Software reliability is defined as the probability of failure-free operation of software over a specified time period and environment. Key factors influencing reliability include fault count, which is impacted by code size/complexity and development processes, and operational profile, which describes how users operate the system. Software reliability methodologies aim to improve dependability through fault avoidance, tolerance, removal, and forecasting, with the latter using models to predict reliability mathematically based on factors like time between failures or failure counts.