Exact Maximum Likelihood Estimation Using Masked System Data

Dennis K.J. Lin, John S. Usher, Frank M. Guess

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

This paper estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. We extend the results of Usher & Hodgson (1988) by deriving exact maximum likelihood estimators (MLE) for the general case of a series system of 3 exponential components with independent masking. Their previous work shows that closed-form MLE are intractable, and they propose an iterative method for the solution of a system of 3 Nonlinear likelihood equations. They do not, however, prove convergence for their iterative method. As such, we show how this system of Nonlinear equations can be replaced by a single quartic equation, whose solution is straight-forward. Since it does not depend upon the convergence of numerical solution algorithms, the results are exact. Though the resulting estimators are somewhat lengthy & cumbersome to find manually, they can be written as a straightforward computer code. The calculations can then be easily performed on a personal computer. This method for reducing the likelihood equations to simpler-to-solve forms can be extended readily to a higher number of components. In many cases for more than 3 components it is easier while for others it is more complicated; even in the more complicated cases, this simplification makes the problems much more tractable.

Original languageEnglish (US)
Pages (from-to)631-635
Number of pages5
JournalIEEE Transactions on Reliability
Volume42
Issue number4
DOIs
StatePublished - Jan 1 1993

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Maximum likelihood estimation
Iterative methods
Maximum likelihood
Nonlinear equations
Personal computers

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Electrical and Electronic Engineering

Cite this

Lin, Dennis K.J. ; Usher, John S. ; Guess, Frank M. / Exact Maximum Likelihood Estimation Using Masked System Data. In: IEEE Transactions on Reliability. 1993 ; Vol. 42, No. 4. pp. 631-635.
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Exact Maximum Likelihood Estimation Using Masked System Data. / Lin, Dennis K.J.; Usher, John S.; Guess, Frank M.

In: IEEE Transactions on Reliability, Vol. 42, No. 4, 01.01.1993, p. 631-635.

Research output: Contribution to journalArticle

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