1. First, let us view the data
First, let us view the data. (Plot it on a Normal Probability Chart) See Figure 1.
[See thread “Calculating axis values of normal probability plot” for the attachments on how to create these Normal Probability or Hazen Plots (Similar to Anderson-Darling Plots).]
This figure shows the X-bar data for the averaged four individual data points plotted against its distribution value (sigma or Z-score).
Observations:
Only ~ 18.5% of the parts are within the spec. limits.
The X-bar data point appears to be a non-normal. This is data series 15, which is an out of the control limits on your X-bar control chart. Since the process is NOT STABLE or out‑of‑control, the process needs to be corrected before proceeding in calculating any indicators. All Indicators assume that the process is in control. However, for this discussion we will continue the analysis.
Calculations:
Cpk = (USL-mean)/(3*Rbar/d2)
Cpk = (863.3 – 863.5) / (3 * 0.2 / 2.059)
Cpk = (-.2) / (0.2914)
Cpk =
This makes sense because the mean is above the USL.
On these charts straight lines are normal distributions (see the “If Normal” line). With the exception of the out-of-control data point, the data appears normal. This is to be expected since you have averaged 4 individual data points.
Figure 1

2. Let us look at the individual data points. See Figure 2
Let us look at the individual data points. See Figure 2. This figure shows us some interesting information about the process.
Observations:
This chart shows the data as collected. It demonstrates that your gage measures are in 0.5 increments (as you stated) and are “Chunky” as Bev stated.
Only ~ 17.6% of the parts are within the spec. limits.
Note: that none of the data points within specification touches the “If Normal” line, therefore, the underlying distribution is probably not normal. This is not an issue, but something to watch.
Figure 2

3. On Figure 3, I have added gage error bars (the best error calculation potential). The “If Normal” line passes through all the individual data points with gage error, so the underlying distribution maybe normal.
Figure 3

4. Figure 4 shows that IF gage error is biased then all of the piece could be above spec.

5. Figure 5 shows a “worse case” “Possible Normal” line, which displays a much higher distribution than the calculations. For non-critical dimensions (where Cpk values of 1.67 to 2 are desired), this is the robust normal distribution line to use. (Shades of Mikel Harry’s 1.5 sigma shift.)
Figure 5

6. Figure 6 has all the previous figure items shown on it
Figure 6 has all the previous figure items shown on it. Figure 6 also shows the “worse case” “Possible Normal” line transposed to display the process centered to the specifications, i.e.: Cp.
Figure 6

7. Figure 7 shows the process centering process on a less cluttered chart.
Observation:
The process cannot robustly meet the specifications of the dimension.
Figure 7

8. Figure 8 shows the “If Normal” and a “worse case” “Possible Normal” distributions transposed such that the parts are targeted to the high limit. All ” “Possible Normal” parts are within specification while some of the parts in the “worse case” “Possible Normal” fall below specification.
Summary of Observations:
Only 17 to 18 percent of the parts MAY meet specifications.
Process mean and average are above the upper spec.
The process is NOT STABLE (i.e.: out‑of‑control).
Data is very “Chunky”
The underlying distribution is probably not normal. (This is not an issue, but something to watch.)
The underlying distribution maybe normal. (Is it normal or is it not?)
The process is not robust enough to meet specification even if centered.
Recommendations:
1)      Determine why the process is not stable (two distributions intertwined?).
2)      Reduce variation
3)      Center the process
Unfortunately, you CANNOT perform the recommendations because your gage system cannot describe the data with enough detail. It is hiding what is going on within the process. So, the starting point should be:
[QUOTE=harry;362637]
…, you may want to read a related thread: Gage R&R 10:1 Tolerance to Gage Discrimination Rule Explanation[/QUOTE]
to eliminate Bev’s Chunky data.
Figure 8