The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Field data analyses for products with multiple-modes of failure

고장원인이 여럿인 제품의 사용현장 데이터 분석

  • 배도선 ((305-701) 대전시 유성구 구성동 373-1, 한국과학기술원 산업공학과) ;
  • 최인수 ((305-701) 대전시 유성구 구성동 373-1, 한국과학기술원 산업공학과) ;
  • 황용근 ((150-042) 서울시 영등포구 당산동 2가 11-5, 주식회사 큐빅테크)
  • Published : 1995.03.01
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Abstract

This paper is concerned with the method of estimating lifetime distributin from field data for products with multiple modes of failure. When product failures occur within warranty period, a manufacturer can obtain failure-record data; failure times, causes of failure, and covariates. Since these data are seriously incomplete for satisfactory inference, that is, only failures occured during warrantly period may be recorded, it is usually necessary to incoporate the failure-record data by taking a supplementary sample of items obtained following up a portion of products that survive warranty time. The log linear function is considered as a model for describing the relation between failure time of a product and covariates. General methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and their asymptotic properties are studied, and specific formulas for exponential or Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extensions to calendar time warranty or calendar and obtaining time warranty are also considered.

사용현장에서의 고장데이터는 미리 정해진 보증기간동안 고장이 발생한 제품으로부터 얻어지는 고장시간, 고장원인, 설명변수값과 보증기간동안 고장나지 않는 제품 중 일정비율을 추적조사하여 얻은 설명변수 값들로 구성된다. 사용현장에서 얻어지는 이와 같은 데이터를 이용하여 제품수명분포의 모수가 설명변수와 대수선형관계일 때, 수명분포의 모수에 대한 의사(pseudo) 최우추정량을 구하고 그 점근성질을 규명하였으며, 고장원인별 제품수명이 와이블분포를 따를 때의 의사최우추정량과 점근분산을 구하였다. 제품의 보증기간이 달력시간이고 제품의 고장이 운영시간에 의존하는 경우와 제품의 보증이 달력시간과 운영시간의 혼합인 경우의 분석방법도 제시하였다. 또한 모의 실험을 통하여 추적조사비율에 따른 효과를 알아보았다.

Keywords

References

  1. IEEE Transaction on Reliability v.R-40 Optimal Simple step-Stress accelerated life tests with competing causes of failure Bai,D.S.;Chun,Y.R.
  2. Mathematical Methods of Statistics Cramer,H.
  3. Econometric Theory v.2 On consistency and inconsistency of estimating equations Crowder,M.
  4. The theory of competing risks David,H.A.;Moeschberger,M.L.
  5. Journal of Quality Technology v.14 Pitfalls and practical considerations in product life analysis Hahn,G.J.;Meeker,W.Q.
  6. Technometrics v.13 Maximum likelihood for multi-risk model Herman,R.J.;Patell,K.N.
  7. Annals of the Institute of Statistical Mathematics v.25 Asymptotic relations between the likelihood estimating function and maximum likelihood estimator Inagaki,N.
  8. IMSL library:reference manual International Mathematical and Statistical Libraries, Inc.
  9. Technometrics v.30 Estimation of reliability in field-performance studies Kalbfleisch,J.D.;Lawless,J.F.
  10. Technometrics v.25 Statistical methods in reliability Lawless,J.F.
  11. IEEE Transaction of Reliability v.R-33 Analysis of incomplete data in competing risks model Miyakawa,M.
  12. Applied Life Data Analysis Nelson,W.
  13. Technometrics v.27 Estimation of lifetime parameters from incomplete field data Suzuki,K.
  14. Journal of the American Statistical Association v.80 Nonparametric estimation of lifetime distributions from a record of failures and follow-ups Suzuki,K.