Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

Area of Science:

• Reliability Engineering
• Statistical Inference
• Accelerated Life Testing

Background:

• High-reliability product life testing requires extensive durations, necessitating methods like accelerated life tests (ALTs) to expedite evaluation.
• ALTs employ harsher conditions, reducing product life expectancy and often resulting in censored data due to practical constraints.
• Censored data, where complete failure times are unknown, presents challenges in accurately estimating product reliability.

Purpose of the Study:

• To investigate and compare the effectiveness of two censoring schemes—type-I progressive hybrid censoring (PHCS) and type-II progressive censorship (PCS)—within a step stress partially accelerated life test (SSPALT) framework.
• To estimate unknown parameters using maximum likelihood estimation (MLE) and construct approximate confidence intervals (ACIs) for reliability assessment.
• To evaluate the performance of estimators based on root mean squared error (RMSE), relative absolute bias (RAB), interval length, and coverage probability (CP).

Main Methods:

• The study utilizes the step stress partially accelerated life test (SSPALT) model.
• Failure times are modeled using the NH distribution, with the tampered random variable (TRV) model accounting for stress level changes.
• Maximum Likelihood Estimation (MLE) is employed for parameter estimation, and asymptotic theory is used for constructing approximate confidence intervals (ACIs).

Main Results:

• Simulation studies indicate that the type-I progressive hybrid censoring scheme (type-I PHCS) generally outperforms the type-II progressive censorship scheme (type-II PCS).
• Type-I PHCS demonstrates superior performance in terms of lower RMSEs and RABs for point estimates.
• Approximate confidence intervals derived from type-I PHCS exhibit better characteristics, including shorter lengths and higher coverage probabilities (CPs).

Conclusions:

• The type-I progressive hybrid censoring scheme is recommended for step stress partially accelerated life tests due to its superior estimation accuracy and interval precision.
• The findings provide valuable insights for optimizing life testing strategies for high-reliability products under accelerated conditions.
• A practical application using insulating fluid failure times validates the proposed methodology.