Question

The analyst took four batches of water bottles at different times of the day and recorded the average amount filled.

Use the data set below to create the control chart indicated to check if the water filling process is in control.

Create the control charts and answer the questions in Excel and upload the file.

1. Create the xbar control chart for this data set. Assume that σ = 0.75.

Discuss why or why not the water filling process is in control.

2. Create the R control chart using this data set.

Discuss why or why not the water filling process is consistent. This is the same data set as in question 8, number 1.

Water bottle filling process
sample	batch 1	batch 2	batch 3	batch 4
1	20.4	19.8	19.3	21.0
2	20.0	19.2	21.2	19.5
3	20.1	21.1	19.8	20.9
4	19.9	21.0	20.0	20.5
5	19.0	21.1	20.6	21.8
6	20.0	20.3	20.1	19.0

Answer 1

Here D3 =0 and D4 = 2.004

So now we calculater Xbar and R values for each sample.

Now we calculate the control limits for Xbar chart

The Xbar chart can be drawn as-

Comment : As all the points lie within the control limits, we can conclude that the water filling process is in control.

Now we calculate control limits for R chart

The R chart can be drawn as-

Comment: The lower control limit of R chart is 0.

So as all the points lie within the control limits, we can conclude that the water fillibg process is in control.