Question

32. Short Answer Question We have m = 5 preliminary samples of size n = 3 (some numbers have unfortunately been erased by accident by a clumsy co-op student): 27.9 31.83 i 1,1 2,2 1 27.1 29.4 2 30.6 32.5 3 25.7 35.5 4 31.1 23.2 5 24.1 34.2 S; 1.3 1.07 4.91 1.9 30.4 32.4 30 25 27.4 total: 7.9 26.43 28.57 145.13 10.1 32 5.15 16.57 What is the control chart (give the interval) for X from R?

Please provide the full answer with description. Thank you!

Answer 1

Solution;

From the given data,

Here, we are given that m=5 and n=samplesize=3. Now we complete the following incomplete table:

i	xi,1	xi,2	xi,3	Ci	ri	si
1	27.1	29.4	27.2	27.9	2.3	1.3
2	30.6	32.5	32.4	31.83	1.9	1.07
3	25.7	35.5	30	30.4	1.8	4.91
4	31.1	23.2	25	26.43	7.9	4.14
5	24.9	34.2	27.4	28.57	10.1	5.15
			Total	145.13	32	16.57

Now we have to construct the control chart for
X
from $\overline{R}$ :

We know the control limits are given as

mo LCL =T - n

CL = T

то UCL = ī + n

where    = 145.13 / 5=29.026

Σ C m

and = 6.4/1.693 = 3.780   (where d₂= 1.693 which is obtained from the control chart table)

R d

LCL = 29.026 - (5* 3.780/ 1.7320) = 18.1140

CL = 29.026

UCL = 29.026 + (5* 3.780/ 1.7320) = 39.9379