## 7 Reliability andMaintainability Study
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **T** & **B** & **F** & \\ \hline  & **Distribution** & **Shape Parameter** & **Scale Parameter** & **Threshold Parameter** \\ \hline
**M1** & PLP & 1.188240 & 2,897.780 & \\
**M2** & 3-Parameter Lognormal & 7.605470 & 0.608045 & \(-\)492.123 \\
**M3** & Loglogistic & 7.349810 & 0.629060 & - \\
**M4** & 3-Parameter Lognormal & 7.461030 & 0.662900 & \(-\)202.097 \\
**M5** & 3-Parameter Lognormal & 7.316650 & 0.745964 & \(-\)319.530 \\
**M6** & PLP & 3.854810 & 105,624.00 & - \\
**Line** & 3-Parameter Weibull & 1.172200 & 351.7110 & \(-\)0.504266 \\ \hline  & **T** & **T** & **R** & \\ \hline  & **Distribution** & **Shape parameter** & **Scale parameter** & **Threshold parameter** \\ \hline
**M1** & 3-Parameter Lognormal & 2.845020 & 0.881735 & 2.326200 \\
**M2** & Lognormal & 2.851880 & 0.751212 & - \\
**M3** & 3-Parameter Lognormal & 2.783340 & 1.027960 & 5.460160 \\
**M4** & 3-Parameter Weibull & 1.099800 & 19.270200 & 5.942560 \\
**M5** & 3-Parameter Logloglistic & 2.371370 & 0.517507 & 2.513060 \\
**M6** & 3-Parameter Loglogistic & 8.940480 & 0.001388 & \(-\)7570.100 \\
**Line** & 3-Parameter Lognormal & 2.768580 & 0.874643 & 2.122030 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimation of parameters for TBF and TTR at machine and line level. Figure 6: Probability density function, survival function, and hazard function TBF (**a**) and TTR (**b**) of the entire line are shown graphically in conjunction with the appropriate distributions andtheir statistics. The reliability diagram of the complete manufacturing system and each machine is depicted in Figure 7. The subsequent observations can be formulated: (a) to accomplish a 75% reliability standard for the pasteurization/homogenization machine (M1), the maintenance has to be executed before 960 min or 16 hours or 2 shifts. In other words, for a 75% success in the reliability level of the M1, the maintenance staff should plan preventive maintenance immediately after two working days of operation. (b) For \(\text{Rsyst}\) (240) = 0.5270 meaning that the line shall not fail for 240 min of function with solely a 52.70% probability. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Time** & **Rel M1** & **Rel M2** & **Rel M3** & **Rel M4** & **Rel M5** & **Rel M6** & **Rel Line** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 5: Reliability at machine and the entire ice cream level for different time intervals. Figure 7: Diagram at machine and the entire ice cream manufacturing system level. Maintainability is the possibility that a failed machine/component or complete manufacturing system will be reinstated to functional effectiveness during a time period when the restoration is carried out in accordance with the specified procedures [56], hence, it is the likelihood of restoration in a particular time period. In other words, maintainability is marked as a measurement of how readily a product can be maintained or repaired. Therefore, excellent maintainability of a product is going to expand the product's serviceability and reparability, lessen the expense of maintenance, and guarantee that the product would meet requirements for its determined usage [57]. In Table 6, maintainability of the complete manufacturing system and each machine is estimated for various time periods, the subsequent observations can be made: (a) for Msyst (60) = 0.9298, meaning there is a 92.98% possibility that any malfunction in the ice cream system is going to be repaired in 60 min. (b) The shortest maintainabilities are noted at the exogenous machine (M6), and the ice cream machine (M3). The maintainability should be upgraded chiefly on those machines along with the complete manufacturing system. (c) A 100% possibility exists that any collapse in the ice cream production system shall be repaired in t > 150 min.