Suppose you are a quality control manager and want to know if a run of good product is is showing an important change in your product quality or not. Depending on situation a runs test could be useful for you. David Booth

More in general, everytime you suspect a non-random distribution of of cases along a temporal dimension (e.g. positive/negative results, arrivals of young/old patients to a clinical ward, burst of neuronal activities..) the run test is a 'prima facie' approach, The discovery of a non-random temporal variability is of utmost importance in all the research fields...

However, runs tests generally do not make efficient use of available information. W.J. Conover, Practical Nonparametric Statistics, Wiley was, I think, the source Conover used at an event I attended quite a number of years ago when he said they were weak tests. (I designed a test for a specific purpose that was a type of runs test where information was scant at any rate.) Then you need a way to represent the effect size, which can be difficult. (I did have that covered. It required a lot of programming support.)

Runs tests are usually substantially inefficient because, say, for a longest runs test, there is generally no distinguishing between two cases with the same longest run length, with one of them having several more runs nearly as long, and the other not having any other runs (over 1) at all. And more importantly in my view, how then do you determine a definition for the effect size? Please don't rely on isolated p-values, as an isolated p-value is virtually meaningless.

So yes, as David noted, there could be a number of uses for runs tests under the area of quality control. You could use one to see how many planes in a row left on time for a given airline in a given week. Other uses are possible. But often, you can likely do something better.

PS -

Ah. I now see Alessandro Giuliani's response, and I think 'prima facie' is a good term, especially if he means 'preliminary.'

Respected David Eugene Booth Sir,

Thank you so much for your kind words.

Respected Alessandro Giuliani Sir,

Thank you so much. I will read more literature on it.