Phát hiện sự thay đổi trong hồ sơ Conway–Maxwell–Poisson bằng biểu đồ CUSUM và EWMA dựa trên phần dư deviance dưới điều kiện đa cộng tuyến

Statistische Hefte - Trang 1-47 - 2023
Ulduz Mammadova1, M. Revan Özkale1
1Faculty of Science and Letters, Department of Statistics, Çukurova University, Adana, Turkey

Tóm tắt

Theo dõi các hồ sơ với phản hồi đếm là một tình huống phổ biến trong các quá trình công nghiệp và đối với một quá trình phân phối đếm, mô hình hồi quy Conway–Maxwell–Poisson (COM-Poisson) cho ra kết quả tốt hơn đối với các biến đếm phân tán thiếu và quá mức. Trong nghiên cứu này, chúng tôi đề xuất các biểu đồ CUSUM và EWMA dựa trên các phần dư deviance thu được từ mô hình COM-Poisson, được điều chỉnh bởi các ước lượng PCR và lớp r–k. Chúng tôi đã tiến hành một nghiên cứu mô phỏng để đánh giá hiệu ứng của các dạng thay đổi bổ sung và nhân với nhiều kích thước thay đổi khác nhau, số lượng biến dự đoán và nhiều mức độ phân tán, cũng như so sánh hiệu suất của các biểu đồ điều khiển được đề xuất với các biểu đồ điều khiển trong tài liệu về độ dài chu kỳ trung bình và độ lệch chuẩn của độ dài chu kỳ. Hơn nữa, một tập dữ liệu thực tế cũng được phân tích để xem hiệu suất của các biểu đồ điều khiển mới được đề xuất. Kết quả cho thấy sự vượt trội của các biểu đồ điều khiển mới được đề xuất so với một số đối thủ, bao gồm các biểu đồ điều khiển CUSUM và EWMA dựa trên ML, PCR và phần dư deviance ridge trong sự hiện diện của đa cộng tuyến.

Từ khóa

#Conway–Maxwell–Poisson #hồi quy #CUSUM #EWMA #phần dư deviance #phân tán #đa cộng tuyến

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