During process capability should initial focus be to improve centering or reduce variability

OVERVIEW: A two-step process for 30,000-foot-level metric assessment is described in a 2008 4 book-volume series on the Integrated Enterprise Excellence system:
1. Is the process predictable; i.e., the process has a recent region of stability?
2. If predictable, what do you predict; i.e., make a process capability statement

Predictability is assessed through an individuals control chart is used to assess predictability. If a process is predictable, then a probability plot can be used to determine prediction estimate. To create this assessment using a probability plot, one would input into Minitab the specification limits.

QUESTION: The following problem is not addressed in literature.

Product Spec: 0.9 +/-0.01
Mean 0.9 units
Variation +/-0.01 units

Though an individuals chart, the process is determined to be stable. Measurements lie within upper control limit (UCL) and lower control limit (LCL). The process has a mean 1.02 units and UCL of 1.04 units and LCL of 1.00 units. Voice of the process is 1.02 +/- 0.02

First Approach: First change mean from 1.02 to 0.90 and the reduce variation from +/-0.02 to +/-0.01.

Second Approach: First reduce variation from +/-0.02 to +/-0.01 and then change mean from 1.02 to 0.90.

Which is the correct/better approach, Approach 1 or Approach 2?

What is the reason?

SOLUTION: An approach that uses simulation is as follows, given that the data are normally distributed:
1. For a predictable process, a probability plot creation of all the data and at the same time have Minitab statistical software, for example, determine a best estimate for the percentage of non-conformance.
2. Generate a large random number of samples, for example 1000, for the Approach 1 situation described above from a normal distribution with the shifted mean and baseline standard deviation value.
3. Randomly generate a large number of samples for Approach 2 situation described above from a normal distribution with the reduced standard deviation and baseline mean.
4. For each of the generated random data sets, create a probability plot with the specification limits.
5. Compare non-conformance percentage for the two situations. The lower non-conformance percentage would be the best initial approach. The lowest percentage could also be compared to the existing base-line percentage to quantify the benefit from the expected improvement shift for the initial step.