Question

An operator trainee is attempting to monitor a filling process that has an overall average of 705 cc. The average range is 17 cc. If you use a sample size of 6, what are the upper and lower control limits for an R-chart?

Answer 1

Answer and Explanation:

The computation of the upper and lower control limits for R-chart is shown below:

Upper Control limit of $\bar x$ chart is

$\bar x$ + A2 × $\bar R$

=705 + 0.483 × 17

=713.21

Lower Control Limit Of $\bar x$ Chart is

$\bar x$- A2 × $\bar R$

= 705 - 0.483 × 17

= 696.789

The A2 value could be taken from the X bar and R bar chart having a sample size of 6

Now  

Upper control limit of R Chart

= D4 ×  $\bar R$

= 2.004 × 17

= 34.068

And,

Lower limit of R chart

=  D3 × $\bar R$

= 0.076  × 17

= 1.292

The D3 value is not available for the sample size 6 so we took the values of sample size 6

Also the D3, D4, and A2 could be taken from X bar tables and the range chart