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: Asymmetrical process capability index, Bayesian inference. 1 Introduction Since the early 70s the evaluation of process capability in industrial applications has been a subject of great deal of interest to study. In a general sense, a quality characteristic of interest denoted by X describes the output of the process and observed values of X must lie between a lower and an upper specification limit. Process capability means the ability to produce items according to the required specifications and since there are no consensus in how to measure this ability, many indices have