[SystemSafety] Estimating time to next fault report

[Derek M Jones]

Martyn,

> This seems to me to be curve-fitting of poorly understood and inaccurate data, presented with no error probabilities and no analysis of underlying mechanisms. tl;dr totally useless. Convince me I’m mistaken.

The plots are in sorted order, and that's what a
plot of values drawn from an exponential data looks
like when plotted in sorted order.

Yes, doing it this way is confusing, but I could not
think of something better.  The lighter blue line in the
plot contains several kinks, because of a change in
rate of discovery (perhaps because of an increase in the
number of users).

The plots in this data (linked to in the post) are much
better behaved (because they come from a controlled
experiment)
https://shape-of-code.com/2018/03/25/top-must-read-paper-on-software-fault-analysis/

The data is rarely understood, rather than poorly understood.

In what way is the data inaccurate?

The analysis makes some assumptions:
"(assuming that the report relates to a coding mistake and
is not a request for enhancement or something the user did wrong,
and the number of active users remains the same and the program
is not changed)"
and it's unlikely that the data meets any of these assumptions.

Including the variability that these assumptions exclude into
the models will make them more complicated and introduce more
unknowns.

The models given are the simplest and involve the fewest number
of unknowns.



> Regards
> 
> Martyn
> 
>> On 7 Jan 2026, at 13:24, Derek M Jones <derek at knosof.co.uk> wrote:
>>
>> All,
>>
>> A Happy New Year to you all.
>>
>> After the arrival of a fault report for a program
>> what is the expected elapsed time until the next
>> fault report arrives?
>>
>> The answer depends on whether you are interested in
>> the next report of a known fault (i.e., already reported
>> at least once), or the next report of an unknown fault.
>>
>> An analysis of the problem here
>> https://shape-of-code.com/2026/01/04/modelling-time-to-next-reported-fault/
>>
>> tl;dr: Modelling time to next previously unreported fault has
>> an analytic solution that depends on variables whose values
>> have to be approximately approximated.
>>
>> --
>> Derek M. Jones           Evidence-based software engineering
>> blog:https://shape-of-code.com
>>
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> 

-- 
Derek M. Jones           Evidence-based software engineering
blog:https://shape-of-code.com