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Non‐parametric Predictive Inference for Age Replacement with a Renewal Argument
Author(s) -
CoolenSchrijner P.,
Coolen F. P. A.
Publication year - 2004
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.561
Subject(s) - inference , function (biology) , mathematics , parametric statistics , upper and lower bounds , percentile , argument (complex analysis) , distribution (mathematics) , mathematical optimization , computer science , statistics , artificial intelligence , mathematical analysis , biochemistry , chemistry , evolutionary biology , biology
We consider an age replacement problem with cost function based on the renewal reward theorem. However, instead of assuming a known probability distribution for the lifetimes, we apply Hill's assumption $A_{(n)}$ for predicting probabilities for the lifetime of a future item. Lower and upper bounds for the survival function of a future item are used, resulting in upper and lower cost functions. Minimizing these upper and lower cost functions to obtain the optimal age replacement times is simplified due to the special form of these functions. To discuss some features of our approach, we first study the consequences of using $n$ equally spaced percentiles from a known distribution instead of $n$ observed data. Secondly, we report on a simulation study where the lifetimes are simulated from known distributions, so that the optimal replacement times corresponding to our approach can be compared with the theoretical optimal replacement times. Copyright © 2004 John Wiley & Sons, Ltd.