As a non-statistician, here's the approach I took about 10 years ago. There was clustering software available for purchase, but it was quite expensive. So here is my workaround approach.
Sum up each 30 minutes: total N and # failues.
Start at the beginning of the data and compute: what would happen if we added in the second 30 minutes to the first? Would the success rate be significantly different for the combination vs. the first? If so, the second segment begins a new cluster. If not, the first two segments combined become cluster #1. Keep on incorporating a segment until the cluster becomes different.
You get to fiddle with the segment size and the definition of "significantly different".
In the end, this approach produced very similar results to off-the-shelf software that cost hundreds of thousands of dollars. On the other hand, if you start at the end of the data and work backwards in time, the results would change dramatically. Also note, clusters are not defined "within the day". More like a "bucket" than a "cluster", a cluster could end up spanning more than a day or less than a day, and could include portions of two (or more) days. At any rate, perhaps this gives you some ideas you could apply.
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