Testing process precision for truncated normal distributions

Process precision index C_p has been widely used in the manufacturing industry to provide numerical measures of process precision, which essentially reflects product quality consistency. Precision measures using C_p for normal processes, contaminated normal processes, have been investigated extensively, but are neglected for truncated normal processes. Truncated normal processes are common in the manufacturing industry, particularly, for factories equipped with automatic machines handling fully inspections, and scrap/rework products falling outside the specification limits. If the processes follow the normal distribution, then the inspected products (processes) must follow the truncated normal distribution. In this note, we consider the precision measure for truncated normal processes. We investigate the analytically intractable sampling distribution of the estimated C_p, and obtain a rather accurate approximation. Using the results, we develop a practical testing procedure for practitioners to use in their in-plant applications.