Example $($Unequal sample sizes$)$: A factory manufacturing small bolts. To check the quality of the bolts, the manufacturer selected $10$ samples of different sizes from the manufacturing process time to time. $H\frac{e}{?}$ she visually inspected each selected bolt for certain defects. After the inspection, he$/$she obtained the following data:

$\backslash$table$[[\backslash$table$[[$Sample$],[$Number$]],1,2,3,4,5,6,7,8,9,10],[$Sample size,$200,100,200,400,100,100,200,250,50,100],[\backslash$table$[[$Number of$],[$Defectives$]],10,4,8,24,8,3,2,5,5,10]]$

Find center line, upper and lower control limits and construct p$-$chart. Does the process appear to be under control with respect to the proportion of defective bolts?

Solve this example yourself