We present an analytical approach to accurately model the phase sensitivity, and provide simple analytical formulae, useful in the design, comparison and optimization of multiplexed amplified interferometric fiber-optic based sensor systems. The phase sensitivity model incorporates the various key noise contributions including receiver noise, amplified spontaneous emission (ASE) induced noise, active sources noise and other phase noise terms. We define and present a novel term `Demod phase sensitivity' to take into account the effects from noise aliasing in systems based on time division multiplexed (TDM) architectures. An experiment was conducted that confirmed the appropriateness and accuracy of the phase sensitivity model. The approach is widely applicable but particular appropriate for fiber-optic sensor systems using amplifiers and TDM.