scholarly journals Extreme value statistical analysis to determine the endurance limit of a 1045 induction hardened steel alloy

2011 ◽  
Vol 10 ◽  
pp. 607-612
Author(s):  
A.B. Nissan ◽  
K.O. Findley ◽  
A.S. Hering
Keyword(s):  
Statistical Analysis ◽  
Endurance Limit ◽  
Extreme Value ◽  
Hardened Steel ◽  
Steel Alloy

scholarly journals Statistics of the largest geomagnetic storms per solar cycle (1844-1993)

1997 ◽  
Vol 15 (6) ◽  
pp. 719-728 ◽  
Author(s):  
D. M. Willis ◽  
P. R. Stevens ◽  
S. R. Crothers
Keyword(s):  
Statistical Analysis ◽  
Solar Cycle ◽  
Geomagnetic Storm ◽  
Extreme Values ◽  
Geomagnetic Storms ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Relative Dispersion ◽  
Solar Cycles ◽  
Aa Index

Abstract. A previous application of extreme-value statistics to the first, second and third largest geomagnetic storms per solar cycle for nine solar cycles is extended to fourteen solar cycles (1844–1993). The intensity of a geomagnetic storm is measured by the magnitude of the daily aa index, rather than the half-daily aa index used previously. Values of the conventional aa index (1868–1993), supplemented by the Helsinki Ak index (1844–1880), provide an almost continuous, and largely homogeneous, daily measure of geomagnetic activity over an interval of 150 years. As in the earlier investigation, analytic expressions giving the probabilities of the three greatest storms (extreme values) per solar cycle, as continuous functions of storm magnitude (aa), are obtained by least-squares fitting of the observations to the appropriate theoretical extreme-value probability functions. These expressions are used to obtain the statistical characteristics of the extreme values; namely, the mode, median, mean, standard deviation and relative dispersion. Since the Ak index may not provide an entirely homogeneous extension of the aa index, the statistical analysis is performed separately for twelve solar cycles (1868–1993), as well as nine solar cycles (1868–1967). The results are utilized to determine the expected ranges of the extreme values as a function of the number of solar cycles. For fourteen solar cycles, the expected ranges of the daily aa index for the first, second and third largest geomagnetic storms per solar cycle decrease monotonically in magnitude, contrary to the situation for the half-daily aa index over nine solar cycles. The observed range of the first extreme daily aa index for fourteen solar cycles is 159–352 nT and for twelve solar cycles is 215–352 nT. In a group of 100 solar cycles the expected ranges are expanded to 137–539 and 177–511 nT, which represent increases of 108% and 144% in the respective ranges. Thus there is at least a 99% probability that the daily aa index will satisfy the condition aa < 550 for the largest geomagnetic storm in the next 100 solar cycles. The statistical analysis is used to infer that remarkable conjugate auroral observations on the night of 16 September 1770, which were recorded during the first voyage of Captain Cook to Australia, occurred during an intense geomagnetic storm.

Application of Extreme Value Statistical Analysis to Distribution of Peening Marks Obtained by Water Jet Peening

2002 ◽  
Vol 2002 (0) ◽  
pp. 485-486
Author(s):  
Inami KAZUNORI ◽  
Toshihiko YOSHIMURA ◽  
Ren MORINAKA ◽  
Noboru SAITO
Keyword(s):  
Statistical Analysis ◽  
Extreme Value ◽  
Water Jet

A Statistical Appraisal of the Prot Method for Determination of Fatigue Endurance Limit

1957 ◽  
Vol 24 (2) ◽  
pp. 214-218
Author(s):  
W. A. Hijab
Keyword(s):  
Statistical Analysis ◽  
General Formula ◽  
Endurance Limit ◽  
Statistical Efficiency ◽  
Great Saving ◽  
Secondary Result ◽  
Fatigue Endurance

Abstract A statistical analysis of the precision of the estimate of endurance limit as determined by the Prot method is carried out. This analysis shows that the Prot method cannot achieve a great saving in the number of specimens required, for its statistical efficiency is found to be even less than that of its other two competitors, the probit and staircase methods. This fact, coupled with serious objections to its assumptions, renders its usefulness highly questionable. A secondary result of the analysis is that the optimum efficiency of the Prot method is achieved when only two rates of increase of stress, as widely separated as possible, are used. A derivation of a general formula, of which the Prot method is a particular case and which makes explicit all assumptions necessary for the valid derivation of the Prot method, is also given.

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