Monitoring the mean of autocorrelated observations with one generally weighted moving average control chart

Traditionally, using a control chart to monitor a process assumes that process observations are normally and independently distributed. In fact, for many processes, products are either connected or autocorrelated and, consequently, obtained observations are autocorrelative rather than independent. In this scenario, applying an independence assumption instead of autocorrelation for process monitoring is unsuitable. This study examines a generally weighted moving average (GWMA) with a time-varying control chart for monitoring the mean of a process based on autocorrelated observations from a first-order autoregressive process (AR(1)) with random error. Simulation is utilized to evaluate the average run length (ARL) of exponentially weighted moving average (EWMA) and GWMA control charts. Numerous comparisons of ARLs indicate that the GWMA control chart requires less time to detect various shifts at low levels of autocorrelation than those at high levels of autocorrelation. The GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in a process mean.     

The efficient estimation of tail probabilities for extremes of moving average processes using conditional simulation

This paper describes a conditional simulation technique which can be used to estimate probabilities associated with the distribution of the maximum of a real-valued process which can be written in the form of a moving average. The class of processes to which the technique applies includes non-stationary and spatial processes, and autoregressive processes. The technique is shown to achieve a considerable variance reduction compared with the obvious simulation-based estimator, particularly for estimating small upper-tail probabilities.     

Monitoring process mean using generally weighted moving average chart for exponentially distributed characteristics

In this article, we will present a control chart using normal transformation and generally weighted moving average (GWMA) statistic when the quality characteristic follows the exponential distribution. We will develop the necessary measures to monitor the mean of the process using GWMA statistic and analyze the performance using simulation. The average run lengths for monitoring process average are given for various process shifts. The performance of the proposed chart is examined and compared with the existing control chart. The proposed control chart is effective for the monitoring of small shifts in the mean process. The application of the proposed chart is illustrated with the help of simulated data.     

Mixed sampling plan based on exponentially weighted moving average statistic

ABSTRACT

We will design a new mixed acceptance sampling plan based on the exponentially weighted moving average statistic in this article. The plan parameters of the proposed plan are determined by an optimization problem. The efficiency of the proposed plan is compared with the existing attribute sampling plan. An industrial example is given for illustration purpose.     

Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes

Control charts are a powerful statistical process monitoring tool often used to monitor the stability of manufacturing processes. In quality control applications, measurement errors adversely affect the performance of control charts. In this paper, we study the effect of measurement error on the detection abilities of the exponentially weighted moving average (EWMA) control charts for monitoring process mean based on ranked set sampling (RSS), median RSS (MRSS), imperfect RSS (IRSS) and imperfect MRSS (IMRSS) schemes. We also study the effect of multiple measurements and non-constant error variance on the performances of the EWMA control charts. The EWMA control chart based on simple random sampling is compared with the EWMA control charts based on RSS, MRSS, IRSS and IMRSS schemes. The performances of the EWMA control charts are evaluated in terms of out-of-control average run length and standard deviation of run lengths. It turns out that the EWMA control charts based on MRSS and IMRSS schemes are better than their counterparts for all measurement error cases considered here.     

Improved estimation for Poisson INAR(1) models

We consider the first-order Poisson autoregressive model proposed by McKenzie [Some simple models for discrete variate time series. Water Resour Bull. 1985;21:645–650] and Al-Osh and Alzaid [First-order integer valued autoregressive (INAR(1)) process. J Time Ser Anal. 1987;8:261–275], which may be suitable in situations where the time series data are non-negative and integer valued. We derive the second-order bias of the squared difference estimator [Weiß. Process capability analysis for serially dependent processes of Poisson counts. J Stat Comput Simul. 2012;82:383–404] for one of the parameters and show that this bias can be used to define a bias-reduced estimator. The behaviour of a modified conditional least-squares estimator is also studied. Furthermore, we access the asymptotic properties of the estimators here discussed. We present numerical evidence, based upon Monte Carlo simulation studies, showing that the here proposed bias-adjusted estimator outperforms the other estimators in small samples. We also present an application to a real data set.     

A central limit theorem for the sample autocorrelations of a Lévy driven continuous time moving average process

In this article we consider Lévy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A comparison with the classical setting of discrete moving average time series shows that in the last case a correction term should be added to the classical Bartlett formula that yields the asymptotic variance. An application to the asymptotic normality of the estimator of the Hurst exponent of fractional Lévy processes is also deduced from these results.     

On the estimation of the marginal density of a moving average process

The authors present a new convolution‐type kernel estimator of the marginal density of an MA(1) process with general error distribution. They prove the √n; ‐consistency of the nonparametric estimator and give asymptotic expressions for the mean square and the integrated mean square error of some unobservable version of the estimator. An extension to MA(q) processes is presented in the case of the mean integrated square error. Finally, a simulation study shows the good practical behaviour of the estimator and the strong connection between the estimator and its unobservable version in terms of the choice of the bandwidth.     

Monitoring process mean and dispersion with one double generally weighted moving average control chart

Control charts are widely known quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum double generally weighted moving average chart (referred as Max-DGWMA), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed Max-DGWMA chart is compared with that of the Max-EWMA, Max-DEWMA, Max-GWMA and SS-DGWMA charts, using time-varying control limits, through Monte–Carlo simulations. The comparisons reveal that the proposed chart is more efficient than the Max-EWMA, Max-DEWMA and Max-GWMA charts, while it is comparable with the SS-DGWMA chart. An automotive industry application is presented in order to implement the Max-DGWMA chart. The goal is to establish statistical control of the manufacturing process of the automobile engine piston rings. The source of the out-of-control signals is interpreted and the efficiency of the proposed chart in detecting shifts faster is evident.     

