Question

It is desired to develop a means chart and a range chart for a process that puts a cola drink
into bottles.  The nominal goal is to put 16 oz. into each bottle.  The data were obtained from 25 of size 4
A. Construct means and range charge obtained information and 3-sigma limits.
B. Then graph the data on the chart.  Identify any samples that indicate the process is out of
control.
		Pop into Bottles Problem
Sample number	Item 1	Item 2	Item 3	Item 4
1	16.01783	16.00249	16.00451	15.94237
2	15.98764	16.00713	15.97385	16.00362
3	16.00253	16.00251	15.97343	15.98449
4	16.01994	16.00793	16.00592	15.97239
5	15.99596	16.00336	16.00137	15.98503
6	15.9938	15.99357	16.00254	15.98667
7	15.98799	15.99871	15.97896	15.95939
8	16.01234	16.00982	15.98147	15.9929
9	16.00267	15.99257	15.98403	15.99413
10	16.01079	16.00738	16.00969	15.95743
11	16.0093	16.00942	15.97481	16.00514
12	15.99942	16.00028	15.97622	15.9607
13	15.98469	16.00018	15.99772	15.95608
14	16.01878	15.99014	15.97092	15.95334
15	16.00395	15.9985	16.00445	15.95483
16	16.00048	15.99394	15.97393	15.96496
17	16.00953	15.99736	16.00449	15.9914
18	15.99745	15.99101	15.9846	16.00898
19	16.01559	16.00196	15.9869	15.96941
20	16.01938	16.00702	15.98757	16.00441
21	15.98027	15.99967	15.97739	15.96144
22	16.0127	16.00559	15.97053	15.96983
23	16.00743	16.00365	15.97541	15.97034
24	15.98654	16.00141	16.00254	15.96317
25	16.00996	15.99368	15.97339	15.94784

Answer 1

The solution to both the parts is given below:

A X bar R chart will be made in this regard...

The Grand Mean and the Overall Range is calculated below:

Grand Mean is just the overall average of the group means and the Overall Range is the average of the group range.

Range = Maximum Value - Minimum Value

Formulas:

Table for A₂

In this case A₂ will be 0.729 as the sample size is 4.

So,

From X bar R Chart formulas,

LCL = 15.99 - 0.729*0.0388 = 15.962 (Lower Control Limit)

UCL = 15.99 + 0.729*0.0388 = 16.02 (Upper Control Limit)

Based on 3 Sigma limit:

LCL = 15.99 - 3*0.0388 = 15.874 (Lower Control Limit)

UCL = 15.99 + 3*0.0388 = 16.11 (Upper Control Limit)

Control Chart

Here, the two black lines denotes the LCL (Lower Control Limit) and the UCL (Upper Control Limit)

Here as all the points are under the control limits, so the process is under control...

End of the Solution...