You are employed as quality manager in a company manufacturing computer monitors. A critical element in the production process is to control the size $($in mm$)$ of the protective glass in front of the screen. According to the design, the manufacturing process has been stable with mean tension equal to $274$ mm and process standard deviation of $33$ mm$.$

The operator measures the size on a sample of four monitors each hour, as shown in the following table collecting the last $20$ samples.

Sample Measurements Sample mean Std dev

$1238\mathrm{.}5276\mathrm{.}3235\mathrm{.}5273\mathrm{.}3255\mathrm{.}921\mathrm{.}9$

$2315\mathrm{.}1306\mathrm{.}3241289\mathrm{.}2287\mathrm{.}933\mathrm{.}1$

$3248\mathrm{.}1206\mathrm{.}3254\mathrm{.}1320\mathrm{.}1257\mathrm{.}247\mathrm{.}0$

$4217\mathrm{.}9301\mathrm{.}3274\mathrm{.}2260\mathrm{.}3263\mathrm{.}434\mathrm{.}8$

$5332\mathrm{.}9247\mathrm{.}7285\mathrm{.}3237\mathrm{.}1275\mathrm{.}843\mathrm{.}4$

$6309\mathrm{.}3236\mathrm{.}8202\mathrm{.}8239247\mathrm{.}044\mathrm{.}7$

$7272\mathrm{.}4276\mathrm{.}2279\mathrm{.}6244\mathrm{.}2268\mathrm{.}116\mathrm{.}2$

$8286\mathrm{.}1252\mathrm{.}2263\mathrm{.}8274\mathrm{.}8269\mathrm{.}214\mathrm{.}6$

$9261\mathrm{.}3263\mathrm{.}9252\mathrm{.}9345\mathrm{.}8281\mathrm{.}043\mathrm{.}5$

$10324\mathrm{.}3234\mathrm{.}3308\mathrm{.}2275\mathrm{.}4285\mathrm{.}639\mathrm{.}8$

$11269\mathrm{.}4250\mathrm{.}2232269\mathrm{.}2255\mathrm{.}217\mathrm{.}9$

$12169\mathrm{.}8334\mathrm{.}4335\mathrm{.}6321\mathrm{.}8290\mathrm{.}480\mathrm{.}6$

$13346\mathrm{.}9365\mathrm{.}4376\mathrm{.}9363\mathrm{.}5$ to be calculated to be calculated

$14237\mathrm{.}2286\mathrm{.}1248\mathrm{.}9264\mathrm{.}6259\mathrm{.}221\mathrm{.}2$

$15259\mathrm{.}8218\mathrm{.}4297\mathrm{.}2280\mathrm{.}2263\mathrm{.}934\mathrm{.}0$

$16240\mathrm{.}1253\mathrm{.}2303\mathrm{.}6301\mathrm{.}1274\mathrm{.}532\mathrm{.}6$

$17287\mathrm{.}8296\mathrm{.}8238\mathrm{.}7280\mathrm{.}3275\mathrm{.}925\mathrm{.}7$

$18340\mathrm{.}9305\mathrm{.}4304\mathrm{.}9303\mathrm{.}5$ to be calculated to be calculated

$19348\mathrm{.}9385\mathrm{.}4384\mathrm{.}9383\mathrm{.}5$ to be calculated to be calculated

$20301\mathrm{.}3351281\mathrm{.}1259\mathrm{.}8298\mathrm{.}339\mathrm{.}0$

You are requested to:

$$ Choose the correct SPC chart to represent the problem;

$$ Calculate UCL and LCL for the relevant chart$/$s;

$$ Comment on the overall process and on specific samples.