An Accelerated Life Model Analog for Discrete Survival and Count Data

Area of Science:

• Reliability Engineering
• Statistical Modeling
• Survival Analysis

Background:

• Continuous accelerated life models are widely used but limited for discrete data.
• Discrete failure time and count data present unique analytical challenges.
• Existing methods often lack flexibility for diverse hazard shapes.

Purpose of the Study:

• To develop a unified strategy for applying continuous accelerated life models in a discrete setting.
• To offer a flexible and unique modeling approach for discrete reliability data.
• To adapt existing methods for handling various discrete data distributions and censoring types.

Main Methods:

• Conversion of established continuous accelerated life distributions to their discrete counterparts.
• Theoretical demonstration of the reusability of existing continuous-data software for discrete censoring (left, right, interval).
• Leveraging the inherent structure of likelihood equations for discrete data analysis.

Main Results:

• The proposed modeling approach successfully accommodates discrete data with symmetric, left-skewed, and right-skewed distributions.
• Demonstrated effectiveness on both simulated and real-world datasets.
• Overcame limitations of traditional discrete modeling approaches.

Conclusions:

• The developed approach offers significant flexibility for discrete failure time and count data analysis.
• The discrete Weibull model, a special case, effectively handles Poisson-distributed data.
• The method provides high flexibility for both Poisson and non-Poisson distributed data, validated theoretically and through simulations.