Explore BrainMass

# Six sigma

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

For Statistics for Quality Control

© BrainMass Inc. brainmass.com September 26, 2022, 5:28 pm ad1c9bdddf
https://brainmass.com/statistics/conditional-probability-distribution/six-sigma-13304

#### Solution Preview

We can describe such design using a tree diagram.
<br>Here, we define all events that can happen and assign a probability of an individual event for each branch.
<br>For example, in the first layer (or sample1), there are two probable events:
<br>- an out-of-control condition is detected, probability=1 - &#946;
<br>- an out-of-control condition is not detected, probability=&#946;
<br>Notice that ...

#### Solution Summary

1. A quality characteristic is monitored by a control chart designed so the probability that a certain out-of-control condition will be detected on the first sample following the shift to that state is 1 - &#946;. Find the following:

a) The probability that the out-of-control condition will be detected on the second sample following the shift.

b) The probability that the out-of-control condition will be detected on the mth sample following the shift.

c) The expected number of sub-groups analyzed before the shift is detected.

d) The probability that the first sample following the shift produces a statistic that plots inside the control limits.

e) The probability that the first sample following the shift produces a statistic that plot inside the control limits.

f) The probability that two consecutive samples produce statistics that plot out-side of the control limits.

g) The probability that at least one of the next m samples yields values of the test statistics that plot out-side the control limits.

\$2.49