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<p>This note rectifies an inaccuracy in the likelihood function of the step-stress partially accelerated life test (SSPALT) model under the adaptive Type-I progressively hybrid censoring scheme (Type-I APHCS) as presented by Ismail (Stat Pap 57(2):271–301, 2016). The initial formulation erroneously incorporates a survival term at the stress-change time <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> for units that persist in testing under accelerated conditions. This term is unjustified, as no removals take place at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> in the adaptive scheme. We present the revised likelihood expression and verify its alignment with known formulations. The non-adaptive Type-I PHC approach in the same publication remains valid as it accurately considers scheduled deletions at <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>. Researchers utilizing the adaptive Type-I APHCS must apply the adjusted likelihood to guarantee valid statistical inference.</p>

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Comment on “Statistical inference for a step-stress partially-accelerated life test model with an adaptive Type-I progressively hybrid censored data from Weibull distribution”

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • T. S. Taher

摘要

This note rectifies an inaccuracy in the likelihood function of the step-stress partially accelerated life test (SSPALT) model under the adaptive Type-I progressively hybrid censoring scheme (Type-I APHCS) as presented by Ismail (Stat Pap 57(2):271–301, 2016). The initial formulation erroneously incorporates a survival term at the stress-change time \(\tau \) τ for units that persist in testing under accelerated conditions. This term is unjustified, as no removals take place at \(\tau \) τ in the adaptive scheme. We present the revised likelihood expression and verify its alignment with known formulations. The non-adaptive Type-I PHC approach in the same publication remains valid as it accurately considers scheduled deletions at \(\tau \) τ . Researchers utilizing the adaptive Type-I APHCS must apply the adjusted likelihood to guarantee valid statistical inference.