Specific Signal Detection Charts Using Generalized Likelihood Ratios

نویسندگان

  • George C. Runger
  • Murat C. Testik
چکیده

Simulations are done to compare the performances of Generalized Likelihood Ratio (GLR) and Cuscore charts for detecting specific signals hidden in noise. Two different types of signals are considered: a sine wave and a linear trend. Two different cases are analyzed, a known signal form and parameter and a known signal form but unknown signal parameter. Both the initial performances and steady-state performances of these charts are given. Introduction Signals in the form of linear, exponential, or sinusoidal patterns are common in manufacturing processes. These patterns should be detected fast in order to reduce variations in the product quality features. Commonly used control charts are designed for detecting global forms of signals and their performance may be much worse than that of a specially designed chart. Specific signal detection charts have increased sensitivity to a single form of signal at the cost of less sensitivity to other types of signals that may be hidden in the noise. Therefore, these charts are mostly used as supplements to general statistical monitoring charts instead of replacing them. Cumulative score (Cuscore) charts were introduced to detect specific signals hidden in the noise (see, Box and Ramirez (1992), Box and o n ~ Luce (1997), and o n ~ Luce (1999)). The Cuscore statistic is based on the concept of Fisher’s efficient scores statistic. An alternative method for signal detection is to use a Generalized Likelihood Ratio (GLR) to develop a control statistic for detecting the presence of a known signal in the process data. See, for example, Lai (1995). In this paper, we compare GLR charts to Cuscore charts. Average run length simulation results are provided for the cases when the signals are a linear trend and a sine wave. Specific Signals Let Y be the monitored quality characteristic of interest with the sequential observations t t y a μ = + , ..., 1,2, , 0 = t where μ is the mean of Y , t a is the normally distributed white-noise sequence with mean zero and standard deviation σ , and t is the sequence order or time. Suppose that at unknown time , τ this statistically stable process is disturbed and that the form of this disturbing signal is known and can be represented by a function ) , , ( τ θ t f . Therefore, ( , , ) , 0,1,2, ..., t t y f t a t μ θ τ = + + = Cuscore Charts A Cuscore with handicap t k is obtained by plotting cumulative scores 1 max[{ ( ) ( , , )} ; 0] , 1,2,..., t t t t S S y k f t t θ τ − = + − = versus the sequence t , ( o n ~ Luce (1999)). A control limit, h is used to test for the presence of the hidden signal in the process, i.e. as soon as t S h ≥ an alarm is triggered for the presence of the hidden signal. o n ~ Luce (1999) suggested different Cuscore charts to be used depending on whether the signal is bounded or unbounded. For unbounded signals, a second reinitialization, which sets t = τ in ) , , ( τ θ t f when 0 t S ≤ is suggested. For bounded signals, the signal value ) , , ( τ θ t f is not reinitialized every time 0 ≤ t S . Generalized Likelihood Ratio Charts A GLR approach does not make the assumption of the known change time, but uses a maximum likelihood estimate (MLE) of the change time (see, Lai (1995)). For the normally distributed errors t a , the GLR statistic is Spring Research Conference Section on Quality & Productivity (Q&P)

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Evaluation of an Adaptive Generalized Likelihood Ratio Charts for Monitoring the Process Mean

When the objective is quick detection both small and large shifts in the process mean with normal distribution, the generalized likelihood ratio (GLR) control charts have better performance as compared to other control charts. Only the fixed parameters are used in Reynolds and Lou’s presented charts. According to the studies, using variable parameters, detect process shifts faster than fixed pa...

متن کامل

An Improved Automatic EEG Signal Segmentation Method based on Generalized Likelihood Ratio

It is often needed to label electroencephalogram (EEG) signals by segments of similar characteristics that are particularly meaningful to clinicians and for assessment by neurophysiologists. Within each segment, the signals are considered statistically stationary, usually with similar characteristics such as amplitude and/or frequency. In order to detect the segments boundaries of a signal, we ...

متن کامل

Adaptive Signal Detection in Auto-Regressive Interference with Gaussian Spectrum

A detector for the case of a radar target with known Doppler and unknown complex amplitude in complex Gaussian noise with unknown parameters has been derived. The detector assumes that the noise is an Auto-Regressive (AR) process with Gaussian autocorrelation function which is a suitable model for ground clutter in most scenarios involving airborne radars. The detector estimates the unknown...

متن کامل

Approximating the step change point of the process fraction non conforming using genetic algorithm to optimize the likelihood function

Control charts are standard statistical process control (SPC) tools for detecting assignable causes. These charts trigger a signal when a process gets out of control but they do not indicate when the process change has begun. Identifying the real time of the change in the process, called the change point, is very important for eliminating the source(s) of the change. Knowing when a process has ...

متن کامل

Asymptotic normality and analysis of variance of log-likelihood ratios in spiked random matrix models

The present manuscript studies signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked cases in these models and with flexible priors on the signal component that allow dependence across spikes. We derive asymptotic normality for the log-likeli...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002