QUESTION 15 If X-double bar 20, n-4, R-bar- 0.5, and x-bar from a sample is 19.7

Question

QUESTION 15 If X-double bar 20, n-4, R-bar- 0.5, and x-bar from a sample is 19.735, then it indicates that for that sample the process is (conside chart only) 0 a. out of control ot. in control c. not enough information is given to answer the question O d-none of the above QUESTION 16 fX 15.95, R-0.29,n4. Suppose a sample mean - 15.7. The sample mean indicates (consider both x-bar and R charts) 0 a. process is in control Ob- process is out of control OC. Sample mean is too small Od.not enough information is given to answer the question

Explanation / Answer

Question 15

Control limits for X bar chart are given as :

X-double bar - A2 * R-bar = Lower limit

X-double bar +A2 * R-bar = Upper limit

where A2 is a constant obtained from dodge and romig's sampling inspection tables by looking the value corresponding to n = 4.

we obtain A2 = 0.729

Lower limit = 20 - 0.729 * 0.5 = 19.6355

Upper limit = 20 + 0.729 * 0.5 = 20.3645

A process is said to be in control if the sample mean lies between the control limits.

Since, x-bar from sample = 19.735 which lies between 19.6355 and 20.3645 , we can say that the process is in control.

It indicates that for that sample the process is in control.

Question 16

Uisng the same formulas for control limits :

Lower limit = 15.95 - 0.729 * 0.29 = 15.73859

Upper limit = 15.95 + 0.729 * 0.29 = 16.16141

A process is said to be in control if the sample mean lies between the control limits.

Since, x-bar from sample = 15.7 which lies outside 15.73859 and 16.16141 , we can say that the process is out of control.

The sample mean indicates process is out of control.

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