An improved adaptive EWMA control chart for monitoring time between events with application in health sector

Abstract

Nonconforming events rarely occur in high-quality processes, and the time between events ((Formula presented.)) is likely to be followed by a skewed distribution, such as an exponential distribution. This paper proposes the upper and lower-sided improved adaptive exponentially weighted moving control charts for monitoring (Formula presented.) data modeled by the exponential distribution. The proposed control charts are labeled as (Formula presented.) control charts, that is, the (Formula presented.) and (Formula presented.) control chart, respectively. The (Formula presented.) control chart detects the upward shifts, while the (Formula presented.) control chart identifies the downward shifts in the process. The Monte Carlo simulations are used to approximate the run length distribution of the proposed control charts. Numerical results associated with various performance measures, such as average run length ((Formula presented.)), standard run length ((Formula presented.)), median run length ((Formula presented.)), extra quadratic loss ((Formula presented.)), relative average run length ((Formula presented.)), and performance comparison index ((Formula presented.)) are computed. The proposed control charts compared to the respective existing control charts, such as (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.) control charts, at a single shift, as well as over a specified range of shifts. The comparison reveals that the proposed control charts outperform the existing control charts for both single specified shifts and over a certain range of shifts. Finally, real-life data of hospital stay time for male patients with traumatic brain injury are analyzed for the applicability of the (Formula presented.) control chart in the health sector. 2023 John Wiley & Sons Ltd.