A control chart for variance based on squared ranks

Elena Cristina Villanueva-Guerra, Vìctor Gustavo Tercero-Gómez, Alvaro Eduardo Cordero-Franco, William Jay Conover

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A nonparametric control chart for variance is proposed. The chart is constructed following the change-point approach through the recursive use of the squared ranks test for variance. It is capable of detecting changes in the behaviour of individual observations with performance similar to a self-starting CUSUM chart for scale when normality is assumed, and a relatively better power when assessing nonnormal observations. A comparison is also made with two equivalent nonparametric charts based on Mood and Ansari-Bradley statistics. When dealing with symmetrical distributions, the proposed chart shows smaller (better) out-of-control average run length (ARL), and a competing performance otherwise. In addition, sensitivity to changes in mean and variance at the same time was tested. Extensive Monte Carlo simulation was used to measure performance, and a practical example is provided to illustrate how the proposed control chart can be implemented in practice.

Original languageEnglish
Pages (from-to)3537-3562
Number of pages26
JournalJournal of Statistical Computation and Simulation
Volume87
Issue number18
DOIs
StatePublished - Dec 12 2017

Keywords

  • SPC
  • Squared ranks test
  • change-point
  • nonnormal
  • self-starting

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