Problem 2 (determine the appropriate sample size for p-chart) A fraction nonconforming control chart is to be established with a center line of 0.01 and two-sigma control limits. (a) How large should the sample size be if the lower control limit is above zero

n > 396 or n≥ 397

Step-by-step explanation:

Given

Center line, p = 0.01

2 sigma control limit, L=2;

For a 2 sigma control limit, the size of the sample size if the lower control limit is > 0 is given as;

n > ((1-p) / p) L²

Substitute 2 for L and 0.01 for p in the above expression

n > ((1-p) / p) L² becomes

n > ((1-0.01) / 0.01) * 2²

n > ((0.99/0.01)) * 2²

n > 99 * 2²

n > 99 * 4

n > 396

So, the sample size should be greater than 396 (at least 397).

We can represent it as

n > 396 or n≥ 397