Parameters appearing in deterministic optimization (DO) models are kept constant during optimization, though uncertainty in these parameters is an inherent and unavoidable. Investigations about the effect of these uncertain parameters (UP) on the final outcomes are, therefore, necessary. Chance-Constrained Programming (CCP) can handle such situations by introducing the probability of constraint satisfaction and converting optimization under uncertainty problems into an equivalent deterministic optimization problem (EDOP). However, the most popular variant of this method neglects the aspects of parameter dependency for the ease of the analysis. Under the conditions when the correlations exist among UPs, the use of joint CCP with parameter dependency information is necessary to avoid misleading results arising from the assumption of no correlation. To show the impact of dependency of UPs on the outcomes of optimization, joint CCP has been adopted in this study for an industrial grinding process (IGP), which is non-linear in nature in terms of its system states as well as UPs. The effects of both confidence level and correlation coefficient have been shown on the Pareto optimal (PO) front for different sets of distributions among UPs while handling a multi-objective optimization problem (MOOP) of the Grinding Process. © 2020 Taylor & Francis.