The statistical OPEA models indicate an anomaly in the solar X-ray flare energy levels

We have recognized an anomaly on the solar activity cycle, while we researching on the question that there can be two different flare mechanisms working on the stellar surface. We discuss an anomaly in the solar flare activity levels in the cycle minima and maxima from the 20th to 22nd Solar Activity Cycles, depending on the models and analyses of the X-ray data. In this study, we used the GOES satellite data accumulated from 1976 to 1989 and detected 670 solar flares. We have separately carried out two independent statistical analyses for the examination of the solar flare activity. Firstly, we derived the equivalent durations distribution via the total durations of flares. Contrary to our expectations based on flare stars, it seems that this distribution is modelled by four different fits, instead of just one model fit. We found that the model parameters, such as $plateau$, $half-time$, and $span$, vary via time in the different trends from the Solar Activity Cycle. Secondly, we have derived the cumulative frequency models for solar flares. Contrary to the studies in the literature, we found that these frequency models do not take shape depending on the minimum or maximum of a solar activity cycle. If these results are not an unexpected anomaly, this study indicates that the existence of a different trend can be revealed apart from the solar activity cycle for the flare energy level variation, when the solar flare behaviour is separately determined for each cycle and they are compared with each other.