Statistical Analysis of Marginal Count Failure Data

Rezaul Karim, Wataru Yamamoto, Kazuyuki Suzuki

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


Manufacturers want to assess the quality and reliability of their products. Specifically, they want to know the exact number of failures from the sales transacted during a particular month. Information available today is sometimes incomplete as many companies analyze their failure data simply comparing sales for a total month from a particular department with the total number of claims registered for that given month. This information - called marginal count data - is, thus, incomplete as it does not give the exact number of failures of the specific products that were sold in a particular month. In this paper we discuss nonparametric estimation of the mean numbers of failures for repairable products and the failure probabilities for nonrepairable products. We present a nonhomogeneous Poisson process model for repairable products and a multinomial model and its Poisson approximation for nonrepairable products. A numerical example is given and a simulation is carried out to evaluate the proposed methods of estimating failure probabilities under a number of possible situations.

Original languageEnglish
Pages (from-to)173-186
Number of pages14
JournalLifetime Data Analysis
Issue number2
Publication statusPublished - 2001
Externally publishedYes


  • EM algorithm
  • Marginal data
  • Multinomial distribution
  • Nonhomogeneous Poisson process (NHPP)
  • Poisson approximation

ASJC Scopus subject areas

  • Applied Mathematics


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