Process capability indices (PCIs) aim to quantify the capability of a process of quality characteristic (X) to meet some specifications that are related to a measurable characteristic of its produced items. One such quality characteristic is life time of items. The specifications are determined through the lower specification limit (L), the upper specification limit (U), and the target value (T). Maiti et al. (2010) have proposed a generalized process capability index that is the ratio of proportion of specification conformance to proportion of desired conformance. Bayesian estimation of the index has been considered under squared error loss function. Normal, exponential (nonnormal), and Poisson (discrete) processes have been taken into account. Bayes estimates of the index have been compared with the frequentist counterparts. Data sets have been analyzed.