Sample size (n)=4 a) What are the control limits for the mean chart b) What are the control limits for the range chart c) Is the process in control?   Thank you so much for your help! I tried the problem myself and got  a)(19.7,20.1) and b) (0,0.78)

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When answering a question of this nature, we need to ask ourselves the type of data we have?

1.Continuous or discrete? 

From the sample size we can safely assume is it Continous.

2. What is our sample size, n?


3. Based on the above sample size, which chart will be used to obtain the control limits? 

A sample size 2<n<10 uses Xbar-R Chart.

Now we have identified which chart we are using, we can answer our questions:

1. Control limits for the mean chart: 

The equation of the lower control limit from Xbar-R chart: `barX-3(barR)/(d_2)`

` `

`barX =0.3631`

`barR =0.0837`

` `

`d_2 = 2.059`

The lower control limit = 0.241


The equation of the upper control limit from Xbar-R chart: `barX+3(barR)/(d_2)`

The upper control limit = 0.485


2. The control limit for the range chart: 

`D_3 = 0, D_4 =2.282, bar_R = 0.0837`


The equation of the lower limit from Xbar-R chart: `D_3barR`

 lower  control limit = 0

The equation of the upper limit from Xbar-R chart: `D_4barR`

upper control limit = 0.191

3. Is the process in control? 

The R-chart determines if the system or process is in control. If the R chart is out of control, then the process is not stable.


a) (0.241, 0.485)

b) (0, 0.191)

c) Depends on stability of R chart.

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