Trade-Space Exploration Comparison of Parametric Cost Models for Satellite Anomalies with RMSE and RRMSE

Abstract

Satellites are essential for modern communication, navigation, and Earth observation, but their operation in the harsh space environment makes them vulnerable to anomalies and failures, resulting in significant financial losses. This research investigates the relationship between the design life of satellite subsystems and the cost of anomalies, using data from the Seradata database. Three statistical models, Exponential, Weibull, and Poisson distributions, were applied to cost data for four critical subsystems: antenna, payload, power system, and attitude control. Each model was fitted using one-variable (cost only) and two-variable approaches (design life and cost) to evaluate subsystems' behaviour independently and in combination. The performance of each model was assessed using the Root Mean Square Error (RMSE) and the Relative RMSE (RRMSE). Among all models, the Exponential distribution consistently produced the best results. For instance, the payload subsystem achieved the lowest RMSE and RRMSE of 115.73 and 41.66% in the two-variable case. Similarly, the attitude control subsystem showed strong performance with an RMSE of 110.57 and RRMSE of 40.59%. In contrast, the Poisson distribution yielded the highest errors across most subsystems, with the antenna subsystem reaching an RMSE of 489.87 and RRMSE of 102.65% in the two-variable fitting. The Weibull model demonstrated mixed performance, performing moderately for the payload subsystem (RMSE 186.21, RRMSE 67.03%), but poorly for the power system and antenna subsystems, particularly when two variables were used.

ABSTRAK: Satelit memainkan peranan penting dalam komunikasi moden, navigasi, dan pemerhatian bumi, namun operasinya dalam persekitaran angkasa lepas yang ekstrem menjadikannya terdedah kepada anomali dan kegagalan, sekali gus membawa kepada kerugian kewangan yang besar. Kajian ini mengkaji hubungan antara jangka hayat reka bentuk subsistem satelit dengan kos anomali menggunakan data daripada pangkalan data Seradata. Tiga model statistik iaitu taburan Eksponen, Weibull, dan Poisson telah digunakan pada data kos bagi empat subsistem kritikal: antena, muatan, sistem kuasa, dan kawalan sikap. Setiap model dipadankan menggunakan pendekatan satu pemboleh ubah (kos sahaja) dan dua pemboleh ubah (jangka hayat reka bentuk dan kos) bagi menilai tingkah laku subsistem secara individu dan gabungan. Prestasi setiap model dinilai menggunakan Ralat Punca Min Kuasa Dua (RMSE) dan Relatif RMSE (RRMSE). Antara semua model, taburan Eksponen secara konsisten memberikan dapatan terbaik. Sebagai contoh, dalam subsistem muatan, ia mencapai nilai RMSE dan RRMSE terendah iaitu 115.73 dan 41.66% masing-masing bagi kes dua pemboleh ubah. Begitu juga, subsistem kawalan sikap menunjukkan prestasi kukuh dengan RMSE 110.57 dan RRMSE 40.59%. Sebaliknya, taburan Poisson menghasilkan ralat tertinggi dalam kebanyakan subsistem, dengan subsistem antena mencatatkan RMSE 489.87 dan RRMSE 102.65% dalam padanan dua pemboleh ubah. Model Weibull pula menunjukkan prestasi bercampur, sederhana dalam subsistem muatan (RMSE 186.21, RRMSE 67.03%) tetapi lemah bagi subsistem sistem kuasa dan antena, khususnya apabila dua pemboleh ubah digunakan.