Question

QUESTION 20 Five samples of size 12 were collected. The data are provided in the following table:

Sample number 1 2 3 4 5

Sample mean 4.80 4.62 4.81 4.55 4.92

Sample standard deviation 0.30 0.33 0.31 0.32 0.37

The upper control limit (UCL) and lower control limit (LCL) for an s-chart are:

1.LCL = 0.0971, UCL = 0.5868.

2.LCL = 0.1154, UCL = 0.5366.

3.LCL = 0.1011, UCL = 0.6109.

4.LCL = 0.1034, UCL = 0.6246.

5.LCL = 0.0994, UCL = 0.6006.

Answer 1

I will try to draw the x-bar chart and s-charts.

So, for s-chart:

LCL = 0.115

UCL = 0.537

So, the best option is option 2 - LCL = 0.1154, UCL = 0.5366. This is also explained by the formulae used as shown below:

Formulae used:

x-bar chart:

s chart: