A process is in control at X bar=100,R bar=7.3 with n=4.If the process level shifts to 101.5, with the same R bar,what is the probablity that the next X bar point will fall outside the old control limits?

Could anybody tell me the solutions to help me out? Thank you so much.

Regards,
Link

A process is in control at X bar=100,R bar=7.3 with n=4.If the process level shifts to 101.5, with the same R bar,what is the probablity that the next X bar point will fall outside the old control limits?

Could anybody tell me the solutions to help me out? Thank you so much.

Regards,
Link

Yes, this is good question. I remember this one during my CQE prepartion few years back.

The most important point in this problem is equating

3*S subsript X bar = A2 * R bar
In the problem you have n, hence refer tables to get the value of A2 constant.
You have R bar.
Now you can calculate S subsript X bar using the above equation.

Next calculate UCL for X bar chart using the forumula,
X double bar+ A2* R bar.
In the problem you have n, hence refer tables to get the value of A2 constant.
X double Bar, R Bar : given.

Given X double Bar ( Average of subgroup averages), With the Calculated UCL X bar and S subsript X bar you can calculate Z Upper

using the formula, (USL for Xbar-X double bar)/ S subsript X bar.

Knowing Z value, you can find the area outside the UCL Xbar in the normal curve.

final answer is 0.0158. You try to work this out by yourself as mentioned above for aquiring more practice.

Regards,
Govind.