Rotary dial dialing time calculation

The total time = (dial rotation time for every digit) + (pulse time for every digit) + (inter-digit gaps). The 33% duty ratio only fixes how each pulse period is split into make (33%) and break (67%); it does not change the pulse period.

Digits and pulses (number 0119144414630, 13 digits; digit 0 gives 10 pulses):

Total pulses $= 58$.

Nominal rate (10 pps): pulse period $T = 1/10 = 100$ ms (make 33.3 ms, break 66.7 ms).

$$\begin{aligned} t &= 13 \times 600 + 58 \times 100 + 12 \times 200 \\ &= 7800 + 5800 + 2400 \\ &= 16000\ \text{ms} = 16.0\ \text{s} \end{aligned}$$

Worst case (slowest rate, 10% tolerance → 9 pps): $T = 1/9 = 111.1$ ms.

$$\begin{aligned} t_{max} &= 7800 + 58 \times 111.1 + 2400 \\ &= 7800 + 6444.4 + 2400 = 16644.4\ \text{ms} \end{aligned}$$

(At the fastest rate, 11 pps, $T = 90.9$ ms and $t_{min} = 15472.7$ ms.)

Answer: about 16.0 s at the nominal 10 pps; up to 16.64 s in the worst case (9 pps). (12 inter-digit gaps are counted, between the 13 digits.)