**7. Validation of proposed framework**

In section, we compute the rate of failure to ensure the result experimentally of the proposed framework and follow the six steps for reliability estimation [10, 22]. We divide the entire input class into several subclass and for estimating reliability following equation required as:

$$R(t) = \sum\_{i=1}^{6} \frac{h\_i}{n\_i} P(e\_i) \tag{22}$$

*P e*ð Þ*<sup>i</sup>* is the probability specified from input operation data. *ni* is the number of trials from each comparable class. *hi* is a number of trial cases that are failed.

To estimate the actual reliability **Table 4** data will be used.

Now using Eq. (22) we estimate actual reliability as:

$$Rel\_{actual} = 1 - \sum\_{i=1}^{6} \frac{h\_i}{n\_i} \, P(e\_i) = 0.9899999$$

Now we compare estimated (predicted) and actual reliability as:

$$\begin{aligned} Reli(diff) &= Rel\_{actual} - Reli\_{estimated} \\ &= 0.989999 - 0.974359 \\ &= 0.01564 \end{aligned}$$

Hence, the error percentages can be computed as:

$$Error \%= \frac{Rel(d\hat{y}f)}{Rel\_{actual}}\\X100 = \frac{0.01564}{0.989999}\\X100 = 1.57981\%$$

Hence, the accuracy of proposed reliability computed of proposed framework is ð100 � *error*%Þ ¼ 98*:*4201% that indicates the validation of our work.


**Table 4.** *Reliability estimation using [22].* *Reliability Analysis of Instrumentation and Control System: A Case Study of Nuclear Power… DOI: http://dx.doi.org/10.5772/intechopen.101099*
