Q$1.$ Our shoe manufacturing company wants to improve its processes by considering the errors and inaccuracies in production processes. We want to apply p$-$chart and c$-$chart models and compare the results. Accordingly, determine the UCL and LCL values of the company according to each of the two models and display them on the graph. Sample size: $100$ products.

$\backslash$table$[[$Sample$,$Number of defects,Proportion defective$],[1,7,0\mathrm{.}07],[2,4,0\mathrm{.}04],[3,6,0\mathrm{.}06],[4,8,0\mathrm{.}08],[5,6,0\mathrm{.}06],[6,0,0\mathrm{.}00],[7,4,0\mathrm{.}04],[8,8,0\mathrm{.}08],[9,9,0\mathrm{.}09],[10,12,0\mathrm{.}12],[11,4,0,04],[12,7,0,07]]$

Q$2.$ Considering the results, the company implemented the $x-$chart model to improve its logistics activities. Below are the stages from the products obtained after production until they are delivered to the customers. Finally, apply the method and calculate the UCL and LCL values. Please comment on the company's control limits and defects, $)=3$;$=0,502$;$n=(100$

$\backslash$table$[[$Sample$,$Collecting,Labelling,Warehousing,Transportation,Delivery$],[1,3\mathrm{.}87,4\mathrm{.}02,5\mathrm{.}50,5,20,5\mathrm{.}30],[2,4,05,4,07,5\mathrm{.}20,5,00,4\mathrm{.}90],[3,3,96,4,05,5\mathrm{.}00,4,56,4,95],[4,3,91,4,10,4,96,4\mathrm{.}68,4,82],[5,3\mathrm{.}68,3\mathrm{.}95,4\mathrm{.}99,5,20,4,87],[6,3,72,3,99,4,85,5\mathrm{.}50,4\mathrm{.}88],[7,3,87,4,03,5,30,5,10,4,94],[8,3,86,4,03,5\mathrm{.}60,4\mathrm{.}89,5\mathrm{.}10],[9,3,95,4,12,4,94,4\mathrm{.}91,5\mathrm{.}20],[10,3\mathrm{.}90,4,16,4,93,5\mathrm{.}01,4,90]]$