Buffer Capacity

To show the global effect of each pattern on TR and simplify the analysis, average TR results for experiments with different $P_{A}$ were calculated. For instance, results for a balanced $P_{A}(-)$ were calculated as the average TR of experiments with patterns $(-,-),(-, /),(-,),(-, \Lambda$, and $(-, \mathrm{V})$. Furthermore, as TR results have very different magnitudes for different $\varepsilon$ and $\alpha$ values, Fig. 2 shows "normalised" TR results (nTR), which were calculated by dividing the average TR results of each $P_{A}$ by the average overall TR value of all experiments with the same $N, \varepsilon, \alpha$ and $\mathrm{BC}$ values. It is worth noting that results regarding $\mathrm{P}_{\mathrm{B}}$ are not shown as they were equivalent. Full TR results with their corresponding Dunnett's and Tukey's tests results can be found in the "A ppendix", Tables 4 and 5 , respectively.

Fig. 2 nTR results for $P_A$ with $a N = 5$, $b N = 8$ and $c N = 11$

Results shown in Fig. 2 suggest that the performance of buffer allocation patterns is highly dependent on the values of $N, \varepsilon$ and $\alpha$. For example, the ascending $P_{A}$(/) performed very well with $\varepsilon=70 \%$, which was only outperformed by the balanced pattern when $B C = 6$ and $\alpha < 3$ for lines with $N \geq 8$. Figure 2 also suggests that the balanced pattern performs better with increasing values of $\mathrm{N}, \mathrm{BC}$ and $\varepsilon$, while the ascending pattern performs better with decreasing values of $N, B C$ and $\varepsilon$, and increasing values of $\alpha$. These results are also confirmed by Tables 4 and 5, as experiments with the pattern (/ , /) were found to have statistically significant differences with the control (balanced pattern) only when $\varepsilon = 70 \%$. Thus, increasing values of $\varepsilon$ resulted in lesser relative differences among the patterns, suggesting that the effect of buffer allocation patterns on TR is highly dependent on the reliability of the machines.

On the other hand, the descending $P_{A}$ ( \ ) was the worst pattern in terms of TR for all scenarios, a result confrmed by Tables 4 and 5 as experiments with the pattern (\ , \) had the lowest TR in all experimental conditions. Interestingly, the bowl ($V$) and inverted bowl patterns ($\Lambda$) changed their relative performance with increasing $N$ values, since the ($\Lambda$) pattern was almost on par with the good performance of ($-$) when $N = 8$ for some scenarios; whereas the ($V$) pattern seemed to have an overall good performance for scenarios with $\mathrm{N}=11, \mathrm{BC}=6$ and $\alpha \geq 2$.

Similar to Fig. 2, Fig 3 shows the normalised ABL results ($nABL$) showing the relative performance in each experimental scenario (different values of $N, \varepsilon, \alpha$ and $BC$) per $P_A$.

Fig. 3 $nABL$ results for $P_A$ with $a N = 5, b N = 8$ and $c N = 11$

Figure 3 suggests that ABL results are more consistent than TR results in terms of $P_A$ performance, since the ascending pattern is always the best-performing (with lower ABL) and the descending pattern is always the worst. Tables 6 and 7 in the "Appendix" confirm this conclusion by showing that the best pattern in terms of ABL for all scenarios is (/,/), while the worst pattern for almost all scenarios is (\,\). Contrary to the interaction effect between $P_A$ and $\varepsilon$ on TR, higher values of $\varepsilon$ resulted in a higher influence of $P_A$ on ABL, especially with lower values of $N$.

The Analysis of Variance test (Table 2) shows that both reliability-related factors ($\varepsilon$ and $\alpha$) have the highest influence on $TR$, followed by $BC$ and the interaction between $\varepsilon$ and $\alpha$. As seen in Figs. 2 and 3, the interactions between $BP$ and $BC$, $N$, $\varepsilon$ and $\alpha$ are also significant, albeit they have a lower effect on $TR$ when compared to single factors. For ABL, $BC$ is the most important factor, followed by $BP$ and the interaction between $BP$ and $BC$. Therefore, the performance of ABL is more dependent on selecting a good (bad) pattern.

Table 2 Analysis of variance test for TR and ABL