Multiple-stress model for one-shot device testing data under exponential distribution

Narayanaswamy BALAKRISHNAN, Man Ho Alpha LING

Research output: Contribution to journalArticlespeer-review

35 Citations (Scopus)


Left- and right-censored life time data arise naturally in one-shot device testing. An experimenter is often interested in identifying the effects of several stress variables on the lifetime of a device, and furthermore multiple-stress experiments controlling simultaneously several variables, result in reducing the experimental time as well as the cost of the experiment. Here, we present an expectation-maximization (EM) algorithm for developing inference on the reliability at a specific time, as well as the mean lifetime of the device based on one-shot device testing data under the exponential distribution when there are multiple stress factors. We use the log-linear link function for this purpose. Unlike in the typical EM algorithm, it is not necessary to obtain maximum likelihood estimates (MLEs) of the parameters at each step of the iteration. By using the one-step Newton-Raphson method, we observe that the convergence occurs quickly. We also use the jackknife technique to reduce the bias of the estimate obtained from the EM algorithm. In addition, we discuss the construction of confidence intervals for some reliability characteristics by using the asymptotic properties of the MLEs based on the observed Fisher information matrix, as well as by the jackknife technique, the parametric bootstrap methods, and a transformation technique. Finally, we present an example to illustrate all the inferential methods developed here. Copyright © 2012 IEEE.
Original languageEnglish
Pages (from-to)809-821
JournalIEEE Transactions on Reliability
Issue number3
Publication statusPublished - Sept 2012


Balakrishnan, N., & Ling, M. H. (2012). Multiple-stress model for one-shot device testing data under exponential distribution. IEEE Transactions on Reliability, 61(3), 809-821. doi: 10.1109/TR.2012.2208301


  • Asymptotic method
  • Binary data
  • Confidence intervals
  • Expectation-maximization algorithm
  • Exponential distribution
  • Jackknife
  • Least-squares method
  • Multiple-stress model
  • Oneshot device
  • Parametric bootstrap
  • Point estimation


Dive into the research topics of 'Multiple-stress model for one-shot device testing data under exponential distribution'. Together they form a unique fingerprint.