Template:Exponential Distribution Example: Likelihood Ratio Bound for Reliability

Example 7: Likelihood Ratio Bound on Reliability
For the data given in Example 5, determine the 85% two-sided confidence bounds on the reliability estimate for a $$t=50$$. The ML estimate for the time at $$t=50$$ is $$\hat{R}=50.881%$$.

Solution to Example 7

In this example, we are trying to determine the 85% two-sided confidence bounds on the reliability estimate of 50.881%. This is accomplished by substituting $$t=50$$ and $$\alpha =0.85$$ into the likelihood ratio bound equation. It now remains to find the values of $$R$$ which satisfy this equation. Since there is only one parameter, there are only two values of $$t$$ that will satisfy the equation. These values represent the $$\delta =85%$$ two-sided confidence limits of the reliability estimate $$\hat{R}$$. For our problem, the confidence limits are:


 * $${{\hat{R}}_{t=50}}=(29.861%,71.794%)$$