Question

The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box-filling line to be set so that the process average weight per packet is 42grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of 8packets and weighs each packet. When the process is in control, the range in the weight of each sample has averaged 6 grams. a. Design an R- and an x overbarx-chart for this process. The UCL Subscript Upper RUCLR equals grams and the LCL Subscript Upper RLCLR equals grams. (Enter your response rounded to two decimal places.) The UCL Subscript x overbarUCLx equals grams and the LCL Subscript x overbarLCLx equals grams. (Enter your responses rounded to two decimal places.) b. The results from the last 5 samples of 8packets are shown below. Is the process in control? Explain.                                                                                Sample x overbarx R 1 41 10 2 43 3 3 42 8 4 41 5 5 40 7 The process variability is ___statistical control and the process average is ____statistical control. Therefore, the entire process is ___control.

Answer 1

a)

For sample size = 8, A2 = 0.373, D3 = 0.136 and D4 = 1.864

UCLR = D4*R-bar = 1.864*6 = 11.184 = 11.18 grams (Rounded to 2 decimal places)
R-bar = 6 grams
LCLR = D3*R-bar = 0.136*6 = 0.816 = 0.82 grams (Rounded to 2 decimal places)

UCLx-bar = x-bar-bar + A2*R-bar = 42+0.373*6 = 44.238 = 44.24 grams (Rounded to 2 decimal places)
x-bar-bar = 42 grams
LCLx-bar = x-bar-bar - A2*R-bar = 42-0.373*6 = 39.762 = 39.76 grams (Rounded to 2 decimal places)

b)

Sample	xBar	R
1	41	10
2	43	3
3	42	8
4	41	5
5	40	7

Graph Data

Sample	xBar	x-bar-bar	LCL	UCL
1	41	42	39.762	44.238
2	43	42	39.762	44.238
3	42	42	39.762	44.238
4	41	42	39.762	44.238
5	40	42	39.762	44.238

Graph Data

Sample	Range	R-bar	LCL	UCL
1	10	6	0.816	11.184
2	3	6	0.816	11.184
3	8	6	0.816	11.184
4	5	6	0.816	11.184
5	7	6	0.816	11.184

As all the sample mean(x-bar) and sample range (R) fall within control limits of x-bar and R-chart we can say , The process variability is in statistical control and the process average is in statistical control. Therefore, the entire process is in control.