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Updated: Sep 8, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Optimum test planning for heterogeneous inverse Gaussian processes.

Chien-Yu Peng¹, Hideki Nagatsuka², Ya-Shan Cheng³

¹Institute of Statistical Science, Academia Sinica, Taipei, Taiwan. chienyu@stat.sinica.edu.tw.

Lifetime Data Analysis

|June 12, 2022

Summary

This study derives an explicit algebraic expression for the Fisher Information Matrix (FIM) of heterogeneous inverse Gaussian (IG) processes. This enables the development of optimum test plans for highly reliable products, reducing uncertainty in degradation modeling.

Keywords:

Conjugate distribution Destructive degradation Orthogonality Random effects Repeated measures

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Area of Science:

Reliability Engineering
Statistical Modeling
Degradation Analysis

Background:

Heterogeneous inverse Gaussian (IG) processes are widely used for modeling product degradation.
A key challenge is the absence of analytical expressions for the Fisher Information Matrix (FIM), hindering optimal test plan design.

Purpose of the Study:

To derive an explicit algebraic expression for the FIM of IG processes with random slopes.
To develop methods for determining optimum test plans based on the derived FIM.
To analyze the influence of experimental costs and parameter values on test plan optimization.

Main Methods:

Derivation of the FIM for IG processes with random slopes using algebraic methods.
Application of profile optimum plans to determine D- and V-optimum test plans, with and without cost constraints.
Conducting sensitivity analysis to assess the impact of various factors on optimum planning.

Main Results:

An explicit algebraic expression for the FIM of heterogeneous IG processes with random slopes was successfully derived.
The study presents a method for obtaining D- and V-optimum test plans, considering cost constraints.
Sensitivity analysis reveals how experimental costs and parameter planning values affect optimal test plan selection.

Conclusions:

The derived FIM expression reduces uncertainty associated with numerical approximations in IG process modeling.
The proposed methodology facilitates the design of efficient and cost-effective test plans for highly reliable products.
The findings provide valuable insights for optimizing experimental designs in reliability engineering.