Monitoring the Exponential Distribution Parameter Using an Extended EWMA Statistic

ABSTRACT

Statistical process monitoring is an important aspect in quality control, reliability theory, and biomedical engineering, where detecting changes in the process at an early stage is of prime importance. In many real‐world problems, the process may show strong right skewness, and the process may not follow normal theory. In such cases, the process may follow a non‐normal distribution, such as the exponential distribution. In such cases, the traditional control charts may not perform satisfactorily. Even though the exponentially weighted moving average (EWMA) control chart is widely used, as it is efficient in detecting small and medium‐sized shifts, in the case of strongly skewed exponential distributions, the performance may not be satisfactory. In this study, an extended exponentially weighted moving average (EEWMA) control chart is proposed. The proposed chart builds on the traditional EWMA chart by adding an extra smoothing term that uses information from both current and past observations. The control limits are determined based on the statistical properties of the exponential distribution. The coefficient for the proposed chart is determined by simulation to attain the desired in‐control performance. Simulation results demonstrate that the proposed EEWMA chart detects shifts faster than the traditional EWMA chart.