Power Analysis of Two Kolmogorov --- Smirnov Type Criteria in Testing the Cox Power Model for the Progressively Censored Samples

Abstract

Testing a technical system often leads to a problem of comparing reliability indicators of their elements in different modes (operation in different climatic zones, comparing results of laboratory tests and real operation data, etc.). At the same time, laws of the element time to failure distribution are unknown. Nature of the available data causes additional difficulties in solving this problem, i.e. a failure of one element in a sequential system leads to the fact that time to failure of the remaining usable elements remains unknown (censored). In this regard, it becomes relevant to solve such a problem using the nonparametric (free from knowing distribution) methods. Previously, the authors developed a Kolmogorov --- Smirnov type criterion making it possible to check power dependence of the reliability functions with elements of the sequential systems (nonparametric Cox power model). Statistics of this criterion uses the Kaplan --- Meier estimates of the elements reliability functions constructed from developments in systems composed of them. However, a feature of the Kaplan --- Meier estimates is their slow convergence to the theoretical reliability function on the distribution right tail, which could lead to a decrease in the criterion power (decrease in sensitivity). Here, another criterion of the Kolmogorov --- Smirnov type is proposed to solve a similar problem, its statistics is not using the Kaplan --- Meier estimates and is based on comparing estimates of the system reliability functions. Exact and asymptotic distributions of its statistics are obtained. Detailed study of the two criteria power is carried out using numerical analysis and statistical simulation. The Cox parameter estimates accuracy is obtained by minimizing the compared criteria statistics and is analyzed using the Monte Carlo methods

Please cite this article in English as:

Timonin V.I., Tiannikova N.D. Power analysis of two Kolmogorov --- Smirnov type criteria in testing the Cox power model for the progressively censored samples. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2024, no. 2 (113), pp. 57--73 (in Russ.). EDN: KDBJJP

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