Problem $10-23($Algo$)$

Ten samples of $15$ parts each were taken from an ongoing process to establish a p$-$chart for control. The samples and the number of defectives in each are shown in the following table:

SAMPLE n NUMBER OF DEFECTIVE ITEMS IN THE SAMPLE

$1151$

$2153$

$3152$

$4150$

$5153$

$6152$

$7150$

$8153$

$9153$

$10153$

Determine the p$$

$,$ Sp

$,$ UCL and LCL for a p$-$chart of $95$ percent confidence $(1\mathrm{.}96$ standard deviations$).$