The Notes: If you inspect 50 automobile windshields and find 266 nonconformities, determine the upper and lower control limits for the c-charts.

Friday, September 19, 2014

The upper and lower class limits for the c-chart are given by the formula:

$\displaystyle{U}{C}{L}_{{c}}={\overline{{c}}}+{3}\sqrt{{\overline{{c}}}}$

$\displaystyle{L}{C}{L}_{{c}}={\overline{{c}}}-{3}\sqrt{{\overline{{c}}}}$

$\displaystyle{\overline{{c}}}$ = Number of defects/Observations

$\displaystyle{\overline{{c}}}=\frac{{266}}{{50}}={5.32}$

$\displaystyle{U}{C}{L}_{{c}}={5.32}+{3}\sqrt{{5.32}}$

$\displaystyle{U}{C}{L}_{{c}}={12.23953756}$

$\displaystyle{U}{C}{L}_{{c}}\approx{12.24}$

$\displaystyle{L}{C}{L}_{{c}}={5.32}-{3}\sqrt{{5.32}}$

$\displaystyle{L}{C}{L}_{{c}}={5.32}-{6.919537557}=-{1.599537557}$

$\displaystyle\therefore{L}{C}{L}_{{c}}={0}$

The Notes