TIME-BETWEEN-EVENTS CONTROL CHARTS BASEDON THE TRANSMUTED WEIGHTED EXPONENTIALDISTRIBUTION FOR SHIFT DETECTION

Abstract

This study introduces a novel control charting methodology based on the transmuted weighted exponential distribution (TWED) for monitoring time-between-events (TBE) data in industrial processes. Traditional Shewhart-type charts often rely on assumptions of normality and equal sampling probabilities, limiting their effectiveness in skewed or biased scenarios. The proposed TWED-TBE chart addresses these limitations by incorporating transmutation and weighting parameters, enhancing sensitivity to process shifts. Control limits for the TWED-TBE chart were derived analytically using the exact distribution of the monitoring statistic. Monte Carlo simulations were employed to evaluate chart performance under varying in-control average run lengths ( $A R L_0=200,250,300,370,500$ ). The parametric configuration $\lambda=5, \omega=2$ (area-biased), and $\beta=0.8$ yielded superior results in detecting shifts. The chart consistently outperformed existing TBE-based $t$-charts, achieving significantly lower $A R L_1$ values across a range of shift magnitudes ( $\delta=0.1$ to 1.0 ).

Percentage reductions in $A R L_1$ exceeded $90 \%$ in small shift scenarios, highlighting the chart's robustness. The proposed chart was further validated using simulated and real-world time-to-failure data. In both cases, TWED-TBE charts effectively identified shifts with greater accuracy and earlier detection compared to traditional methods. The findings confirm the utility of the TWED framework in enhancing the responsiveness of control charts under skewed lifetime data. This approach offers practical benefits for industries requiring reliable early detection of process deviations.

Received: August 4, 2025
Revision: August 27, 2025
Accepted: August 30, 2025