## 3 Experimentation
### Grouping of Data
#### 3.2.3 Meta-Analysis Test Steps  
To check the level of heterogeneity meta-analysis test is used. It is a statistical technique for combining findings from independent studies. In the present study, variability of the failure data among the three engines for each subsystem is tested using Meta-analysis. Variability means differences in statistical results obtained between the individual failed data and pooled failure data for a particular subsystem [31; 32; 33]. In Table 4, the column \"downtime hours\" describes the total downtime hours of a particular engine for the problem related to a specific subsystem mentioned at the top of the table. The total run of the engine column indicates the total time in hours the engine has worked. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**S.No.**} & \multirow{2}{*}{
\begin{tabular}{c} **The** \\ **Subsystems** \\ \end{tabular} } & \multirow{2}{*}{**Event**} & \multirow{2}{*}{**Failures for Engine 1**} & \multirow{2}{*}{**Failures for Engine 2**} & \multirow{2}{*}{**Failures for Engine 3**} \\ \hline \multirow{6}{*}{\(1\)} & \multirow{6}{*}{Air supply} & \multirow{2}{*}{Failures} & Start & 0 & 0 & 0 \\ \cline{3-8}  & & End & & 9146 & & 8340 & 8756 \\ \cline{3-8}  & & & & & 422 & \(\bullet\) & 77 \\ \cline{3-8}  & & & & \(\bullet\) & 1022 & \(\bullet\) & 3662 \\  & & & & \(\bullet\) & 3058 & \(\bullet\) & 5335 \\  & & & & & \(\bullet\) & 4537 & \(\bullet\) & 5981 \\ \hline \multirow{6}{*}{\(2\)} & \multirow{6}{*}{Self-starting} & Start & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} \\ \cline{3-8}  & & End & & 9146 & & 8340 & 8756 \\ \cline{3-8}  & & & & \(\bullet\) & 1246 & \(\bullet\) & 423 & \(\bullet\) & 1920 \\  & & & & \(\bullet\) & 1290 & \(\bullet\) & 608 & \(\bullet\) & 2717 \\  & & & & \(\bullet\) & 2146 & \(\bullet\) & 1369 & \(\bullet\) & 3267 \\  & & & & \(\bullet\) & 3741 & \(\bullet\) & 2566 & \(\bullet\) & 3458 \\  & & & & \(\bullet\) & 4474 & \(\bullet\) & 3682 & \(\bullet\) & 4375 \\  & & & & \(\bullet\) & 8387 & \(\bullet\) & 7132 & \(\bullet\) & 5970 \\ \hline \multirow{6}{*}{\(3\)} & \multirow{6}{*}{Fuel supply} & Start & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} \\ \cline{3-8}  & & End & & 9146 & & 8340 & 8756 \\ \cline{3-8}  & & & & \(\bullet\) & 423 & & \(\bullet\) & 112 \\  & & & & \(\bullet\) & 663 & & \(\bullet\) & 412 \\  & & & & \(\bullet\) & 2122 & \(\bullet\) & 1326 & \(\bullet\) & 1851 \\  & & & & \(\bullet\) & 5978 & \(\bullet\) & 3362 & \(\bullet\) & 2076 \\  & & & & & & & \(\bullet\) & 4904 \\ \hline \multirow{6}{*}{\(4\)} & \multirow{6}{*}{Lubrication} & Start & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} \\ \cline{3-8}  & & End & & 9146 & & 8340 & 8756 \\ \cline{3-8}  & & & & & \(\bullet\) & 1584 & \(\bullet\) & 855 \\ \cline{3-8}  & & & & \(\bullet\) & 2566 & \(\bullet\) & 2341 & \(\bullet\) & 1970 \\  & & & & \(\bullet\) & 4844 & \(\bullet\) & 2579 & \(\bullet\) & 3473 \\  & & & & \(\bullet\) & 5270 & \(\bullet\) & 3570 & \(\bullet\) & 4840 \\  & & & & & \(\bullet\) & 4486 & \(\bullet\) & 5830 \\ \hline \multirow{6}{*}{\(5\)} & \multirow{6}{*}{Cooling} & Start & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} \\ \cline{3-8}  & & End & & 9146 & & 8340 & & 8756 \\ \cline{3-8}  & & & & & & & \(\bullet\) & 170 \\ \cline{3-8}  & & & & & \(\bullet\) & 1823 & \(\bullet\) & 278 \\ \cline{3-8}  & & & & \(\bullet\) & 3000 & \(\bullet\) & 497 \\ \cline{3-8}  & & & & \(\bullet\) & 3680 & \(\bullet\) & 1431 \\ \cline{3-8}  & & & & \(\bullet\) & 5104 & & \(\bullet\) & 1760 \\ \cline{3-8}  & & & & & & \(\bullet\) & 3909 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Common Beta Hypothesis test failure data in hours.