A company is checking in the second part of the year the behaviour of the sample proportion p of defective items. The operator takes not of the items requiring rework and the total weekly production over $30$ weeks $($from week $23$ to $52).$

Week

Subgroup no$.$

Requiring rework

Total production

Proportion $($p$)$

$23$

$1$

$44$

$3571$

$0\mathrm{.}01232148$

$24$

$2$

$59$

$3623$

$0\mathrm{.}01628485$

$25$

$3$

$33$

$3554$

$0\mathrm{.}00928531$

$26$

$4$

$40$

$3753$

$0\mathrm{.}01065814$

$27$

$5$

$21$

$2562$

$0\mathrm{.}00819672$

$28$

$6$

$36$

$3492$

$0\mathrm{.}01030928$

$29$

$7$

$16$

$3280$

$0\mathrm{.}00487805$

$30$

$8$

$32$

$3881$

$0\mathrm{.}0082453$

$31$

$9$

$13$

$3866$

$0\mathrm{.}00336265$

$32$

$10$

$12$

$3949$

$0\mathrm{.}00303874$

$33$

$11$

$48$

$3674$

$0\mathrm{.}01306478$

$34$

$12$

$65$

$3586$

$0\mathrm{.}01812605$

$35$

$13$

$65$

$3140$

$0\mathrm{.}02070064$

$36$

$14$

$70$

$3673$

$0\mathrm{.}01905799$

$37$

$15$

$48$

$3619$

$0\mathrm{.}01326333$

$38$

$16$

$33$

$3455$

$0\mathrm{.}00955137$

$39$

$17$

$33$

$3696$

$0\mathrm{.}00892857$

$40$

$18$

$64$

$3811$

$0\mathrm{.}01679349$

$41$

$19$

$38$

$3835$

$0\mathrm{.}00990874$

$42$

$20$

$28$

$3818$

$0\mathrm{.}00733368$

$43$

$21$

$82$

$3938$

$0\mathrm{.}02082275$

$44$

$22$

$80$

$3843$

$0\mathrm{.}02081707$

$45$

$23$

$29$

$4134$

$0\mathrm{.}007015$

$46$

$24$

$46$

$3663$

$0\mathrm{.}01255801$

$47$

$25$

$33$

$3391$

$0\mathrm{.}00973164$

$48$

$26$

$1$x

$4$x$52$

to be calculated

$49$

$27$

$2$y

$3$y$46$

to be calculated

$50$

$28$

$1$z

$41$z$8$

to be calculated

$51$

$29$

$1$t

$39$t$6$

to be calculated

$52$

$30$

$1$x

$38$y$4$

to be calculated

Note: please substitute the letters $"$x$","$y$","$z$"$ and $"$t$"$ with:

$-"$x$"-->$ the second number of your student ID

$-"$y$"-->$ the third number of your student ID

$-"$z$"-->$ the fourth number of your student ID

$-"$t$"-->$ the fifth number of your student ID

So$,$ should your student ID be: $14680841$:

$-$ x $-->4$

$-$ y $-->6$

$-$ z $-->8$

$-$ t $-->0$

You are requested to:

Fill out the table with the remaining values of sample proportion based on your specific student ID;

Choose the correct SPC chart to represent the problem;

Calculate UCL and LCL for the relevant chart$/$s;

Comment on the overall process and on specific samples.