Risk aggregation with dependence and overdispersion based on the compound Poisson INAR(1) process

Abstract

This paper considers an extension of the classical discrete time risk model for which the claim numbers are assumed to be temporal dependence and overdispersion. The risk model proposed is based on the first-order integer-valued autoregressive (INAR(1)) process with discrete compound Poisson distributed innovations. The explicit expression for the moment generating function of the discounted aggregate claim amount is derived. Some numerical examples are provided to illustrate the impacts of dependence and overdispersion on related quantities such as the stop-loss premium, the value at risk and the tail value at risk.     

Forward Moving Average Representation in Multivariate MA(1) Processes

Forward-moving average coefficients are in general different from their corresponding backward-moving average coefficients in multivariate stationary time series. There is lack of practical methods to derive forward-moving average coefficients from the backward ones. In this article, we establish a new practical approach for obtaining the forward-moving average coefficients for multivariate moving average processes of order one.     

The power of the tests of robinson (1994) in the context of fractionall[y integrated moving average models

We examine in this article the power of the tests of Robinson (1994) for testing I(d) statistical models in the presence of moving average (MA) disturbances. The results show that the tests behave relatively well if we correctly assume that the disturbances are MA. However, assuming white noise or autoregressive disturbances, the power of the tests against one-sided alternatives is very low.     

Estimation of parameters of yamada et al. model and modification of the model

Yamada, Ohba and Osaki (1983) suggested an important NHPP model for software failure phenomenon. So far little work has been done on the problem of estimating its parameters. We present here some conditions for the likelihood estimates to be finite, positive and unique. We also suggest a modification of the model. The performance measures and statistical inferences of the modified model are discussed here. The modified model is applied to software failure data and the results are compared with Jelinski-Moranda [4] and some existing important NHPP models     

Zero-Inflated NGINAR(1) process

In this paper, we develop a zero-inflated NGINAR(1) process as an alternative to the NGINAR(1) process (Risti?, Nasti?, and Bakouch 2009 Risti?, M. M., A. S. Nasti?, and H. S. Bakouch. 2009. A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. Journal of Statistical Planning and Inference 139:2218–26.[Crossref], [Web of Science ®] , [Google Scholar]) when the number of zeros in the data is larger than the expected number of zeros by the geometric process. The proposed process has zero-inflated geometric marginals and contains the NGINAR(1) process as a particular case. In addition, various properties of the new process are derived such as conditional distribution and autocorrelation structure. Yule-Walker, probability based Yule-Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Forecasting performances of the model are discussed. Application to a real data set shows the flexibility and potentiality of the new model.     

On the assessment of various factors effecting the improvement in CD4 count of aids patients undergoing antiretroviral therapy using generalized Poisson regression

An important marker for identifying the progression of human immunodeficiency virus (HIV) infection in an individual is the CD4 cell count. Antiretroviral therapy (ART) is a treatment for HIV/AIDS (AIDS, acquired immune-deficiency syndrome) which prolongs and improves the lives of patients by improving the CD4 cell count and strengthen the immune system. This strengthening of the immune system in terms of CD4 count, not only depends on various biological factors, but also other behavioral factors. Previous studies have shown the effect of CD4 count on the mortality, but nobody has attempted to study the factors which are likely to influence the improvement in CD4 count of patients diagnosed of AIDS and undergoing ART. In this paper, we use Poisson regression model (GPR) for exploring the effect of various socio-demographic covariates such as age, gender, geographical location, and drug usage on the improvement in the CD4 count of AIDS patients. However, if the CD4 count data suffers from under or overdispersion, we use GPR model and compare it with negative binomial distribution. Finally, the model is applied for the analysis of data on patients undergoing the ART in the Ram Manohar Lohia Hospital, Delhi, India. The data exhibited overdispersion and hence, GPR model provided the best fit.     

On first-order integer-valued autoregressive process with Katz family innovations

This paper considers the first-order integer-valued autoregressive (INAR) process with Katz family innovations. This family of INAR processes includes a broad class of INAR(1) processes with Poisson, negative binomial, and binomial innovations, respectively, featuring equi-, over-, and under-dispersion. Its probabilistic properties such as ergodicity and stationarity are investigated and the formula of the marginal mean and variance is provided. Further, a statistical process control procedure based on the cumulative sum control chart is considered to monitor autocorrelated count processes. A simulation and real data analysis are conducted for illustration.     

Optimal exponentially weighted moving average (EWMA) plans for detecting seasonal epidemics when faced with non-homogeneous negative binomial counts

Exponentially weighted moving average (EWMA) plans for non-homogeneous negative binomial counts are developed for detecting the onset of seasonal disease outbreaks in public health surveillance. These plans are robust to changes in the in-control mean and over-dispersion parameter of the negative binomial distribution, and therefore are referred to as adaptive plans. They differ from the traditional approach of using standardized forecast errors based on the normality assumption. Plans are investigated in terms of early signal properties for seasonal epidemics. The paper demonstrates that the proposed EWMA plan has efficient early detection properties that can be useful to epidemiologists for communicable and other disease control and is compared with the CUSUM plan.     

Predictive inference for linear and multivariate linear models with ma(1) error processes

The prediction distributions of future responses from the linear and multivariate linear models with errors having a first order moving average (MA(1)) process have been derived. First, we obtained the marginal likelihood function for the moving average parameter 6 and from this likelihood function we estimate the maximum likelihood estimates (MLE) of θ. Using the estimated value θ, we have derived the prediction distributions as well as prediction regions for the future responses. An example has been included.