2. A process is being controlled with an np-chart, and it is known that when the

Question

2. A process is being controlled with an np-chart, and it is known that when the A process is in control, the proportion ofdefective products is 0.02. Three-sigma control limits are used and the procedure calls for taking daily samples of n=100 items a) (10 pts) What are the 3-sigma control limits this control chart? b) (10pts) What is for this control chart? c) (10 pts) If the proportion of defective products were to suddenly shift to 0.05, what is the probability that the shift would be detected on the first subsequent sample? ARL (Spts) For the shifted proportion of part c), what is the probability it is detected within two samples? d) 02 -01)-22 LcL uuot

Explanation / Answer

2. a)

np-charts are the contro charts for attributes, used for sample of equal size, n.

Here, n=100

proportion of defective product (p)=0.02

Total number of defective products (np) = 100(0.02)=2

Hence, For three sigma, Upper Control Limit = np+3p = np+ 3 [np(1-p)]1/2 = 2+ 3[2(1-0.02)]1/2= 6.2

and Lower Control Limit = np+3p = np- 3 [np(1-p)]1/2 = 2- 3[2(1-0.02)]1/2= -2.2

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