Combined Shewhart–EWMA and Shewhart–CUSUM monitoring schemes for time between events

Abstract

To improve the detecting abilities of upward and downward parameter changes in high‐quality process, two combined schemes by integrating memory‐type, that is, exponentially weighted moving average (EWMA) or cumulative sum (CUSUM), and memoryless, that is, Shewhart, are proposed for monitoring the time between events (TBE), which is modeled as an exponential distributed variable. A Monte Carlo simulation method is employed to obtain the Run Length () properties, that is average run length (), of the proposed schemes for different parameter settings. The nearly optimal monitoring parameter combinations under different change size are obtained by minimizing the out‐of‐control with the satisfied in‐control . Using the designed parameters, the performance of the proposed monitoring schemes is compared with the existing EWMA and CUSUM TBE. The results show that the proposed combined Shewhart–EWMA or Shewhart–CUSUM TBE generally perform better than the corresponding EWMA or CUSUM TBE for large changes and they also show better performance than the Shewhart TBE for small changes. Finally, a real dataset of organic light‐emitting diode (OLED) failure time from Sumsung company is employed to indicate the usage and implementation of combined TBE schemes.