Question

A metals refining company recently implemented a new process for producing high-quality iron nuggets directly from raw iron ore and coal. To assess the capability and stability of the process, a quality engineer sampled and measured the percentage change in carbon content every 4 hours. The following table presents the % change in carbon content measurement the 33 samples. (a) Assess process control and stability. What is the standard deviation estimate of the in control, stable process? (b) Prepare a normal probability plot of the % change in carbon content measurements. At alpha = 0.05, do the data fit a normal distribution? (c) If the % change in carbon content specification is 3.50 +/- 0.50, estimate the process capability.

No.	% Change in Carbon Content
1	3.25
2	3.30
3	3.23
4	3.51
5	3.10
6	3.60
7	3.65
8	3.50
9	3.40
10	3.35
11	3.48
12	3.50
13	3.25
14	3.60
15	3.55
16	3.60
17	3.55
18	3.48
19	3.42
20	3.40
21	3.50
22	3.78
23	3.70
24	3.50
25	3.45
26	3.75
27	3.52
28	3.10
29	3.25
30	3.40
31	3.20
32	3.45
33	3.30

Answer 1

Answer:-

Given That:-

A metals refining company recently implemented a new process for producing high-quality iron nuggets directly from raw iron ore and coal. To assess the capability and stability of the process, a quality engineer sampled and measured the percentage change in carbon content every 4 hours. The following table presents the % change in carbon content measurement the 33 samples.

(a) Assess process control and stability. What is the standard deviation estimate of the in control, stable process?

If we calculate the standard deviation, we will have the figures of 0.1720

Standard deviation =

Based on this, value we have 0.1720 for standard deviation

(b) Prepare a normal probability plot of the % change in carbon content measurements. At alpha = 0.05, do the data fit a normal distribution?

After using the excel function Normal.dist (observation , mean, standard deviation, 0) we will have the fololowing graph for the distribution:

At alpha = 0.05

We need to calculate the upper and lower limit on both the side.

t value at alpha = 0.05 at degree of freedom 32 is   2.0369

So lower limit is = mean - 2.0369 * standard deviation /

= 3.4430 - 2.0369 * 0.1720 /

= 3.3820

upper limit is = mean + 2.0369 * standard deviation /

= 3.4430 + 2.0369 * 0.1720 /

= 3.5040

(c) If the % change in carbon content specification is 3.50 +/- 0.50, estimate the process capability.

Upper specific limit is 3.5 + 0.5 which is 4

Cpu = upper specific limit - process mean/standard error

Cpu = (4 - 3.44) / (3 * 0.0299)

= 6.1999

For lower specific limit is 3.5 - 0.5 = 3

Cpl = process mean - lower specific limit/ standard error

Cpl = (3.44 - 3) / (3 * 0.0299)

Cpl = 4.9316

Sp process capability is 4.9316 (minimum of 6.1999 and 4.9316)

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