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Different estimation techniques and data analysis for constant-partially accelerated life tests for power

Ghadah A Alomani1, Amal S Hassan2, Amer I Al-Omari3

  • 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia.

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Summary

Partial accelerated life tests (PALTs) require robust estimation strategies. This study compares classical and Bayesian methods for the power half-logistic distribution, finding maximum product of spacing and Bayesian approaches most effective for reliability engineering.

Keywords:
Acceleration factorConstant stressCramér von-MisesMaximum likelihood estimationPartially accelerated life testsPower half-logistic distributionWeighted least squares

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Area of Science:

  • Reliability Engineering
  • Statistical Modeling
  • Accelerated Life Testing

Background:

  • Partial accelerated life tests (PALTs) are crucial when standard accelerated life testing (ALT) results do not extrapolate to real-world usage conditions.
  • Estimating reliability parameters under PALTs presents significant challenges, particularly with complete data sets.
  • The power half-logistic distribution is frequently used to model lifetime data in reliability studies.

Purpose of the Study:

  • To investigate and compare various classical and Bayesian estimation techniques for parameters of the power half-logistic distribution under constant PALTs.
  • To evaluate the performance of these estimation methods using metrics like mean squared error (MSE), absolute average bias, interval length, and coverage probability.
  • To assess the efficacy of constructed Bayesian credible intervals versus approximate confidence intervals.

Main Methods:

  • Utilized several classical estimation techniques: Anderson-Darling, maximum likelihood, Cramér-von-Mises, ordinary least squares, weighted least squares, and maximum product of spacing.
  • Employed Bayesian estimation methods for parameter and acceleration factor estimation.
  • Conducted a simulation study to compare the performance of all methods.
  • Constructed both approximate confidence intervals and Bayesian credible intervals.

Main Results:

  • The maximum product of spacing estimation method demonstrated superior performance in most scenarios, achieving minimum MSE and average bias.
  • Bayesian estimation methods generally outperformed other techniques when considering both MSE and average bias.
  • Bayesian credible intervals exhibited higher coverage probabilities and shorter average lengths compared to approximate confidence intervals.
  • Analysis of two real-world engineering data sets confirmed the practical applicability of the proposed methods.

Conclusions:

  • The maximum product of spacing and Bayesian methods are highly recommended for parameter estimation in constant PALTs with power half-logistic distributed data.
  • Bayesian credible intervals offer a more reliable alternative to approximate confidence intervals for assessing parameter uncertainty.
  • The investigated estimation strategies are practical and applicable to real-world engineering reliability problems.