Statistical Inference on a Flexible Loss-based Capability Index for Normal Processes

This article presents a new index for evaluating the manufacturing processes based on a non-symmetric and flexible loss function. The proposed index offers flexibility in capturing varied process deviations and aligns with practical manufacturing requirements. A combination of the squared error and absolute error loss functions can be considered as the model for the loss function. The Monte Carlo simulation procedure is discussed and investigated for the proposed loss-based index in three significant statistical problems, including: (1) the point estimation of the loss-based process capability index, (2) the construction of confidence intervals for the capability index, and (3) testing the capability on the basis of the non-symmetric loss function. To demonstrate the practicality and implementation of the proposed simulation methodology, illustrative examples are derived from a pipe manufacturing industry. These results exemplify the utility of the loss-based process capability index in addressing real-world challenges, such as assessing process capability and ensuring quality compliance.