Variable sample size and variable sampling interval Shewhart control chart with estimated parameters

Maoyuan Zhou ()
Additional contact information
Maoyuan Zhou: Civil Aviation University of China

Operational Research, 2017, vol. 17, issue 1, No 2, 17-37

Abstract: Abstract The theoretical results about variable sample size and sampling intervals (VSSI) Shewhart control chart are concerned with the case where the mean and standard deviation of the given process are known. However, in practice the mean and standard deviation are unknown. In this case, the common treatment is to estimate the unknown parameters using historical data. After determining the parameters we treat the control limits as though fixed. Up to now we have no idea about the average time to signal (ATS) of VSSI $${\bar{X}}$$ X ¯ charts when the control limits are estimated. This paper will calculate the mean of the ATS for VSSI $${\bar{X}}$$ X ¯ charts when the control limits are estimated in three different ways. The results show that parameter estimation has significant effect on the in-control ATS, but has little effect on the out-of-control ATS. These results could show us some good reference idea for choosing adequate number of sample groups m and the sample size n of historical data. Finally, this paper obtains the optimal design of the maximum sample size $$n_2$$ n 2 when other parameters are fixed.

Keywords: Average time to signal; Variable sample size and sampling interval; Parameter estimation; Statistical process control (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s12351-015-0214-9 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:operea:v:17:y:2017:i:1:d:10.1007_s12351-015-0214-9

Ordering information: This journal article can be ordered from
https://www.springer ... search/journal/12351

DOI: 10.1007/s12351-015-0214-9

Access Statistics for this article

Operational Research is currently edited by Nikolaos F. Matsatsinis, John Psarras and Constantin Zopounidis

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