## 7 Reliability andMaintainability Study
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **T** & **B** & **F** & \\ \hline
**Distribution** & **M1** & **M2** & **M3** & **M4** & **M5** & **M6** & **Line** \\ Weibull & - & 0.425 & 0.682 & 0.881 & 0.624 & - & 4.347 \\ Lognormal & - & 1.771 & 1.217 & 0.429 & 3.839 & - & 16.91 \\ Exponential & - & 2.338 & 0.802 & 3.644 & 0.873 & - & 7.217 \\ Loglogistic & - & 0.907 & 0.486 * & 0.345 & 1.531 & - & 11.44 \\
3-Parameter Weibull & - & 0.525 & 0.682 & 0.77 & 0.599 & - & 4.239 * \\
3-Parameter Lognormal & - & 0.399 * & 0.487 & 0.335 * & 0.542 * & - & 4.7 \\
2-Parameter Exponential & - & 2.017 & 0.930 & 3.116 & 0.904 & - & 7.203 \\
3-Parameter Loglogistic & - & 0.422 & 0.513 & 0.349 & 0.627 & - & 5.642 \\ Smallest Extreme Value & - & 7.627 & 6.412 & 7.909 & 7.969 & - & 20.43 \\ Normal & - & 2.739 & 4.146 & 3.974 & 3.425 & - & 7.085 \\ Logistic & - & 1.719 & 3.292 & 2.62 & 2.746 & - & 5.66 \\ \hline  & & & **T** & **T** & **R** & & \\ \hline
**Distribution** & **M1** & **M2** & **M3** & **M4** & **M5** & **M6** & **Line** \\ Weibull & 2.07 & 1.212 & 2.084 & 1.33 & 2.998 & 3.086 & 7.088 \\ Lognormal & 0.938 & 1.015 * & 1.053 & 1.005 & 0.801 & 3.105 & 1.729 \\ Exponential & 5.202 & 3.776 & 3.526 & 5.943 & 5.819 & 3.329 & 18.81 \\ Loglogistic & 1.185 & 1.121 & 1.138 & 1.149 & 0.776 & 2.698 & 2.501 \\
3-Parameter Weibull & 0.936 & 1.513 & 0.755 & 0.618 * & 1.472 & 2.695 & 3.058 \\
3-Parameter Lognormal & 0.832 * & 1.262 & 0.622 * & 0.884 & 0.591 & 2.839 & 1.119 * \\
2-Parameter Exponential & 1.317 & 1.281 & 0.832 & 0.895 & 1.913 & 3.318 & 5.683 \\
3-Parameter Loglogistic & 0.985 & 1.436 & 0.630 & 0.932 & 0.585 * & 2.436 * & 1.692 \\ Smallest Extreme Value & 15.281 & 13.35 & 8.133 & 5.161 & 14.75 & 2.697 & 58.28 \\ Normal & 6.904 & 4.02 & 5.093 & 2.85 & 8.442 & 2.839 & 26.02 \\ Logistic & 4.195 & 2.553 & 3.844 & 2.635 & 4.713 & 2.437 & 16.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The Anderson–Darling statistics for TBF and TTR at machine and line level. The smaller the statistic value. the better the model fitting (i.e., in column of M2 for TBF the lowest value is 0.399 which belongs to the 3-parameter lognormal distribution). The survival functions, probability density functions, probability plot, and repair/hazard functions of TBFs and TTRs and their statistics throughout the entire ice cream manufacturing system are shown in Figure 6. It was pointed out that: (a) initially the TBF has an expanding failure rate reaching 95 min following a lessening failure rate, proving that solely during the first 95 min of function, subsequent to a stoppage (due to a malfunction), the system has a real possibility of failure, then once time progresses this likelihood is decreased. (b) The TTR has an expanding repair rate reaching 10.5 min. Provided the repair process has not been concluded in the initial 10.5 min, in that case, the possibility to repair the failure lessens with time. Table 5 depicts the reliability of the complete system and each machine for various time periods, and the subsequent observations can be formulated: (a) the reliability of the manufacturing system, during the function of one hour is 88.06%, in 8 h (work period) or 480 min of function it is 23.65%, (b) the longest reliabilities are formulated at the pasteurization/homogenization machine (M1), and exogenous machine (M6), and (c) the shortest reliabilities are noted at the machine's packaging machine (M5), and freezer tunnel (M4).