Pinch analysis is a physical insight-based optimization technique, applicable to conservation problems for a wide range of resources (such as energy, water, hydrogen, cooling water, etc.). Principally, it has been applied to optimize the external resource, to satisfy unmet demands in source-sink allocation problems, with deterministic flows and deterministic quality parameters (such as contamination concentration in water and hydrogen conservation problems). However, in many applications, quality and flow parameters of different sources may not be deterministic due to changes in environmental as well as operational conditions (e.g., changes in product mix and/or feed characteristics). In this paper, the applicability of pinch analysis has been extended to resource conservation networks with uncertain qualities and flows for the operation of individual sources and demands with the desired reliability. The uncertainties in source quality and source flows are incorporated through different probability distributions with known means and standard deviations. The stochastic constraints, due to uncertainties associated with flow and quality parameters of the sources, are converted to deterministic equivalents by use of chance-constrained programming. The resultant deterministic problem is approximated to a linear programming problem in order to address it through pinch analysis techniques. Applicability of the proposed methodology is demonstrated for water and hydrogen conservation networks, and the results are verified through Monte Carlo simulations.