Falcon landings are now more reliable than any other rocket's launches, ever

With today's 101st consecutive landing success Falcon boosters have a longer uninterrupted streak of good landings than any other rocket had good launches. The longest success streak of a non-Falcon rocket belongs to Delta II which had a chain of exactly 100 launches from May 1997 to September 2018 (when it launched for the last time before its retirement). There are claims that Souyz U had a longer streak, but they are reportedly incorrect: Its upper stage failed during Cosmos 2243 launch in April 1993, triggering auto-destruct of its secret payload [source1](https://arstechnica.com/science/2022/02/spacexs-falcon-9-rocket-has-set-a-record-for-most-consecutive-successes/) [source2](https://www.guinnessworldrecords.com/world-records/most-successful-commercial-rocket-launcher)

So how does that translate into reliability? One could naïvely just take the number of launch or landing successes and divide it by a total number of attempts (both good and failed). But this would yield a way too pessimistic result as it penalizes vehicles which had an initial learning curve, because, for example, they were new (and more modern) developments vs being based on legacy tech. Just answer the question: which hypothetical rocket would you rather fly if both had 100 launches and 4 failures but the first of them had all the failures in the first 25 flights (say flights 1, 5, 17, 25) while the other has failures more or less evenly distributed (say flights 18, 41, 62, 79)? The former is expected to be safer. But the naïve model (incorrectly) says they are equivalent.

Actually, a better model is to take all the launches since the start of the longest streak of successes, as this accommodates for the initial learning curve. The former rocket would be counted from flight 26 with 0 subsequent failures (75 long chain of successes), while the latter would be counted from flight 19 but would have 3 failures (79:3 success:failure ratio or 3 failures out of 82).

Now, how to estimate reliability (i.e. the probability of success) with some set confidence? Let's use the handy handout by late prof. Richard M. Dudley [here](https://math.mit.edu/~rmd/650/binomconfints.pdf) (it's one of the top Google results). The method described is "secure", i.e. it is strictly mathematically proven that in no circumstances the confidence is overestimated (some other less conservative methods sometimes overestimate confidence, for example the confidence ends up not 95% as stated but say 91%; but it's not the case with this one). The algorithm is in the appendix on page 18.

The calculation for the former hypothetical example rocket is trivial, with 95% confidence its reliability would be within 94.88% and 100%. For the latter one, it'd be a bit more complex, the 95% confidence interval of its reliability is 91.84% to 99.47%.

Going back to Falcon, the calculation is simple: With 95% confidence its demonstrated **landing** reliability is 96.20% to 100%. It's slightly better than Delta II historical (after its last flight) **launch** reliability 95% confidence range of 96.16% to 100%. Of course as the chain of successful landings goes on, the demonstrated reliability will improve. But this is what we could conservatively say now.

NB. Falcon 9 demonstrated launch reliability is 97.85% to 100%, again with 95% confidence.

NB2. For Falcon Heavy we have way too little data for a useful result: 95% confidence interval is extremely wide at 47.82% to 100%. To narrow it down it would take much deeper analysis using a lot of non-public info.