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Therefore, several authors recommend using a single chart that can simultaneously monitor ¯ and S. [8] McCracken, Chackrabori and Mukherjee [9] developed one of the most modern and efficient approach for jointly monitoring the Gaussian process parameters, using a set of reference sample in absence of any knowledge of true process parameters.
In probability theory and statistics, a Hawkes process, named after Alan G. Hawkes, is a kind of self-exciting point process. [1] It has arrivals at times 0 < t 1 < t 2 < t 3 < ⋯ {\textstyle 0<t_{1}<t_{2}<t_{3}<\cdots } where the infinitesimal probability of an arrival during the time interval [ t , t + d t ) {\textstyle [t,t+dt)} is
Measurement of process variables is essential in control systems to controlling a process. The value of the process variable is continuously monitored so that control may be exerted. Four commonly measured variables that affect chemical and physical processes are: pressure, temperature, level and flow.
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time.
A process capability analysis may be performed on a stable process to predict the ability of the process to produce "conforming product" in the future. A stable process can be demonstrated by a process signature that is free of variances outside of the capability index. A process signature is the plotted points compared with the capability index.
The notation AR(p) refers to the autoregressive model of order p.The AR(p) model is written as = = + where , …, are parameters and the random variable is white noise, usually independent and identically distributed (i.i.d.) normal random variables.
In probability theory, a birth process or a pure birth process [1] is a special case of a continuous-time Markov process and a generalisation of a Poisson process. It defines a continuous process which takes values in the natural numbers and can only increase by one (a "birth") or remain unchanged.