A random alarm is a signalling device with random interarrival times having a prescribed probability distribution. In this paper, a specific design for a simple, compact, electronic random alarm mechanism is presented. The design can accommodate any chosen continuous distribution of interarrival times, since these times are obtained by appropriate transformation in a device that produces the uniform probability distribution of some physical quantity. Nonstored-table varieties of this type may be constructed by combining an RC charging network with different types of potentiometers. A general prescription is given here for the output potential of the potentiometer as a function of the angle of rotation, where the angle is a uniformly distributed random variable. The ability of nonstored-table mechanisms to realize arbitrary distributions is dependent upon three theoretical asymptotic considerations concerning the normal distribution, the uniform distribution and independence. An empirical investigation with data from twists of a simulated potentiometer is used to verify that these results are sufficiently robust for practical application.