Two nonparametric analogs of the CUSUM and EWMA control charts based on the Wilcoxon rank-sum test are proposed for detecting process mean shifts. The charts perform well in detecting step mean shifts and better than competing parametric charts when the..

Nonparametric CUSUM and EWMA Control Charts for Detecting Mean Shifts

This paper consists of three main parts. First, we give an introduction to Hill's assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism.

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On Nonparametric Predictive Inference and Objective Bayesianism

A lot of methods and models in classical reliability theory assume that all probabilities are precise, that is, that every probability involved is perfectly determinable. Moreover, it is usually assumed that there exists some complete probabilistic information about the system and component reliability behavior.

/pdf/imprecise-reliability-an-introductory-overview-582zib6vww.pdf

Imprecise Reliability: An Introductory Overview

Current and Potential Statistical Methods for Monitoring Multiple Data Streams for Biosurveillance

http://maths.dur.ac.uk/stats/people/fc/RESS-CCF-141105-rev.pdf

Predictive inference for system reliability after common-cause component failures

New methods for statistical process control are presented, where the inferences have a nonparametric predictive nature. We consider several problems in process control in terms of uncertainties about future observable random quantities, and we develop inferences for these random quantities hased on data available in the form of a reference set. We use Hill's assumption A(n), which enables predietive inferenee while adding only few assumptions to the data observed.

Nonparametric predictive inference in statistical process control

Statistical process control (SPC) is used to decide when to stop a process as confidence in the quality of the next item(s) is low. Information to specify a parametric model is not always available, and as SPC is of a predictive nature, we present a control chart developed using nonparametric predictive inference. The proposed ‘extrema chart’, based on the extrema of a sample of observations from the process, is a generalisation of an existing nonparametric method, which controls a process using single observations. We examine the average run length (ARL) of both the one-sided and two-sided extrema chart, and a simulation study is presented to compare the extrema chart with the well known X¯ chart and CUSUM chart. The disadvantage of these charts is that when the process mean and variation of the in-control process have to be estimated, the ARL is biased. This is not an issue for the extrema chart, as no knowledge about the underlying distribution is required.

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G.R.J. Arts

Papers

Nonparametric predictive inference in statistical process control

Nonparametric Predictive Inference in Statistical Process Control