Process capability indices (PCIs) provide numerical measures on whether a process confirms to the defined capability prerequisite. They have been used to measure the ability of process to decide how well the process meets the specification limits (SLs). The PCIs have been successfully applied by companies for evaluating the quality and productivity performance. In this paper, one of the most important PCIs, process incapability index (C-pp) that provides more process information than other PCIs is analyzed together with the indices inaccuracy (C-ia) and imprecision (C-ip) under uncertainty. When there are some uncertainties in process parameters, traditional PCIs have failed to summarize process performance. Therefore the fuzzy set theory (FST) can be employed to overcome this problem. In this paper, the index C-pp is analyzed by using the FST to obtain more sensitiveness and a deep and flexible analysis. The fuzzy estimations of the index C-pp are derived for both of triangular and trapezoidal fuzzy numbers. The obtained fuzzy incapability index ((C) over tilde (pp)) is applied in a decision making process to determine the most appropriate supplier among alternatives for a construction firm in Turkey.