Question

Tom is the quality control manager for the company XYZ. XYZ recently received some complaints about its product A's quality and the general manager Steve requested Tom to investigate it. To gain a better understanding of the production process, Tom decided to use p-chart to monitor and identify the assignable cause variations. For the next 8 working days, Tom collected 8 samples (each of the size 100 units) and found the following number of defects, 4, 6, 0, 1, 3, 5, 8, 3.
a. What is the defect rate for sample 2? Ignore the percentage sign, and round your answer to the nearest integer. For example, if your answer is 12.34%, input 12.

Your answer is .

b. What is p-bar? Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34. (Note that this is different from question a.)

Your answer is .

c. What is sigma? Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34.

Your answer is .

d. What is upper control limit UCL for this p-chart? Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34.

Your answer is .

e. What is lower control limit LCL? (If LCL is negative, input 0) Ignore the percentage sign, and round your answer to two decimals. For example, if your answer is 12.34%, input 12.34. If your answer is -1.234%, input 0.

Your answer is .

f. How many outlier(s) is(are) identified? Round your answer to the nearest whole number. For example, if the answer is 3.12, input 3.

Your answer is

Answer 1

Answer:

Answer a= Defect rate of sample 2= 6/100 =6

Answer b=

Data  % defect % defect

4      4/800            0.005

6     6/800           0.0075

0     0/800                 0

1      1/800           0.00125

3      3/800           0.00375

5      5/800           0.00625

8      8/800              0.01

3     3/800          0.00375

Sum            0.0375

p bar =0.0375

Answer c= sigma = [p bar(1-p bar) / sample size]]0.5

Sigma = (0.0375*(1-0.0375)/100)^0.5 =0.019

Answer d= UCL=p bar + 3*(Estimated standard deviation) = 0.0375+3*0.019 =0.0945

Answer e= LCL=p bar - 3*(Estimated standard deviation) =0.0375-3*0.019 =-0.0195=0