Order restricted inference for exponential step-stress models

Narayanaswamy Balakrishnan*, Eric Beutner, Maria Kateri

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


In the context of multiple step-stress models, which is a special type of accelerated life-testing model, interest lies on the expected lifetimes of the experimental units under different stress levels. Although the expected lifetime is shortened as the stress level increases, this information has not been incorporated so far into the associated inferential procedures. For this reason, we develop here the order restricted maximum likelihood estimation (MLE) for multiple step-stress models with exponentially distributed lifetimes under Type-I, and Type-II censored sampling situations. Moreover, the existence of the unrestricted MLE for a certain stress level is conditional on observing failures at that particular stress level. Under the order restriction, MLE exist even for stress levels without observed failures, provided that these stress levels are internal. We also discuss hypothesis testing problems under order restrictions.

Original languageEnglish
Pages (from-to)132-142
Number of pages11
JournalIEEE Transactions on Reliability
Issue number1
Publication statusPublished - 12 Feb 2009
Externally publishedYes


  • Cumulative exposure model
  • Hypothesis tests under order restrictions
  • Isotonic regression
  • Multiple step-stress models
  • Order restricted maximum likelihood estimationType-I and Type-II censored sampling


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