In my previous blog post I demonstrated how to compute bootstrap confidence intervals for stress-strength models.
The following R-code may be used for computing likelihood based confidence intervals for stress-strength models.
Definition of the unreliability in case of a stress-strength model
A component may fail when the stress (or load) exceeds the strength. Accordingly, the unreliability of the component is defined as:
where Uhat is the unreliability of the component, fl(·) the probability density function of the load, and Fs(·) the cumulative density function of the strength.
Note that both the load and strength random variables never take negative values. Since both these random variables are non-negative, the lower limit of the above integral changes. That is, the lower limit changes from -∞ to 0, since fl(·) and Fs(·) will be 0 for negative values (i.e., for l<0). As a consequence, the above integral is given by:
The reliability of the component is Rhat=1-Uhat. Continue reading R code for constructing likelihood based confidence intervals for stress-strength models