The given data is m = 30 pbar = 1.00 - 0.90 = 0.10 n = 25 Upper Control Limit =

Question

The given data is

m = 30

pbar = 1.00 - 0.90 = 0.10

n = 25

Upper Control Limit = UCL = pbar + 2 * sqrt (pbar * (1-pbar) / n)

So, UCL = 0.1+2*sqrt(0.1*(1-0.1)/25) = 0.22

And Lower Control Limit = LCL = pbar - 2 * sqrt (pbar * (1-pbar) / n)

So, UCL = 0.1 - 2*sqrt(0.1*(1-0.1)/25) = -0.02

a) So, UCL = 0.22 and LCL = -0.02

b) Tighter Control Limits can be obtained by drawing bigger sample size.

c) Now, n=100. So the new 2 Sigma control limits are :

Upper Control Limit = UCL = pbar + 2 * sqrt (pbar * (1-pbar) / n)

So, UCL = 0.1+2*sqrt(0.1*(1-0.1)/100) = 0.16

And Lower Control Limit = LCL = pbar - 2 * sqrt (pbar * (1-pbar) / n)

So, UCL = 0.1 - 2*sqrt(0.1*(1-0.1)/100) = 0.04

So, UCL = 0.16 and LCL = 0.04

d) The 3 sample data proportion defective are 0.08, 0.13 and 0.03 and the limits are UCL=0.16 and LCL=0.04

The 2 data 0.08 and 0.13 lie between UCL and LCL but the data 0.03 is outside as it is lesser than 0.04.

So, we can say that the process is not in control. So, the process must be corrected or we can set 3 Sigma limits so that process will be in control.

Explanation / Answer

2. A process producing TV tubes has an average yield of 90%, based on 30 samples. Samples taken for inspection have a size of 25.

a. Set up 2 sigma control limits for the mean proportion defective.

b. How can we obtain tighter control limits?

c. Suppose samples of size 100 are taken. What are the new control limits?

d. Three samples, each of size 100, are taken; the numbers defective are 8, 13, and 3. Is the process in control? What action, if any, should be taken?

Please show step by step solution

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