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Optimized np Attribute Control Chart Using Triple Sampling

Authors :
Jose Jorge Muñoz
Manuel J. Campuzano
Jaime Mosquera
Source :
Mathematics, Vol 10, Iss 20, p 3791 (2022)
Publication Year :
2022
Publisher :
MDPI AG, 2022.

Abstract

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (ARL1). Tables of ARL1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of ARL1 detecting small and moderate shifts in the process nonconforming rate in-control (p0) compared with MDSRS and DS-np.

Details

Language :
English
ISSN :
22277390
Volume :
10
Issue :
20
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.b8b68443a7440838a9dd8340c4508b7
Document Type :
article
Full Text :
https://doi.org/10.3390/math10203791