Describe quality of rectangular signal detection
It is a rare individual who develops detection algorithms as a recreational pursuit.  If you are not such a person then the reason for your algorithm should provide, what is favorable and not favorable in some measurable way.

Your question has some ambiguity because random delay, missed transitions, and false transitions is all you have mentioned. "Big Science Tests" are based on probabilistic assumptions (a model) that applies.  If your transitions were random with some rate $\mu$, a Poisson model would be promising.  One might look at why you don't see a one when there is a one which is the error mechanism, which typically in Signal Processing is associated with noise. 

Detection is usually cast as a Hypothesis Test with alternative hypothesis $\mathbf{H_0}$ and $\mathbf{H_1}$  where one hypothesis is signal present and the other is signal absent.

Another sort of hypothesis can be tied to a parameter. As an example, A Poisson Process has a mean rate $\mu$ which can be $\mathbf{H_0}$ and $\mathbf{H_1}$ can be the case the observed mean rate $\mu_{observe} \; \ne \;\mu$

As Mbaz suggests in his comment, missed and false detections can be combined as an error probability which might look like

$$P_{error}= P( \text{ones received}| \text{zeros sent}) P(\text{zeros sent})+ P( \text{zeros received}| \text{ones sent}) P(\text{ones sent})
$$
if the ones and zeros are independent.

The essentail point is that you need to understand your data model to use a standard test.

This is not an exhaustive list of types of statistical tests you can use. and many in signal processing have intractable forms. There are paired tests. There are non parametric tests. There are robust tests. Statisticians are inventing new tests every day.

Your data model on the other hand, is up to you.

Lastly, making things up is actually common and as long as it isn't fake, is often acceptable.