One-Shot Device Testing Data Analysis under Logistic-Exponential Lifetimes with an Application to SEER Gallbladder Cancer Data

TL;DR

This paper develops robust statistical methods for analyzing one-shot device data with logistic-exponential lifetimes, applying them to gallbladder cancer survival data and optimizing inspection times using genetic algorithms.

Contribution

It introduces weighted minimum density power divergence estimators for robust parameter estimation in one-shot device analysis with logistic-exponential lifetimes, applied to biomedical data.

Findings

Robust estimators outperform MLE in simulations.

Optimal inspection times reduce costs while maintaining estimation accuracy.

Application to SEER data demonstrates practical utility.

Abstract

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in the presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where we often evidence that inflicted with a certain disease, survival time would be under different stress factors like environmental stress, co-morbidity, the severity of disease etc. This work is concerned with a one-shot device data analysis and applies it to SEER Gallbladder cancer data. The two-parameter logistic exponential distribution is applied as a lifetime distribution. For robust parameter estimation, weighted minimum density power divergence estimators (WMDPDE) is obtained along with the conventional maximum likelihood estimators (MLE). The asymptotic behaviour of the WMDPDE and the robust test statistic based on the density power divergence measure are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to SEER Gallbladder cancer data. Citing the importance of knowing exactly when to inspect the one-shot devices put to the test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is accomplished through the population-based heuristic optimization method Genetic Algorithm.