Step-stress likelihood inference for the modified Lindley distribution
Year: 2026
Type: article
Abstract: We develop likelihood-based inference for a two-level step-stress accelerated life test (SSALT) under the Modified Lindley (MoL) lifetime model. The distributional parameter is allowed to change at a pre-specified stress-change time through a log-link, with π 1 = e x p β‘ ( π½ 0 ) before the change and π 2 = e x p β‘ ( π½ 0 + π½ 1 ) after the change. Under Type-I hybrid censoring, we derive the corresponding log-likelihood, obtain the maximum likelihood estimators, and construct Wald and profile likelihood-ratio confidence intervals for the model parameters and for decision-relevant functionals, including the mean life, quantiles, and mission-time reliability. We also introduce a Monte Carlo calibration-and-design layer for selecting ( π , π , π‘ e n d ) to meet operating-risk requirements at two planning points while minimizing an operational objective such as expected test duration or total cost. The proposed framework clarifies the role of the Modified Lindley model in SSALT, gives explicit conditions supporting MLE-based inference, uses Type-I hybrid censoring to control test duration while retaining failure information, and includes a preliminary examination of the observed failure times before the hybrid-censored analysis.
Author: Ayman Baklizi
Institution: Yarmouk University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,370
OpenAlex ID: W7153979168