Determining a bulk concentration of a target in a sample using a digital assay with compartments having nonuniform volumes

A system, comprising:

• a barrier-phase liquid;
• a container configured to receive the barrier-phase liquid, to receive a sample including a target, and to generate compartments of the sample suspended in the barrier-phase liquid in response to a shaking of the container, at least one of the compartments having a respective volume that is different from a respective volume of each of at least another one of the compartments;
• a detector configured to determine a characterized number of the compartments each having a respective number of the target that is greater than a threshold number of the target and a characterized volume for each of the compartments having the target greater than the threshold number;
• and
• a microprocessor including firmware to determine a bulk concentration of the target in a source of the sample by generating an estimate of the bulk concentration in response to the characterized number of the compartments having the target greater than the threshold number and the characterized volume for each of the compartments having the target greater than the threshold number, wherein the bulk concentration is determined by a digital-variable-volume-approximation (DVVA) algorithm.