The performance of a path generating linkage is measured in terms of the error in the generated path. The probability of producing its intended path is its reliability. Tighter tolerances in link lengths and joint clearances result in higher reliability but incur more costs. Therefore, it is desirable to understand the trade-off relationship between the costs and reliability. In the current work, a genetic algorithm is used to construct the Pareto trade-off front between cost and reliability by solving a bi-criterion optimisation problem. Statistical moments required to estimate reliability are computed by combining an approximate cumulative density function of error and a 3-point approximation technique. This approach uses a fraction of the samples compared to crude Monte Carlo simulation. The proposed approach is demonstrated on a four bar mechanism tracing a straight line and a closed path. It is observed that the Pareto front generated using the proposed approach with fewer samples compares well with the one generated with crude Monte Carlo simulation with a large sample set, thus offering enormous gains in computational efficiency. Copyright © 2017 Inderscience Enterprises Ltd.