Mat 540 Final Paper

Let us examine the following condition of complete observations given above. Assume that $\Upsilon_{\chi}$ is taken as distribution function whose total failure times is studied using gamma distribution applied to the shape parameters $3$ together with scale parameters $2.$ On side of repair time it goes with the same way failure time with gamma distribution together with shape parameter $1,$ and scale parameter $2$ respectively. The time $\tau$ is examined as the following $\tau=2.5,\tau=5,$ and $\tau=7.5$ for getting a good approximation. For precise value to $\Lambda_{a}(\tau)$ at given time $\tau$ is examined by applying Mathematica. The given $(n)$ indicated in table$(2)$ is the observations number to the operating with repair times, $\widehat{\overline{\Lambda}}_{a}(\tau)$ indicates also the average to $\widehat{\Lambda}_{a}(\tau)$ more than $100$ times repetitions at time $\tau$, where $\widehat{\overline{\theta}}(\tau)$ indicates the mean of sample to estimate the standard error to the estimation where $\Lambda_{a,\rho}$ and $\Lambda_{a,Q}$ indicates $100\%$ upper and lower to the limit of confidence interval to $\Lambda_{a}(\tau)$.\\
The outcome results to the given studies have been illustrated by Table $(2).$ Let $\chi\%$ and $\gamma\%$ considered as average percentage to the censoring rate combined to the repair with failure