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?

**n=4**

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.

SUMMARY:

a) (**0.241, 0.485)**

b) **(0, 0.191)**

c) Depends on stability of R chart.

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