## 4 Data Analysis and Results
### Mean Time between Failures  
The mean time between failures plays a major role in the reliability investigations. It has a significant contribution to the maintenance scheduling and cost prediction. Figure 3 shows the mean time between failures of each component in the unloading system. Clearly, the differential pressure transmitter and the pressure transmitter have the longest time intervals without failures. This is of no surprise to the industry practitioners due to the nature of the instrumentation operation and material of construction. On the other hand, the positive displacement pump and the positive displacement flow meter have the shortest time intervals between consecutive failures due to the design complexity of the rotating mechanisms within the two components. Most importantly, any failure of the flow meter needs to be detected as early as possible to avoid uncertainty variation in fluid measurements. In addition, the strainer has a short period between consecutive failures because usually, such filtration systems need a continuous cleaning of its internal parts and the failures of these components can be observed without a regular frequent cleaning. Therefore, the frequent cleaning of the strainer will lead to an increase in the mean time between the failures. It is noted that all the valves have a medium time between failures, while piping spools have long time intervals between failures. According to some studies discussed earlier in the literature review section, the air eliminator has a relatively low mean time between failures due to the complex design in the separation process that takes place in this portion of the system. In addition, the unloading arms also have a relatively low mean time between failures compared to the piping spools due to the dynamic nature of the swivel joints that connects the arm parts together and the excessive movement they experience externally.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Units Tested** & **Number of Failures** & **Duration (hours)** & **\(\lambda\) (I/hours)** & **MTTF (hours)** \\ \hline UA & 14 & 1 & 25,920 & \(2.75573\times 10^{-6}\) & 362,880 \\ \hline BV & 316 & 328 & 9,324,700 & \(1.11315\times 10^{-7}\) & 8,983,552 \\ \hline PDP & 7 & 3 & 25,920 & \(1.65344\times 10^{-5}\) & 60,480 \\ \hline CV & 14 & 2 & 25,920 & \(5.51146\times 10^{-6}\) & 181,440 \\ \hline GV & 177 & 240 & 3,852,300 & \(3.5198\times 10^{-7}\) & 2,841,071 \\ \hline PZV & 278 & 272 & 7,169,800 & \(1.36464\times 10^{-7}\) & 7,327,957 \\ \hline FM & 7 & 4 & 25,920 & \(2.20459\times 10^{-5}\) & 45,360 \\ \hline PV & 7 & 1 & 25,920 & \(5.51146\times 10^{-6}\) & 181,440 \\ \hline FCV & 316 & 328 & 9,324,700 & \(1.11315\times 10^{-7}\) & 8,983,552 \\ \hline DPT & 55 & 4 & 1,467,500 & \(4.95586\times 10^{-8}\) & 20,178,125 \\ \hline LS & 76 & 37 & 1,862,400 & \(2.61406\times 10^{-7}\) & 3,825,470 \\ \hline PT & 55 & 4 & 1,467,500 & \(4.95586\times 10^{-8}\) & 20,178,125 \\ \hline AE & 50 & 174 & 3,725,900 & \(9.34003\times 10^{-7}\) & 1,070,661 \\ \hline ST & 14 & 8 & 25,920 & \(2.20459\times 10^{-5}\) & 45,360 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Unloading system component test details and results.