Various methods of estimating constant-partially accelerated life tests of the Odd Kappa-Exponential distribution based on complete data

This study aims to address a central issue in continuous partially accelerated life testing for complete failure data by developing and comparing eight estimating methods for the two-parameter Odd Kappa-Exponential distribution, which features a flexible bathtub-shaped hazard rate. We provide the maximum likelihood, least squares, weighted least squares, Cramér-von Mises, Anderson-Darling, right-tail Anderson-Darling, percentile, and maximum product of spacing estimators for estimating the parameters (α,β) and the acceleration factor (θ). An extensive simulation study (N = 10,000 repetitions) shows that the maximum product of spacing estimator dominates alternative estimators when α < 1, at all possible combinations of the sample size and population parameter values. For example, if (α, β, θ)=(0.5, 0.5, 1.5) and the sample size (m1, m2)=(20, 20), then the mean squared error of the maximum product of spacing estimator is reduced 31 % for α (mean squared error of maximum likelihood estimator=0.0194, mean squared error of maximum product of spacing estimator=0.0133) and 14 % for θ (mean squared error of maximum likelihood estimator=0.1344, mean squared error of maximum product of spacing estimator=0.1161) over the maximum likelihood estimator. For the larger samples (m = 300), there is a similar superiority: the maximum of the product of mean squared error of the spacing estimator for θ is less than 2 % of the maximum of the MLE. To illustrate the efficacy of our proposed agonistic classes, we present the results of our analysis for two engineering datasets: insulating fluid breakdown times (m = 26) and steel failure times (m = 20), which demonstrate a superior fit for the two-parameter Odd Kappa-Exponential distribution, as indicated by Kolmogorov-Smirnov p-values greater than 0.63, thereby confirming the effectiveness of our approaches. For the two data sets, the Akaike weights of the two-parameter Odd Kappa-Exponential distribution with increasing magnitude of acceleration exceed those of other competing distributions by more than two times. We suggest using the maximum product of spacing, maximum likelihood, Anderson-Darling, and least squares estimators for CPALT applications with emphasis on accuracy in reliability engineering.