Estimation of reliability in field-performance studies

Likelihood-based methods are developed for the analysis of field-performance studies with particular attention centered on the estimation of regression coefficients in parametric models. Failure-record data are those in which the time to failure and the regressor variables are observed only for those items that fail in some prespecified follow-up or warranty period (0, T]. It is noted that for satisfactory inference about baseline failure rates or regression effects it is usually necessary to supplement the failure-record data either by incorporating specific prior information about x or by taking a supplementary sample of items that survive T ○. General methods are outlined and specific formulas for various likelihood-based methods are obtained when the failure-time model is exponential or Weibull. In these models the methods are compared with respect to asymptotic efftciency of estimation. Several extensions to more complicated sampling plans are considered.

[1]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[2]  N. Breslow,et al.  Statistical methods in cancer research. Vol. 1. The analysis of case-control studies. , 1981 .

[3]  Wayne Nelson,et al.  Applied life data analysis , 1983 .

[4]  R. L. Prentice,et al.  A case-cohort design for epidemiologic cohort studies and disease prevention trials , 1986 .

[5]  Martin Crowder,et al.  On Consistency and Inconsistency of Estimating Equations , 1986, Econometric Theory.

[6]  Nicholas P. Jewell,et al.  Least squares regression with data arising from stratified samples of the dependent variable , 1985 .

[7]  William Q. Meeker,et al.  Pitfalls and Practical Considerations in Product Life Analysis--Part I: Basic Concepts and Dangers of Extrapolation , 1982 .

[8]  V. P. Godambe,et al.  Parameters of superpopulation and survey population: their relationships and estimation , 1986 .

[9]  A. Scott,et al.  Regression Analysis Using Survey Data , 1981 .

[10]  D. Holt,et al.  Regression Analysis of Data from Complex Surveys , 1980 .

[11]  N. Inagaki.  Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator , 1973 .

[12]  D. Cox.  Regression Models and Life-Tables , 1972 .

[13]  A. Scott,et al.  Fitting Logistic Models Under Case‐Control or Choice Based Sampling , 1986 .

[14]  J F Lawless,et al.  Likelihood analysis of multi-state models for disease incidence and mortality. , 1988, Statistics in medicine.

[15]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[16]  Kazuyuki Suzuki,et al.  Estimation of Lifetime Parameters From Incomplete Field Data , 1985 .

[17]  Kazuyuki Suzuki.  Nonparametric Estimation of Lifetime Distributions from a Record of Failures and Follow-Ups , 1985 .

[18]  S. J. Amster,et al.  Planning and conducting field-tracking studies , 1982, The Bell System Technical Journal.

[19]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .