Question

1. A study was conducted on the injection molding process of a vehicle hush panel. Briefly, the process starts with material being fed into the back end of the barrel and screw mechanism. The screw rotates and heat is added, melting the material and moving it to the front. The molten material is injected into a mold. The plastic is cured until it is solidified. This constitutes a cycle. A quality engineer at the General Motors Lansing site collected data on the weight, in grams, of the material for each cycle. This was done by weighting the solidified plastic that comes out of the mold. A subgroup consists of five weight measurements. There are 45 subgroups. Excel data file is provided at WebCT

1. Using all 45 subgroups, compute centerlines and control limits for X-bar and R charts.
2. Actually construct the X-bar and R charts. You can use Excel or other software packages to do this.
3. Identify any subgroups that plot outside the control limits on either of the charts.
4. What can be said about the stability of the process? Our operational definition of stability is no points outside control limits.
5. Construct a histogram for the entire set of 225 measurements. Use cutoff points from 600 to 750 with interval widths of 10. Comment on the shape of the histogram and what it is telling you about the weight of material.
6. What comes out of the mold consists of two parts and a runner. Several of the subgroups contain weights for the two parts without the runner. These subgroups are: 1, 7, 8, 11, 12, 15, 16, 17, 18, 23, 25, 29, and 30. Assuming that this special cause can be eliminated, reconstruct the control charts after first removing these subgroups. Using a computer package to do this. How do the control limits on these charts compare to those in a) and b)? What can you say about the stability of the process now? Again use the one point outside control limits alarm rul.
7. Compute an estimate of the process standard deviation (standard deviation of individual X), excluding the subgroups given in (f). How has the estimate changed?

Answer 1

Part a)

Central Line and control limits for x bar and s chart are calculated in the graphs shown below

X bar chart

UCL 711.3546

CL 699.4979

LCL 687.6409

R Chart

UCL 43.4647

CL 20.55556

LCL 0

Part b

X bar With R observation UCL = 711 .3546 --Average 699.4978 720 LCL = 687.6409 Rule - - --__ violation 710 No ●Yes 700 命令 ◆◆◆ 690 680 670 660 Sigma level: 3

X bar With R observation UCL = 43.4647 --Average 20.5556 100 LCL= .0000 Rule iolation No ●Yes 80 40 2어 Sigma level: 3

Part c

Rule Violations for X-bar
Subgroup	Violations for Points
1.00	Less than -3 sigma
5.00	Greater than +3 sigma
6.00	Greater than +3 sigma
9.00	Greater than +3 sigma
11.00	Less than -3 sigma
14.00	Greater than +3 sigma
18.00	Less than -3 sigma
21.00	Greater than +3 sigma
22.00	Greater than +3 sigma
25.00	Less than -3 sigma
30.00	Less than -3 sigma
11 points violate control rules.

Rule Violations for Range
Subgroup	Violations for Points
1.00	Greater than +3 sigma
7.00	Greater than +3 sigma
8.00	Greater than +3 sigma
11.00	Greater than +3 sigma
12.00	Greater than +3 sigma
15.00	Greater than +3 sigma
16.00	Greater than +3 sigma
17.00	Greater than +3 sigma
18.00	Greater than +3 sigma
23.00	Greater than +3 sigma
25.00	Greater than +3 sigma
29.00	Greater than +3 sigma
30.00	Greater than +3 sigma
13 points violate control rules.

Part d)

Given process is out of Control as points are present outside the 3 sigma limits