# A SkSP-R Plan under the Assumption of Gompertz Distribution
## 5 Real Life Examples  
In this part, two real data sets were chosen for the illustration purpose of the proposed SkSP-R plan. To begin, we examine whether data sets have been fitted to the GmzD or not. To accomplish this purpose, several criteria such as Akaike information criterion (AIC), Bayesian information criterion (BIC), and Kolmogorov-Smirnov statistic (KS) goodness-of-fit test value were used. Moreover, the \(p\)-value associated with the KS test were considered to support the presented results based on the real data sets. Descriptive statistics summary and model fitting results of both data sets are presented in Tables 5 and 6, respectively. Data I: The data include 30 observations of the times of failures and running times for samples of devices from an eld-tracking study of a larger system. Previously, these data were studied by [32]. The data are as follows: 0.02, 0.10, 0.13, 0.23, 0.23, 0.28, 0.30, 0.65, 0.80, 0.88, 1.06, 1.43, 1.47, 1.73, 1.81, 2.12, 2.45, 2.47, 2.61, 2.66, 2.75, 2.93, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, 3.00, Figure 3 shows the histogram density, empirical CDF and P-P plot of the GmzD for the first data set. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Data** & **Estimates** & **L-L** & **AIC** & **BIC** & **KS Value** & \(p\)**-Value** \\ \hline I & \(\alpha=1.3509349,\theta=0.2496109\) & \(-41.34595\) & 86.6919 & 89.4943 & 0.18892 & 0.2346 \\ \hline II & \(\alpha=0.2741801,\theta=0.0024180\) & \(-14.80810\) & 33.61621 & 37.90247 & 0.12676 & 0.2635 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Measures of goodness-of-fit statistics for both data sets. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & \\ \hline \(\beta\) & \(\mu\)/\(\mu_{0}\) & **n** & **c** & **i** & **f** & **k** & \(P_{\text{\it{avg}}}(p)\) & **ASN** & **n** & **c** & **i** & **f** & **k** & \(P_{\text{\it{avg}}}(p)\) & **ASN** \\ \hline \multirow{6}{*}{0.05} & 2 & 103 & 30 & 2 & 0.5 & 1 & 0.9861437 & 102.1556 & 74 & 30 & 2 & 0.5 & 1 & 0.9850251 & 73.54036 \\  & 3 & 100 & 29 & 2 & 0.5 & 1 & 0.9999749 & 99.19212 & 71 & 29 & 2 & 0.5 & 1 & 0.9999796 & 70.39578 \\  & 4 & 97 & 28 & 2 & 0.5 & 1 & 0.999999 & 96.22899 & 69 & 28 & 2 & 0.5 & 1 & 0.999999 & 68.45795 \\  & 5 & 94 & 27 & 2 & 0.5 & 1 & 1.0000000 & 93.26621 & 67 & 27 & 2 & 0.5 & 1 & 1.0000000 & 66.51622 \\  & 6 & 91 & 26 & 2 & 0.5 & 1 & 1.0000000 & 90.30373 & 65 & 26 & 2 & 0.5 & 1 & 1.0000000 & 64.57062 \\  & 7 & 88 & 25 & 2 & 0.5 & 1 & 1.0000000 & 87.34148 & 63 & 25 & 2 & 0.5 & 1 & 1.0000000 & 62.62121 \\  & 8 & 85 & 24 & 2 & 0.5 & 1 & 1.0000000 & 84.37941 & 60 & 24 & 2 & 0.5 & 1 & 1.0000000 & 59.49680 \\ \hline \multirow{6}{*}{0.01} & 2 & 140 & 38 & 2 & 0.5 & 1 & 0.977879 & 139.9565 & 99 & 38 & 2 & 0.5 & 1 & 0.9800148 & 98.96906 \\  & 3 & 137 & 37 & 2 & 0.5 & 1 & 0.9999849 & 136.9594 & 97 & 37 & 2 & 0.5 & 1 & 0.9999871 & 96.97312 \\  & 4 & 133 & 36 & 2 & 0.5 & 1 & 1.0000000 & 132.9498 & 93 & 36 & 2 & 0.5 & 1 & 1.0000000 & 93.96386 \\  & 5 & 130 & 35 & 2 & 0.5 & 1 & 1.0000000 & 129.9533 & 92 & 35 & 2 & 0.5 & 1 & 1.0000000 & 91.9687 \\  & 6 & 127 & 34 & 2 & 0.5 & 1 & 1.0000000 & 126.9567 & 90 & 34 & 2 & 0.5 & 1 & 1.000000 & 89.97305 \\  & 7 & 124 & 33 & 2 & 0.5 & 1 & 1.0000000 & 123.9600 & 88 & 33 & 2 & 0.5 & 1 & 1.0000000 & 87.97693 \\  & 8 & 121 & 32 & 2 & 0.5 & 1 & 1.0000000 & 120.9632 & 85 & 32 & 2 & 0.5 & 1 & 1.0000000 & 84.96881 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Data** & **Minimum** & \(Q_{1}\) & **Median** & **Mean** & \(Q_{3}\) & **Maximum** & **CS** & **CK** \\ \hline I & 0.020 & 0.688 & 1.965 & 1.770 & 2.983 & 3.000 & \(-0.2840467\) & 1.453664 \\ \hline II & 0.550 & 1.375 & 1.590 & 1.507 & 1.685 & 2.240 & \(-0.8999263\) & 3.923761 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Descriptive summary of data sets.