Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution

Wolfgang Kössler () and Janine Ott
Additional contact information
Wolfgang Kössler: Humboldt-Universität zu Berlin
Janine Ott: Humboldt-Universität zu Berlin

AStA Advances in Statistical Analysis, 2019, vol. 103, issue 3, No 6, 437-452

Abstract: Abstract The ordinary variable inspection plans rely on the normality of the underlying populations. However, this assumption is vague or even not satisfied. Moreover, ordinary variable sampling plans are sensitive against deviations from the distribution assumption. Nonconforming items occur in the tails of the distribution. They can be approximated by a generalized Pareto distribution (GPD). We investigate several estimates of their parameters according to their usefulness not only for the GPD, but also for arbitrary continuous distributions. The likelihood moment estimates (LMEs) of Zhang (Aust N Z J Stat 49:69–77, 2007) and the Bayesian estimate (ZSE) of Zhang and Stephens (Technometrics 51:316–325, 2009) turn out to be the best for our purpose. Then, we use these parameter estimates to estimate the fraction defective. The asymptotic normality of the LME (cf. Zhang 2007) and that of the fraction defective are used to construct the sampling plan. The difference to the sampling plans constructed in Kössler (Allg Stat Arch 83:416–433, 1999; in: Steland, Rafajlowicz, Szajowski (eds) Stochastic models, statistics, and their applications, Springer, Heidelberg, pp 93–100, 2015) is that we now use the new parameter estimates. Moreover, in contrast to the aforementioned papers, we now also consider two-sided specification limits. An industrial example illustrates the method.

Keywords: Extreme value index; Fraction defective; Generalized Pareto distribution; Peak over threshold method; Likelihood moment estimate; Zhang–Stephens estimate; 62F10; 62F12; 62G30; 62G32; 62P30 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10182-018-00338-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00338-w

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10182/PS2

DOI: 10.1007/s10182-018-00338-w

Access Statistics for this article

AStA Advances in Statistical Analysis is currently edited by Göran Kauermann and Yarema Okhrin

More articles in AStA Advances in Statistical Analysis from Springer, German Statistical Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().