Closed-form expressions of the run-length distribution of the nonparametric double sampling precedence monitoring scheme

Zwelakhe Magagula, Jean-Claude Malela-Majika (), Schalk William Human, Philippe Castagliola, Kashinath Chatterjee and Christos Koukouvinos
Additional contact information
Zwelakhe Magagula: University of Pretoria
Jean-Claude Malela-Majika: University of Pretoria
Schalk William Human: University of Pretoria
Philippe Castagliola: Nantes Université
Kashinath Chatterjee: Augusta University
Christos Koukouvinos: National Technical University of Athens

Computational Statistics, 2025, vol. 40, issue 1, No 12, 273-299

Abstract: Abstract A significant challenge in statistical process monitoring (SPM) is to find exact and closed-form expressions (CFEs) (i.e. formed with constants, variables and a finite set of essential functions connected by arithmetic operations and function composition) for the run-length properties such as the average run-length ( $$ARL$$ ARL ), the standard deviation of the run-length ( $$SDRL$$ SDRL ), and the percentiles of the run-length ( $$PRL$$ PRL ) of nonparametric monitoring schemes. Most of the properties of these schemes are usually evaluated using simulation techniques. Although simulation techniques are helpful when the expression for the run-length is complicated, their shortfall is that they require a high number of replications to reach reasonably accurate answers. Consequently, they take too much computational time compared to other methods, such as the Markov chain method or integration techniques, and even with many replications, the results are always affected by simulation error and may result in an inaccurate estimation. In this paper, closed-form expressions of the run-length properties for the nonparametric double sampling precedence monitoring scheme are derived and used to evaluate its ability to detect shifts in the location parameter. The computational times of the run-length properties for the CFE and the simulation approach are compared under different scenarios. It is found that the proposed approach requires less computational time compared to the simulation approach. Moreover, once derived, CFEs have the added advantage of ease of implementation, cutting off on complex convergence techniques. CFE's can also easily be built into mathematical software for ease of computation and may be recalled for further work.

Keywords: Shewhart; Control chart; Order statistic; Closed-form expression; Distribution-free; Nonparametric; Precedence; Exact run-length distribution; Performance analysis (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00180-024-01488-z 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:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01488-z

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-024-01488-z

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().