staircase testing confidence and reliability

Staircase testing - confidence and reliability B. R. Rabb Department of Calculation & Simulation, Wartsila Engine Division, Finland Abstract The aim of the fatigue analysis is to obtain a reliable design using the mean value of the fatigue limit reduced to the appropriate probability of failure as the allowed stress amplitude. This reduction requires a thorough knowledge of both the population mean and the population standard deviation. Furthermore, the correct probability distribution of the fatigue limit must be anticipated. Fatigue testing is required to obtain reliable estimates of the fatigue limit and standard deviation. The staircase or up-and-down test method is usually used. The obtained sample values must be transferred to population values by applying the rules of statistics, i.e. by applying confidence levels. However, due to the nature of the staircase test, it is very difficult to obtain a correct value of the sample standard deviation. This can be demonstrated by deriving the correct strength and variance distributions by Monte Carlo simulations of the staircase test. The evaluated sample mean is nor- mally much closer to the correct value. It is therefore possible to evaluate a reliable estimate of the sample standard deviation by calculating it from the observed statistical size effect from two staircase tests with different specimen sizes. Al- though a staircase test is usually evaluated using the normal distribution, the use of this distribution to calculate the safety factor can lead to undesired oversizing. The use of the log normal distribution is therefore recommended for this reduction. The fatigue ratio, i.e. the ratio of the fatigue limit in fully reversed tension com- pression to the tensile strength, as determined from the staircase test is related to the mean tensile strength. If this ratio is used to determine the fatigue limit, the Weibull distribution can be used to estimate the mean value from the minimum value given in the material standard. Transactions on Engineering Sciences vol 40, © 2003 WIT Press, www.witpress.com, ISSN 1743-3533

Upload: others

Post on 16-Oct-2021

3 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

Staircase testing - confidence and reliability

B . R. Rabb Department of Calculation & Simulation, Wartsila Engine Division, Finland

Abstract

The aim of the fatigue analysis is to obtain a reliable design using the mean value of the fatigue limit reduced to the appropriate probability of failure as the allowed stress amplitude. This reduction requires a thorough knowledge of both the population mean and the population standard deviation. Furthermore, the correct probability distribution of the fatigue limit must be anticipated. Fatigue testing is required to obtain reliable estimates of the fatigue limit and standard deviation. The staircase or up-and-down test method is usually used. The obtained sample values must be transferred to population values by applying the rules of statistics, i.e. by applying confidence levels. However, due to the nature of the staircase test, it is very difficult to obtain a correct value of the sample standard deviation. This can be demonstrated by deriving the correct strength and variance distributions by Monte Carlo simulations of the staircase test. The evaluated sample mean is nor- mally much closer to the correct value. It is therefore possible to evaluate a reliable estimate of the sample standard deviation by calculating it from the observed statistical size effect from two staircase tests with different specimen sizes. Al- though a staircase test is usually evaluated using the normal distribution, the use of this distribution to calculate the safety factor can lead to undesired oversizing. The use of the log normal distribution is therefore recommended for this reduction. The fatigue ratio, i.e. the ratio of the fatigue limit in fully reversed tension com- pression to the tensile strength, as determined from the staircase test is related to the mean tensile strength. If this ratio is used to determine the fatigue limit, the Weibull distribution can be used to estimate the mean value from the minimum value given in the material standard.