Question

You are an engineer at a facility that manufactures biodegradable plastic bags. Each bag needs to be within a certain weight, so every hour you sample 4 bags and weight them. The results from the last 8 hours is shown in the table, where the weight is in grams:

Sample	Bag1	Bag2	Bag3	Bag4
1	4.45	4.54	4.46	4.43
2	4.54	4.69	4.58	4.34
3	4.54	4.34	4.47	4.67
4	4.54	4.09	4.41	4.50
5	4.44	4.51	4.51	4.46
6	4.43	4.27	4.59	4.54
7	4.70	4.65	4.82	4.68
8	4.30	4.51	4.62	4.58

1. What is the sample size?
2. Calculate the centre line, UCL, and LCL for an x-bar chart?
3. Calculate the centre line, UCL, and LCL for an R Chart
4. Is your process in control? Explain why and explain your next step should be.
5. The specification limits for this bag is a weight that is between 4.30g and 4.7g. Using the data that is provided, what is the proportion of bag non-conforming in the process? How long will it take to sample a bag out of the specification limits?

Answer 1

a) sample size(n)=8

c) for an R-bar chart

Range
0.11
0.35
0.33
0.45
0.07
0.32
0.17
0.32

D3=0.136

D4=1.864

CL:mean(R)=0.265

UCL:D4*mean(R)=0.49396

LCL:D3*mean(R)=0.03604

variation in process are in control hence process is in control

for an x-bar chart;

x bar
4.47
4.5375
4.505
4.385
4.48
4.4575
4.7125
4.5025

A2=0.373

CL:mean(xbar)=4.50625

UCL:mean(xbar)+A2*mean(R)=4.605095

LCL:mean(xbar)-A2*mean(R)=4.407405

d)

here in x bar chart one value is greater than UCL and one value is less than LCL , this implies that process is statistically out of control.

and hence we have to revise the R-chart by excluding that two points