Peluang Keberhasilan Berhenti Berbuat Dosa Besar dengan Metode Markov Chain dan Metode Analisis Survival Berdistribusi Weibull - Iis Lestari; Asep Triyono; Mona Rizki Ardela; Nadia Nadia (JMT (Jurnal Matematika dan Terapan), 2025)
Sin is any act that is contrary to God's will and commandments that every human being is not immune to sin. The purpose of this study is to analyze the chances of individuals succeeding in istiqamah with the markov chain method and weibull distributed survival analysis. In this study, the major sin behavior is divided into three stages, namely the awareness stage (T), the relapse stage (R), and the istiqamah stage (I). The transition matrix shows that state I is an absorbing state and states T and R are transein states. In this study it was found that the average individual who reached the absorsing state from the transein state was 10 years. From the simulation of 1000 individuals, it is found that the average number of relapses before reaching istiqamah is 3.50 with a standard deviation of 1.72 and a median of 3, meaning that individuals experience relapse before istiqamah between 2 and 4 times. The survival function and hazard function can be estimated and visualized in the form of a curve. These results provide an overview of the chances of an individual achieving istiqamah at the nth time.