The Measurement of a Lepton-Lepton Electroweak Reaction (MOLLER) experiment, approved and scheduled to be conducted at the Thomas Jefferson National Accelerator Facility (JLab), aims to provide a high-precision measurement of the parity-violating asymmetry in the scattering of longitudinally polarized electrons off an unpolarized liquid hydrogen target. Utilizing an 11 GeV upgraded beam, the MOLLER experiment will measure the asymmetry with a precision of 2.4% at an average ( Q^2 ) of 0.0056 (\text{GeV}^2). This experiment is expected to probe new physics beyond the Standard Model of particle physics and provide significant new details on the electroweak world, particularly the weak mixing angle.

To achieve the expected precision, corrections must be applied to the Møller signal for background processes characterized by background asymmetries and fractional dilution factors. Significant contributions to these experimental signal corrections come from pion asymmetries and pion dilution factors, which will be measured using a dedicated pion detector system. The design, development, and prototyping of the pion detector system for the MOLLER experiment are the primary objectives of this thesis. To confirm the effectiveness of the detector system, the outcomes from simulations, cosmic testing carried out at the University of Manitoba, and beam testing carried out at MAMI B microtron in Mainz, Germany, will be compared.

Furthermore, this thesis introduces Bayesian analysis as a novel approach for applying non-experimental signal corrections to experimental values. Serving as a complement to the commonly used frequentist methods, Bayesian analysis is explored for its potential to refine experimental results. By employing Bayesian analysis, the accuracy of corrections applied post-measurement is aimed to be enhanced, thereby improving the overall precision of the MOLLER experiment. The benefits and implications of using Bayesian analysis for theoretical corrections in Parity-Violating Electron Scattering (PVES) experiments are thoroughly examined.

The results provided in this work emphasize the importance of understanding and controlling the parity-violating and parity-conserving asymmetries for pions to achieve the required precision in the MOLLER experiment. The effectiveness of the MOLLER experiment and its potential to improve our understanding of the electroweak interaction and the Standard Model are significantly affected by the results of this research.