Determination of Width Control of Dispersion Process for Single Sample Size in Multivariate Case with Many P=4 Variables
Enjang AS (1), Farid Soleh Nurdin (1), Wawan Setiawan(2), Iwan Gunawan (3), Eri Subekti (2)
1) Universitas Islam Negeri Sunan Gunung Djati, Jl. A.H. Nasution No.105, Cipadung, Cibiru, Kota Bandung
2) Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi no 229, Bandung
3) Universitas Langlangbuana, Jl. Karapitan no.116, Bandung
Abstract
In this study, we discussed the control of multivariate dispersion statistics for a single sample size. The control chart was developed from a multivariate control chart exponentially weighted mean square (MEWMS) with total variance (TV) as the multivariate dispersion size used. Although the MEWMS control chart has more advantages than MEWMA and MCUSUM control charts, it has limitations because it only applies to p = 3 variables. Therefore, the main focus in this study is to determine the L value as a determinant of the MEWMS control boundary width for the variable p = 4 through the simulation method. Based on historical data on controlling the wing component products of Airbus aircraft through simulations with vector mean parameters and covariance matrices, MEWMS Control Chart is quick in detecting changes in variance, while in detecting the average changes is very slow.
Keywords: Dispersion, Total Variance, Covariance Matrix
Topic: Mathematics