The Equivalence of Two Proportions Revisited

The classic conditional test for checking that the difference between two independent proportions is not null may not be appropriate in many circumstances. Dunnett & Gent (1977) showed that in clinical trials, in studies of drugs, etc, the aim is to prove the practical equality (equivalence) of both proportions. On other occasions the aim may be the opposite: i.e. to prove that the two proportions are substantially different (biologically significant). Both cases are usually solved by two one-sided tests (TOST test). In this article, this procedure is shown to be conservative and two true two-sided tests for each case are proposed.     

Moving range EWMA control charts for monitoring the Weibull shape parameter

In this article, we propose an exponentially weighted moving average (EWMA) control chart for the shape parameter β of Weibull processes. The chart is based on a moving range when a single measurement is taken per sampling period. We consider both one-sided (lower-sided and upper-sided) and two-sided control charts. We perform simulations to estimate control limits that achieve a specified average run length (ARL) when the process is in control. The control limits we derive are ARL unbiased in that they result in ARL that is shorter than the stable-process ARL when β has shifted. We also perform simulations to determine Phase I sample size requirements if control limits are based on an estimate of β. We compare the ARL performance of the proposed chart to that of the moving range chart proposed in the literature.     

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.     

Determining the Optimum Process Mean of a One-sided Specification Limit with the Linear Quality Loss Function of Product

Wen & Mergen (1999) proposed a method for setting the optimal process mean when a process was not capable of meeting specifications in the short term. However, they neglected to consider the quality loss for a product within specifications in the model. Chen & Chou (2002) presented a modified Wen & Mergen's (1999) model, including the quadratic quality loss function for a one-sided specification limit. In this paper, we propose the modified Wen & Mergen (1999) cost model including the linear quality loss function of a product for determining the optimal process mean of a one-sided specification limit.     

Detecting mean increases in Poisson INAR(1) processes with EWMA control charts

Processes of serially dependent Poisson counts are commonly observed in real-world applications and can often be modeled by the first-order integer-valued autoregressive (INAR) model. For detecting positive shifts in the mean of a Poisson INAR(1) process, we propose the one-sided s exponentially weighted moving average (EWMA) control chart, which is based on a new type of rounding operation. The s-EWMA chart allows computing average run length (ARLs) exactly and efficiently with a Markov chain approach. Using an implementation of this procedure for ARL computation, the s-EWMA chart is easily designed, which is demonstrated with a real-data example. Based on an extensive study of ARLs, the out-of-control performance of the chart is analyzed and compared with that of a c chart and a one-sided cumulative sum (CUSUM) chart. We also investigate the robustness of the chart against departures from the assumed Poisson marginal distribution.     

One-sided EWMA control charts for monitoring Poisson processes with varying sample sizes

ABSTRACT

Recently considerable research has been devoted to monitoring increases of incidence rate of adverse rare events. This paper extends some one-sided upper exponentially weighted moving average (EWMA) control charts from monitoring normal means to monitoring Poisson rate when sample sizes are varying over time. The approximated average run length bounds are derived for these EWMA-type charts and compared with the EWMA chart previously studied. Extensive simulations have been conducted to compare the performance of these EWMA-type charts. An illustrative example is given.     

