Martin Manufacturing has decided to use an R-Chart to monitor the changes in the

Question

Martin Manufacturing has decided to use an R-Chart to monitor the changes in the variability of their 70.0 pound industrial belts. The production manager randomly samples 6 industrial belts and measures the weight of the sample (in pounds) at 15 successive time periods.

Step 1 of 7: What is the Center Line of the control chart? Round your answer to three decimal places

Step 2 of 7: What is the Upper Control Limit? Round your answer to three decimal places.

Step 3 of 7: What is the Lower Control Limit? Round your answer to three decimal places.

Step 4 of 7: Use the following sample data, taken from the next time period, to determine if the process is "In Control" Or "Out of Control".

Observations: 70.03,70,69.96,69.95,70.12,70.0170.03,70,69.96,69.95,70.12,70.01??
Sample Range: 0.17

Step 5 of 7: Use the following sample data, taken from the next time period, to determine if the process is "In Control" Or "Out of Control".

Observations: 69.99,69.97,69.97,69.98,69.96,70.0369.99,69.97,69.97,69.98,69.96,70.03??
Sample Range: 0.07

Step 6 of 7: Use the following sample data, taken from the next time period, to determine if the process is "In Control" Or "Out of Control".

Observations: 70.05,70.02,70.01,70.03,69.97,69.9770.05,70.02,70.01,70.03,69.97,69.97??
Sample Range: 0.08

Step 7 of 7: You, acting as the production manager, have concluded that the process is "Out of Control". What is the probability that the process is really "In Control" and you have made a Type I Error? Round your answer to three decimal places.

rial Period obs1 obs2 obs3 obs4 obs5 obs6 Sample Range 1 69.95 69.96 70.01 69.96 70.01 70.00 0.06 2 170.04 | 70.03 | 70.01 | 69.98 | 70.04 | 69.96 | 0.08 3 69.99 70.01 70.01 70.0470.0170.03 0.05 4 |70.02 | 70.04 69.98 | 70.04 69.97 | 70.04 | 0.07 5 70.04 69.97 70.04 70.01 70.00 69.970.07 6 69.96 69.96 70.01 70.05 70.0070.010.09 7 |70.03 | 69.99 69.97 69.99 69.98 | 70.05 | 0.08 8 70.00 70.00 70.00 70.03 70.0170.05 0.05 9 69.98 70.05 69.95 69.95 70.0469.98 0.10 10 |70.04 | 70.01 69.96 69.95 69.97 69.99 | 0.09 11 70.02 | 70.05 70.03 | 70.03 70.02 69.97 10.08 12 |70.01 | 69.95 70.02 69.98 70.00 69.96 | 0.07 13 |70.01 | 69.95 69.98 | 70.01 | 69.95 69.98 | 0.06 14 69.99 69.9770.04 70.02 70.03 70.03 0.07 15 70.02 69.97 69.99 70.02 70.02 70.04 0.07 2 Table 0 Table 2

Explanation / Answer

Range Chart:

In the Manufacturing companies, statistical quality control is the most important tool.

By using the SQC we can identified process is in control or out of control.

Control limit for R chart:

sample range R = max(Xi) - min(Xi)

whre i = no of sampling group in our example i = 1,2,3,.........,15

Upper control Limit = UCL = D4 * mean(R)

Lower control Limit = LCL = D3 * mean(R)

and Central line = mean(R)

mean(R) = sum(R) / n

D3 and D4 are constants based on n

In our example, samples are 5 and sample groups are 15

since, D3 = 0 and D4 = 2.57

R = Sample Range = [0.06,0.08,0.05,0.07,0.07,0.09,0.08,0.05,0.10,0.09,0.08,0.07,0.06,0.07,0.07]

mean(R) = 1.09 / 15

= 0.07266667

Therefore,

UCL = 2.57 *  0.07266667

=  0.1867533

LCL = 0 * 0.07266667

= 0

CL = mean(R) = 0.07266667

Step1: Central line = 0.073

Step2: UCL = 0.187

Step3: LCL = 0

Step4: All observation is followed in the sample range.

all observation greater than 0 LCL and all variable less than UCL 0.187.

therefore the process is in control.

For this sample,

Observations: 70.03,70,69.96,69.95,70.12,70.0170.03,70,69.96,69.95,70.12,70.01??
Sample Range: 0.17

Sample Range < UCL

So process is in control.

Step5:

Observations: 69.99,69.97,69.97,69.98,69.96,70.0369.99,69.97,69.97,69.98,69.96,70.03??
Sample Range: 0.07

Sample Range < 0.187

So process is in control.

Step6:

Observations: 70.05,70.02,70.01,70.03,69.97,69.9770.05,70.02,70.01,70.03,69.97,69.97??
Sample Range: 0.08

Sample Range < 0.187

So process is control.

Step6:

Observations: 70.05,70.02,70.01,70.03,69.97,69.9770.05,70.02,70.01,70.03,69.97,69.97??

Sample Range: 0.08

Sample Range < 0.187

So process is in control.

>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>>

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