A New Useful Exponential Model with Applications to Quality Control and Actuarial Data.

Area of Science:

• Probability and Statistics
• Reliability Engineering
• Risk Management

Background:

• The need for flexible probability distributions in modeling complex phenomena.
• Limitations of existing distributions in capturing specific data characteristics.
• Importance of risk assessment and quality control in various industries.

Purpose of the Study:

• Introduce a novel compound probability distribution family: exponentiated Bell G.
• Develop and analyze a special case, the exponentiated Bell exponential (EBellE) model.
• Design a group acceptance sampling plan based on the EBellE model for quality assessment.

Main Methods:

• Compounding approach to derive the exponentiated Bell G family.
• Analytical derivation of essential properties for the new distribution family.
• Maximum likelihood estimation and simulation analysis for parameter estimation.
• Application of risk theory measures (Value-at-Risk, Expected Shortfall).

Main Results:

• The proposed exponentiated Bell G family and its special EBellE model are defined.
• Risk measures are computed for the EBellE model.
• A group acceptance sampling plan is developed using the EBellE model with median as a quality parameter.
• Empirical analysis demonstrates superior performance of the EBellE model over existing extended exponential models.

Conclusions:

• The exponentiated Bell G distribution family offers a valuable addition to statistical modeling.
• The EBellE model provides a robust framework for risk analysis and lifetime data modeling.
• The developed sampling plan enhances quality control through effective product reliability assessment.