Question

(10 points) An np chart is to be established on a painting process that is in statistical control. If 35 pieces are to be inspected every 4 h and the fraction nonconforming is 0.06, determine the central line and control limits.

Answer 1

SOLUTION:-

$\Rightarrow$ Calculate the central line limit for the given system,

CL=nx po

Here, Number in the sample or subgroup is n, and proportion or fraction nonconforming in the samples is _{$p_{0}$}

Substitute 35 for n, and 0.06 for $p_{0}$ in the above equation,

npo = 35 (0.06) = 2.1

Therefore the central limit is 2.1

$\Rightarrow$ Calculate the upper control limit for the above system,

UCL = npo + npo(1 - po)

Substitute 35 for n, and 0.06 for $p_{0}$ in the above equation,

UCL = 35(0.06) + 35(0.06)(1 - 0.06) = 6.31

Therefore the required upper control limit is 6.31

$\Rightarrow$ Calculate the lower control limit for the above system,

LCL = npo - npo(1 - po)

Substitute 35 for n, and 0.06 for $p_{0}$ in the above equation,

LCL = 35(0.06) - /35(0.06)(1 – 0.06) = -2.1lor0.0

Therefore the required lower control limit is 0.