The anomaly detection task is very important in computer science. And there are a lot of anomaly detection methods. Different from some thresholding methods, some unsupervised methods could make us get more accurate and faster result, which is the object of the project. In this paper, I tried to use EWMA and some other methods in two datasets: Webank time consuming indicators dataset and AIOps Challenge dataset. The paper consists nine parts: background of the project, related work, description of algorithms, implementation details, experimental setup and data sets used, experimental results and discussion, future directions, reference and meeting notes.

Workloads may be classified as either internal or external. Internal workloads (heart rate, blood lactate, session rate of perceived exertion (sRPE) are categorised as the individual’s response to an external workload (volume, intensity). sRPE is an easily monitored variable which has been shown to have possible associations with other internal (1) and injury rates (2, 3) in contact sports. This case study describes the internal workload monitoring of a schoolboy rugby player during the entirety of his season (September to March) with the subsequent relationships between workload and time loss injuries being explored. Time loss injuries are defined as injuries which caused the individual to miss training or match play time (4). Acute to chronic workload ratio (ACWR) and exponentially weighted moving average (EWMA) were monitored, a novel ACWR:EWMA ratio was also calculated. High ACWR and low EWMA values were associated with injury occurrence, the ACWR:EWMA ratio may account for this. EWMA may be a better predictor of “time loss” injuries than ACWR. The ACWR:EWMA ratio may merit further scientific exploration in the future.

This paper presents a new discrete counterpart of the mixture exponential distribution by utilizing the survival discretization method. The moment-generating function and associated moment measures are discussed. The distribution’s hazard rate function can assume increasing or decreasing forms, making it adaptable for diverse fields requiring count data modelling. The paper explores four distinct parameter estimation methods and assesses their performance through Monte Carlo simulations. The applicability of this distribution extends to time series analysis, particularly within the framework of the first-order integer-valued autoregressive process. Additionally, the paper explores quality control applications, addressing serial dependence challenges in count data encountered in production and market management. The performance of two distinct control charts, the cumulative sum chart and the exponentially weighted moving average chart, is evaluated for their effectiveness in detecting shifts in the process means under various models. A bivariate Markov chain approach is used to estimate the average run lengths of these charts, offering valuable insights for implementation. Design recommendations for achieving robustness in-control chart applications are provided. The effectiveness of the proposed models and charts is illustrated using a real data, demonstrating their practical superiority.

In this paper we propose the explicit formulas of Average Run Length (ARL) of Exponentially Weighted Moving Average (EWMA) control chart for Autoregressive Integrated Moving Average: ARIMA (p,d,q) (P, D, Q)_L process with exponential white noise. To check the accuracy, the ARL results were compared with numerical integral equations based on the Gauss-Legendre rule. There was an excellent agreement between the explicit formulas and the numerical solutions. Additionally, we compared the computational time between our explicit formulas for the ARL with the one obtained via Gauss-Legendre numerical scheme. The computational time for the explicit formulas was approximately one second that is much less than the numerical approximations. The explicit analytical formulas for evaluating ARL0 and ARL₁ can produce a set of optimal parameters which depend on the smoothing parameter (λ) and the width of control limit (H), for designing an EWMA chart with a minimum ARL₁.