Question

Please help me solve question 5.

5. 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 1.36 SAMPLES 10 7 4 3 2 1 10 8 13 10 7 12 10 13 7 10 12 10 7 10 10 10 9 12 10 11 11 10 12 10 12 10 11 11 10 12 8 9 10 12 11 10 12 a) What is ? b) Ifz 3, what are the control limits for the mean chart? c) If the population process standard deviation is unknown, what are the control limits for the mean chart? What are the control limits for the range chart? d) Is the process in control?

Answer 1

Compute X and R for each sample X is computed as average of the observations for each sample Plot control charts using Xbar, R and control limits R is computed by subtracting the minimum value from the maximum value of each sample Observations LCL UCL UCLR R-chart X-chart Sample # X CL CLR LCLR 1 2 4 5 R #1 10 12 9,60 4 9.86 7.67 12.05 3.80 0.00 8.03 TRUE TRUE TRUE #2 7 11 11 10 9.60 4. 9.86 7,67 12.05 3.80 0.00 8.03 TRUE #3 13 10 10 11 10.60 4 9.86 7.67 12.05 3.80 0.00 8.03 TRUE TRUE TRUE #4 10 10 11 10 12 10.60 2 9.86 7.67 12.05 3.80 0.00 8.03 TRUE # 5 12 10 11 10 10.40 9.86 7.67 12.05 3.80 0.00 8.03 TRUE TRUE 12.05 # 6 7 10 8 12 9 9.20 5 9.86 7.67 3.80 0.00 8.03 TRUE TRUE # 7 10 7 10 8 8.80 3 9.86 7.67 12.05 3.80 0.00 8.03 TRUE TRUE 3.80 #8 13 10 8 10 8 9.80 5 9.86 7.67 12.05 0.00 8.03 TRUE TRUE # 9 8 8 12 12 9.80 4. 9.86 7.67 12.05 3.80 0.00 8.03 TRUE TRUE TRUE TRUE 10 # 10 12 9 12 10.20 4 9.86 7.67 12.05 3.80 0.00 8.03 Average 9.860 3.800 Compute X and R R-Chart R- XX, +...X, = 9.860 8 k k 7 6 R, +R RR = 3.800 R 5 k k Control chart constants corresponding to sample size N 3 Sample size, N 5 0 D3 1 2.114 D4 0 = 0.577 2 4 5 6 7 9 10 A2 Control limits for X-chart X-Chart Control limits for R-chart 14.00 UCLX A,R UCLr DR= 8.033 12.053 12.00 = 10.00 LCLX -A,R LCLr D,R 0.000 7.667 = 8.00 Process control 6.00 oX-value lie outside of control limits. 4.00 Therefore based on X-chart, the process is In Control 2,00 O R-value lie outside of control limits. 0.00 1 2 4 5 6 7 10 Therefore based on R-chart, the process is In Control st m.

a)

Mean = 9.86

b) Using the given process standard deviation,

UCL = 9.86+3*1.36 = 13.94

LCL = 9.86-3*1.36 = 5.78

c) Control limits for mean (Xbar-chart) are:

UCL = 12.053

LCL = 7.667

Control limits for the range chart are following:

UCL = 8.003

LCL = 0

d) Yes, the process is in control