Work

Shewhart-Type TBEA Charts for Monitoring Frequency and Amplitude with Symmetry Structure Under Generalized Weibull and Generalized Log-Logistic Distributions

Year: 2026

Type: article

Abstract: Control charts for monitoring time between events (T) and amplitude (X) have been developed in recent years. Many TBEA charts depend on limited models such as exponential, normal, and gamma distributions and mainly rely on the ratio statistic (XT). This representation ignores the symmetric relationship between event occurrence and event magnitude. This paper proposes Shewhart-type TBEA charts constructed from three statistics (Z1), (Z2), and (Z3) based on (X) and (T). The approach models symmetry between frequency and amplitude using generalized Weibull and generalized log-logistic distributions. The statistics maintain proportional invariance when both variables shift together, which enables balanced monitoring of the process. Several scenarios are examined for detecting upward shifts. Performance is assessed using numerical measures of detection efficiency and average run length. The results show improved detection compared with classical ratio-based TBEA charts. A real data example from a French forest fire database illustrates the ability of the proposed charts to detect simultaneous changes in occurrence rate and burn intensity.

Source: Symmetry

DOI: 10.3390/sym18050750

Authors: Mustafa M. Hasaballah, Arvind Pandey, Pragya Gupta, Oluwafemi Samson Balogun, Farouq Mohammad A. Alam, Mahmoud E. Bakr

Institutions: Central University of Rajasthan, University of Eastern Finland, King Abdulaziz University, King Saud University

Language: English

Topic: Advanced Statistical Process Monitoring

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: King Saud University