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 ****un****reliability 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 *U _{hat}* is the unreliability of the component,

*f*

_{l}

*(·)*the probability density function of the load, and

*F*

_{s}*(·)*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 *f** _{l}(·)* and

*F*will be

_{s}(·)*0*for negative values (i.e., for

*l<0*). As a consequence, the above integral is given by:

The reliability of the component is *R _{hat}*=1-

*U*

_{hat}. Continue reading R code for constructing likelihood based confidence intervals for stress-strength models