Does X-bar charts, required the measurement intervals to be the same length of time?

Good question, one that requires a lot of thought. The time intervals are generally based on equal intervals and the effect of unequal intervals has not been explored. At issue is whether unequal intervals cause a violation of independence of observations.

The answer depends on why intervals are unequal. If you select the intervals based on reports from the front line that there is a problem, then the resulting unequal equal intervals cannot be analyzed using Xbar charts. You have to ask yourself does the sampling procedure lead to samples on certain days being more likely to report out of control cases.

For example consider adaptive sampling. In this approach, additional samples are drawn at first sign of problem. In this case Xbar chart is not appropriate.

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