Petroleum is cracked to make gasoline and other products such as lubricating oil

Question

Petroleum is cracked to make gasoline and other products such as lubricating oil and kerosene. The process is too slow to allow sample sizes greater than one. The following are the octane rating of the output from the process recorded at intervals of thirty minutes each. The objective is to construct appropriate control charts, which can be used to monitor the process. Use alpha = 0.0026. 1. The value of alpha used in control charts is A) The probability of stopping the process, after it has gone out of control B) None of these C) The probability of running the process, after it has gone out of control D) The probability of running the process, when it is in control 2. Which of the following formulas would you use for constructing the appropriate control charts in this problem? Monitoring Mean Monitoring Standard Deviation A) (X - 2.66 R, X + 2.66 R) (0, 3.27 R) B) (X bar - 2.66 R bar, X bar + 2.66 R bar) (D_3 R bar, D_4 R bar) The value of n used for obtaining D_3 and D_4 is 6. C) (X - A_2 R bar, X + A_2 R bar) (D_3 R bar, D_4 R bar) The value of n used for obtaining A_2, D_3, and D_4 is 6. D) (X - A_2 R bar, X + A_2 R bar) (0, 3.27 R bar) The value of n used for obtaining A_2 is 6. 3. The value of R bar to be used in calculating the control limits in this problem is A)3.00 B) 1.33 C) 1.60 D) None of these E) 2.00

Explanation / Answer

Solution

Part (a)

represents the level of significance which is nothing but the probability of committing Type I error, where Type I error refers to the decision of rejecting the null hypothesis when it is actually true.

In the Control Chart context, null hypothesis is ‘process is under control’ and so rejecting null hypothesis implies declaring ‘process is out of control’ which, in turn, would imply that the process would be stopped.

Hence, represents the probability of stopping the process when ‘process is under control’

Since none of the given options fits in, ANSWER is Option B.

Part (b)

Control limits for Xbar-RChart are: (Xdoublebar – A2Rbar, Xdoublebar + A2Rbar) for Xbar chart and (D3Rbar, D4Rbar) for R chart, where Xdoublebar and Rbar are respectively the average of averages and ranges of sub-groups, A2, D3 and D4 are constants obtained from Control Chart Constant Tables.

So, ANSWER is Option C.

Part (c)

Value of Rbar to be used is average of sub-group ranges. Since only one sub-group data is available, Rbar cannot be found out. Hence, ANSWER is Option D.

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