Question

The data for 30 samples of 8 measurements each were collected from a process at Hawkeye Plastics. They’ve asked you to create an x ̅-chart and an s-chart for the process and to interpret the results for them.

a) What values will be used for the centerline, upper control limit, and lower control limit of each chart? (You only need to make a table of the values to answer this question and others like it in this assignment.)

b) Create the control charts.

c) Does the process appear to be in statistical control? Why or why not?

d) The specification for this process is 4.3 ± 1.4. Does the process appear capable of meeting this specification? Why or why not?

Hawkeye Plastics

Sample Data (n = 8)

1 3.9 3.9 4.5 4.2 3.6 4.3 3.8 4.0

2 3.8 4.0 4.5 4.1 3.6 3.7 4.3 3.7

3 3.3 3.9 4.8 4.4 3.7 3.4 3.6 3.7

4 3.6 3.7 4.0 4.4 3.9 3.4 3.4 3.8

5 4.3 3.7 3.6 4.7 3.9 4.4 4.1 4.0

6 3.7 4.4 4.3 4.5 3.8 3.9 4.0 3.7

7 3.4 3.8 3.6 3.6 3.6 4.2 4.4 3.7

8 3.4 3.5 3.6 3.6 4.1 3.5 4.0 3.7

9 4.0 3.7 4.2 3.9 3.5 4.4 3.9 3.5

10 3.7 3.5 3.9 3.9 4.0 3.3 4.2 3.8

11 4.2 3.8 3.9 3.9 3.5 3.7 3.6 3.6

12 3.5 3.9 3.8 3.8 3.5 4.2 3.6 4.3

13 4.1 3.9 3.3 4.1 3.9 3.9 4.3 3.6

14 3.3 3.6 3.9 3.8 4.0 4.0 3.9 3.4

15 3.7 3.7 3.5 3.3 3.7 3.9 3.9 3.4

16 3.6 3.7 4.1 3.7 3.4 3.7 3.8 4.4

17 3.9 3.5 3.9 4.0 3.4 3.7 4.0 3.7

18 3.6 4.1 3.8 3.8 4.4 4.0 3.8 4.0

19 4.1 4.5 4.7 3.9 3.7 3.8 3.3 3.7

20 3.5 3.8 4.2 4.6 4.2 3.3 3.7 3.4

21 4.5 3.2 4.7 3.9 4.1 3.7 3.7 4.0

22 3.1 3.8 3.5 4.0 3.6 3.6 3.7 3.6

23 3.5 4.2 4.1 3.9 3.6 4.1 4.0 3.3

24 3.8 4.2 3.9 3.7 4.1 3.5 3.8 3.6

25 4.2 3.9 3.9 3.7 3.9 4.0 3.5 3.6

26 4.1 4.0 4.3 4.0 3.9 3.5 3.7 4.2

27 4.0 3.5 3.8 3.8 3.8 3.4 3.5 3.9

28 3.9 4.1 4.5 3.9 3.9 3.5 4.0 3.7

29 3.7 3.5 3.3 3.8 4.0 3.5 3.9 3.7

30 3.3 4.0 3.5 3.3 3.9 4.1 3.7 3.7

Answer 1

For n = 8, A2=0.373
A2	0.373
UCLX_bar	= X_double bar+A2R_bar	4.176937
LCLX_bar	= X_double bar-A2R_bar	3.500563

For n = 8, B4=1.815, B3= 0.185
B4	1.815		B3	0.185
UCLs	=B4s_bar	0.554636
LCLs	=B3s_bar	0.056533

a) What values will be used for the centerline, upper control limit, and lower control limit of each chart?

X chart the center line is X_double bar = 3.8, UCL and LCL for x chart given above as UCL_{X_bar ,}LCL_{X_bar}

s chart centerline is s_bar = 0.31, UCL and LCL are given above as UCL_s, LCL_s

_{b) Xchart}

s chart:

c) Yes the process appears to be in statistical control as all values are within the UCL and LCL

d) No because the process is centered around 3.8