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We describe the $\texttt{Period detection and Identification Pipeline Suite}$ ($\texttt{PIPS}$) -- a new, fast, and statistically robust platform for period detection and analysis of astrophysical time-series data. $\texttt{PIPS}$ is an open-source Python package that provides various pre-implemented methods and a customisable framework for automated, robust period measurements with principled uncertainties and statistical significance calculations. In addition to detailing the general algorithm that underlies $\texttt{PIPS}$, this paper discusses one of $\texttt{PIPS'}$ central and novel features, the Fourier-likelihood periodogram, and compares its performance to existing methods. The resulting improved performance implies that one can construct deeper, larger, and more reliable sets of derived properties from various observations, including all-sky surveys. We present a comprehensive validation of $\texttt{PIPS}$ against artificially generated data, which demonstrates the reliable performance of our algorithm for a class of periodic variable stars (RR Lyrae stars).