Question

I need help with the UCL R. I am not sure what I am doing wrong. Thank you!

A process that is considered to be in control measures an ingredient in ounces. Below are the last 10 samples (each of size n- 5) taken. The population process standard deviation is 1.64 Samples 2 3 456 7 8 910 910 13 10 11 9 10 1289 9 9 9 10 9 10 16 71 9 10 10 10 8 9 7 13 8 11 10 10 99 8 10 78 13 a) Standard deviation of the sampling means .733 ounces (round your response to three decimal places). b) With z -3, the control limits for the mean chart are: UCL 12.179 ounces (round your response to three decimal places). LCL7.781 ounces (round your response to three decimal places) c) The control limits for the R-chart are: UCLR 93 ounces (round your response to three decimal places) Enter your answer in the answer box and then click Check Answer.

Answer 1

C) To calculate the upper control limit for the R-chart we have to first calculate the range or R of each set of samples and then calculate the R-bar

Where, Range or R = The difference between the highest and lowest value in each set

R-bar = Sum of R of each set of samples / number of sets of samples

So using the above formula the range or R of each set of samples are

• For set 1 = 11-8 = 3
• For set 2 = 12-9 = 3
• For set 3 = 13-9 = 4
• For set 4 = 11-9 = 2
• For set 5 = 12-8 = 4
• For set 6 = 13-8 = 5
• For set 7 = 10-8 = 2
• For set 8 = 16-7 = 9
• For set 9 = 13-7 = 6
• For set 10 = 13-8 = 5

R-bar = (3+3+4+2+4+5+2+9+6+5)/10 = 43/10 = 4.3

For sample size of 5 the factor for control limits for range(D4) = 2.114 (obtained from table of constraints for X-bar and R chart)

UCL R = R-bar x D4 = 4.3 x 2.114 = 9.090