inverted_index.dimensions, | 111 |
| abstract_inverted_index.predictions | 85 |
| abstract_inverted_index.reliability | 6 |
| abstract_inverted_index.statistical | 96 |
| abstract_inverted_index.transformed | 60, 70 |
| abstract_inverted_index.Distribution | 29 |
| abstract_inverted_index.constraints. | 46 |
| abstract_inverted_index.demonstrated | 91 |
| abstract_inverted_index.distribution | 81 |
| abstract_inverted_index.monotonicity | 45 |
| abstract_inverted_index.reliability, | 128 |
| abstract_inverted_index.reliability. | 115 |
| abstract_inverted_index.corresponding | 125 |
| abstract_inverted_index.distributions | 97 |
| abstract_inverted_index.non-linearity | 112 |
| abstract_inverted_index.Transformation | 13 |
| abstract_inverted_index.transformation | 54 |
| abstract_inverted_index.transformations | 1 |
| cited_by_percentile_year | |
| countries_distinct_count | 2 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.03511229 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |