Perbandingan Min Piawai dan Min Tercantas dalam Carta CUSUM

Abstract

Kertas ini berkenaan dengan penilaian prestasi carta kawalan hasiltambah longgokan (CUSUM) teguh yang dinamakan Carta CUSUM Min Tercantas. Carta CUSUM biasa adalah berasaskan min sampel manakala carta CUSUM teguh berasaskan min tercantas. Beberapa siri simulasi telah dijalankan untuk membandingkan prestasi min tercantas dan min piawai dengan memeriksa nilai purata panjang larian (ARL) dan nisbah antara ARL dengan min dianjak dan ARL dengan min tidak dianjak. Keputusan menunjukkan di bawah proses normal, min tercantas adalah lebih baik bagi sampel bersaiz 5 dan CUSUM min piawai adalah sama baik dengan CUSUM min tercantas apabila saiz sampel bertambah. Walau bagaimana pun, min tercantas adalah lebih baik bagi proses yang amat pencong iaitu sampel disimulasi daripada taburan T Student dan Khi Kuasadua dengan 4, 6 dan 8 darjah kebebasan (dianjak dan diskalakan bagi menghasilkan min dan varians yang sama, iaitu $\mu=0$ dan $\sigma^2=1),$ prestasi min tercantas adalah lebih baik daripada min piawai. Katakunci: CUSUM teguh; min terpiawai; purata panjang larian; titik terpencil. This paper is concerned with the assessment of the performance of a robust Cumulative Sum (CUSUM) chart, which is called the Trimmed CUSUM Chart. A standard CUSUM chart is based on standard mean whilst the robust CUSUM chart is based on the trimmed mean. A series of simulations have been carried out to compare the performance of trimmed mean and standard mean CUSUM procedures by looking at the values of the average run length (ARL) and the ratio between the ARL with a mean shift and ARL without. The results show that for normal process and a sample size of 5, the standard mean CUSUM performs better than the trimmed mean CUSUM, but their performances are equally well as sample size is increased. However, for data with one outlier and highly skewed process, which is sample are simulated from a Student T and Chi Square distributions with 4, 6 and 7 degree of freedom (suitably shifted and scaled to produce common mean and variance, i.e. $\mu=0$ and $\sigma^2=1),$ the trimmed mean seems to perform better than the standard mean CUSUM. Keywords: Robust CUSUM; trimmed mean; average run length; outlier.