Layman's abstract:The np Chart with Guaranteed In-control Average Run Lengths

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  • Author: Alireza Faraz, Cédric Heuchenne, Erwin Saniga
  • Date: 08 September 2017
  • Copyright: © John Wiley & Sons Ltd

Every Friday on Statistics Views, we publish layman's abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format. This article featured today is from the Quality and Reliability Engineering International: The np Chart with Guaranteed In-control Average Run Lengths by Alireza Faraz, Cédric Heuchenne, Erwin Saniga.

Read the layman's abstract below.

Alireza Faraz, Cédric Heuchenne, Erwin Saniga. (2017), The np Chart with Guaranteed In-control Average Run Lengths, Quality and Reliability Engineering International, 33, pages 1057–1066, doi: 10.1002/qre.2091

thumbnail image: Layman's abstract:The np Chart with Guaranteed In-control Average Run Lengths

One employs an np control chart when one performs statistical process control (SPC) on a process where output is measured in terms of the count of defectives in a sample of size n.
To monitor a process, which is the second phase of SPC, or Phase II, one must estimate the parameters of the process; in this case the parameter estimated is p, the probability of a defective in a sample of size n. To do this, one usually takes n samples of size m in the first phase of SPC, called Phase I. A question of some complexity is the determination of m.

In this paper, we show how to use a common method of resampling called bootstrapping to determine m such that a particular performance measure of a control charts effectiveness is obtained. That measure is called the average run length (ARL) when the process is in control. In practice one wishes ARL in control to be very large since it measures the number of samples where the control chart would signal an assignable cause of poor quality given that no cause exists; i.e. this would guarantee that a false signal would not occur very often.

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