home/regression-approach.md

@@ -8,6 +8,7 @@ title: regression approach - powerlaw
 
 
 
+
 ## Dependency
 
 It is assumed the data can be described by a power law, expressed either as Y or X dependent (referring to the second and first axis on a fatigue curve).
@@ -41,7 +42,10 @@ C = 10^{\left(Y_\text{mean} - m X_\text{mean}\right)}
 ```
  
 ## Tollerance bands
+A tollerance band states that a certain percentage of the data lies within or above the prediction statement. It is typically of interest to identify the lower-limits 75/75 or 95/95 to estimate a conservative measure of the blade lifetime. Below image illustrates a set of data points, with a mean (50/50) power curve. 
 <br>
 <div align="center">
 ![power_curve_example](uploads/77a961d851186f96dbe42b8e792e2d86/power_curve_example.png){width=45%}
 </div>
+
+There exist a multitude of methods as to identify these limits such as assuming the data follows a normal- or Weibull distribution. However, in this scenario the upper- and lower quantiles in the distribution are used to identify said limits. The following steps explains the algorithm step by step