Properties of Isotonic Estimators of Mean Lifetime in a Simple Prototype Development Model.
Abstract
Consideration of a simple prototype development/reliability growth model leads to observation of variables X1, X2, ..., Xk; where the Xi are independent and are assumed to have the same distribution type with individual means lambda sub i. The problem is to estimate the lambda sub i, which are assumed to be non-decreasing due to design improvements in the device under development. For many common distributions, estimation via the restricted maximum likelihood principle leads to estimates which are the isotonic regression of the Xi with appropriate weights. This paper finds the distribution of lambda cap sub k, the mle of lambda sub k, when the Xi are exponentially distributed. Lambda cap sub k is then compared with X-bar and Xk, two competing estimates of lambda sub k. Gamma, normal, and Weibull distributed Xi are also considered, and the usefulness of lambda cap sub k is seen to depend on the relative magnitude of the variances and means of the Xi. Results are also examined when the restricted mles are generated assuming the lambda sub i are a non-decreasing and concave function of i. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 16, 1979
- Accession Number
- ADA075578
Entities
People
- Thomas P. Mcwilliams
Organizations
- Stanford University