Of course, the real answer is that the value is not slipping. Look at the average and range chart for the 100 subgroups of size 5 once again. There is no evidence that the process has changed in any way during these 10 segments. The process was not getting worse, nor was it getting better. But the statistics were changing with each segment even though the process remained the same, and these changes resulted in different values for the centered capability ratio.
Statistics always vary over time, and capability indexes are statistics.
Thus, although your process may remain unchanged, your capability indexes will inevitably change over time. The limits on this chart will define the routine variation of the capability value, and as long as no capability values fall outside the limits, the central line of this chart will be the best characterization of your process capability. Before you can interpret a single capability ratio, based upon 50 data, to mean that the bead board process has changed from a capability value of 1.30, you will need a centered capability ratio below 0.88, or above 1.72. Think about what this means about how you interpret capability indexes. Select another article.