Design of Generalized Gamma X̄ and s Control Charts for Monitoring Industrial Process

Abstract

Shewhart control charts are suitable for stable but repetitive production processes used for the subsequent identification of random deviations while indicating breached quality limits. Shewhart control charts are commonly used to determine if a process is under control. Control limits are essential for monitoring process stability and making smart decisions about which processes in industries require attention and development. Control charts that are successful require accurate control limit specification. The constraints of a Shewhart control chart are predicated on the assumption that the process quality characteristics under consideration may be represented by a symmetrical normal distribution. Because industrial processes are rarely normally distributed in practice, using standard Shewhart Control charts with non-normal process data results in erroneous control limits, leading to wrong conclusions. Consequently, this study proposes utilizing the mean and dispersion of quality parameters that follow generalized gamma distributions to construct control chart limits. A simulation analysis was carried out to evaluate the performance of the proposed charts to existing methodologies. The usefulness of the proposed charts was further validated with process data from the manufacturing industries. The results show that the suggested charts may be used to monitor skewed and reverse-J distributions and give appropriate control chart limits that do not trigger false alarms. As a result, the generalized gamma control chart (GG) approach is better suited for non-normal process data and is strongly recommended for monitoring industrial processes.