3. A production process has been defined as part of an industrial equipment manufacturing project. The process is intended to produce steel bolts with a length of 20 cm. The control limits are 19.955cm and 20.045cm.

The measurements made at the end of the process yielded the following results:
20.033cm, 19.982cm, 19,995cm, 20.006cm, 19.970cm, 19.968cm, 19.963cm, 19.958cm, 19.962cm, 19.979cm, 19.959cm.
What should be done?
1. The process is under control. It should not be adjusted.
2. A special cause should be investigated, the process should be adjusted.
3. The control limits should be adjusted.
4. The measuring equipment should be recalibrated.

Answer: 2

To answer your first questions if you see your Lower Control Limit(LCL) is 19.955cm & Upper Control Limit(UCL) is 20.045cm. Which also implies 20 is your mean i.e., (19.955+20.045)/2 = 20

On a control chart, special causes are represented by points beyond the control limits or as non-random points within the control limits. In this case you can see there are points non-random and focussed in between mean and LCL limit and these kinds of points are understood to have a "special cause" and should be investigated.

9. In order to speed up a project, you made a decision to fast-track a phase currently performed with five team members, and another one which was planned to begin in four weeks time with another five team members.

Which of the following activities should you do first?
1. Make sure that all exit criteria of the consecutive phase have been met to ensure the flow of communications in a team situation which is more complex by a factor of 2.
2. Make sure that all entry criteria of the previous phase have been met by planning and performing a phase gate meeting to assess technical aptness.
3. Make sure that all exit criteria of the previous phase have been met by planning and performing a phase gate meeting to assess technical performance.
4. Restructure your team and delegate tasks in order to ensure the flow of communications in a team with the number of communication channels increased by a factor of 4.5.

Answer:4

To answer this questions I should first say the value there is not 4.5 but "45".
Also it is explained in the question that they are fast-tracking the phase performed currently by 5 team members and also another one which was planned to being in 4 weeks i.e., they are fast-tracking two phases at once bye running activities in parallel and so communication between the members is key

When you have 5 members the communication channels are to be 10 but when another 5 members get added it will be (10*9)/2 = 45 and so the answer 4.