Question

Assume you have a process that consists of a 1 page form that you require customers to fill-out. On the form there are 10 fields that have to be filled-in (so it’s possible to have 10 different errors on this form). This month you had 500 forms completed but discovered 40 defects. What is the SQL for the overall process?

Select one:

a. 3.0

b. 3.9

c. 2.2

d. 2.9

Answer 1

$\dpi{100} \fn_cm Total\ number\ of \ defects=\sum_{i=1}^{500} d_i =40\\ The\ estimate \ of \ population \ fraction \ defective\bar{p}= \sum_{i=1}^{500} d_i/ n=40/500=0.08\\ now \ control\ limits for \ fraction \ defective\\ U.C.L_p=\bar{p}+3\sqrt(\frac{\bar p*\bar q}{n})=0.08+3\sqrt(\frac{0.08*0.02}{500})=0.0800096\\ C.L_p=\bar{p}=0.08\\ L.C.L_p=\bar{p}-3\sqrt(\frac{\bar p*\bar q}{n})=0.08+3\sqrt(\frac{0.08*0.02}{500})=0.0799$