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Spectral Estimation
Published in Robert H. Shumway, David S. Stoffer, Time Series: A Data Analysis Approach Using R, 2019
Robert H. Shumway, David S. Stoffer
Figure 7.13 shows the coherence between the SOI and Recruitment series over a wider band than was used for the spectrum. In this case, we used L = 19, df = 2(19)(453/480) ≈ 36 and F2,df–2(.001) ≈ 8.53 at the significance level α = .001. Hence, we may reject the hypothesis of no coherence for values of ρ¯y.x2(ω) that exceed C.001 = .32. We emphasize that this method is crude because, in addition to the fact that the F-statistic is approximate, we are examining the squared coherence across all frequencies with the Bonferroni inequality in mind. Figure 7.13 also exhibits confidence bands as part of the R plotting routine. We emphasize that these bands are only valid for ω where ρy.x2(ω)>0.
Saving Money with Six Sigma Projects
Published in Kim H. Pries, Jon M. Quigley, Reducing Process Costs with Lean, Six Sigma, and Value Engineering Techniques, 2012
When we do hypothesis testing, we need to consider sample size and have some means for establishing the appropriate distribution for the data. Even though we may establish some level of significance during hypothesis testing, it is not always the case that the information we gain is significant in the real world. This detestable term significance is the complement of the term confidence. When we state a confidence interval, we are stating the probability that the single value we have calculated occurs within this region, sometimes called a “confidence band.”
Reliability Assessment of a Bridge Structure Subjected to Chloride Attack
Published in Structural Engineering International, 2018
Bernt J. Leira, Sebastian Thöns, Michael H. Faber
First, a system reliability analysis is performed based on the assumptions described above, with the system failure probability evaluated for a time in operation of t = 60 years. The corresponding failure probability is shown as a function of the scaling parameter in Fig. 8 for the case where no additional information from monitoring or inspection is available. The 95% confidence band is also shown, as represented by the upper and lower curves.