Shewhart control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals

In this paper, we are concerned with pure statistical Shewhart control charts for the scale parameter of the three-parameter Weibull control variable, where, and are the location, the scale and the shape parameters, respectively, with fixed (FSI) and variable (VSI) sampling intervals. The parameters and are assumed to be known. We consider two-sided, and lower and upper one-sided Shewhart control charts and their FSI and VSI versions . They jointly control the mean and the variance of the Weibull control variable X. The pivotal statistic of those control charts is the maximum-likelihood estimator of for the Nth random sample XN=(X1N,X2N,...,XnN) of the Weibull control variable X. The design and performance of these control charts are studied. Two criteria, i.e. 'comparability criterion' (or 'matched criterion') under control and 'primordial criterion', are imposed on their design. The performance of these control charts is measured using the function average time to signal. For the VSI versions, the constant which defines the partition of the 'continuation region' is obtained through the 'comparability criterion' under control. The monotonic behaviour of the function average time to signal in terms of the parameters (magnitude of the shift suff ered by the target value 0), and is studied. We show that the function average time to signal of all the control charts studied in this paper does not depend on the value of the parameter or on 0, and, under control, does not depend on the parameter, when Delta (the probability of a false alarm) and n (sample size) are fixed. All control charts satisfy the 'primordial criterion' and, for fixed, on average, they all (except the two-sided VSI, for which we were not able to ascertain proof) are quicker in detecting the shift as increases. We conjecture - and we are not contradicted by the numerical example considered - that the same is true for the two-sided VSI control chart. We prove that, under the average time to signal criterion, the VSI versions are always preferable to their FSI versions. In the case of one-sided control charts, under the 'comparability criterion', the VSI version is always preferable to the FSI version, and this advantage increases with and the extent of the shift. Our one-sided control charts perform better and have more powerful statistical properties than does our two-sided control chart. The numerical example where n=5,0=1,=0.5, 1.0, 2.0, and Delta=1/370.4 is presented for the two-sided, and the lower and upper one-sided control charts. These numerical results are presented in tables and in figures. The joint influence of the parameters and in the function average time to signal is illustrated.     

Integer-valued moving average (INMA) process

A simple model for a stationary sequence of dependent integer-valued random variables {X_n} is given. The sequence to be called integer-valued moving average (INMA) process, is taken as the “survivals” of i.i.d. non-negative integervalued random variables. It is argued that the model’s structure reflects to some extent the mechanism generating real life data for many counting process and consequently it is useful for modelling such processes. Various properties for the special case in which {X_n} is Poisson INMA (1) process, such as the joint distribution, regression, time reversibility, along with the conditional and partial correlations, are discussed in details. Extension of the INMA of first order to higher order moving average is considered.     

An optimal k of kth MA-ARIMA models under MA(q) models

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated MA(q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that, 5th Exponential Weighted Moving Average (5-th EWMA) Autoregressive Integrated Moving Average (ARIMA) model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM), stock market real data reveals the similar results of the simulation study.     

An optimal k of kth MA-ARIMA models under a class of ARIMA model

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated ARIMA(p, d, q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that 5th exponential weighted moving average (5th EWMA) ARIMA model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM) stock market, real data reveal the similar results of simulation study.     

On-line monitoring data quality of high-dimensional data streams

ABSTRACT

In recent years, effective monitoring of data quality has increasingly attracted attention of researchers in the area of statistical process control. Among the relevant research on this topic, none used multivariate methods to control the multidimensional data quality process, but instead relied on multiple univariate control charts. Based on a novel one-sided multivariate exponentially weighted moving average (MEWMA) chart, we propose a conditional false discovery rate-adjusted scheme to on-line monitor the data quality of high-dimensional data streams. With thousands of input data streams, the average run length loses its usefulness because one will likely have out-of-control signals at each time period. Hence, we first control the percentage of signals that are false alarms. Then, we compare the power of the proposed MEWMA scheme with that of two alternative methods. Compared with two competitors, numerical results show that the proposed MEWMA scheme has higher average power.     

An optimal k of kth MA-ARIMA models under AR(p) models

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated autoregressive AR(p) model. We run a simulation using the three above examining method under specific conditions. The main finding is that the optimal k = 4 and then k = 3. Especially, the fourth WMA ARIMA model, fourth EWMA ARIMA model, and third EWMA ARIMA model are the best forecasting models among others, respectively. For all the six real data reveal the similar results of simulation study.     

On the convergence of some adaptive estimation procedures

In the paper we consider some adaptive procedures for estimating the unknown parameters of autoregressive and moving average processes. In case of AK(p) and MA(1) processes sequences of estimators converging with probability one and In mean square are given     

On the duality between long-run relations and common trends in the i(1) versus(2)model.an application to aggregate money holdings

Long-run relations and common trends are discussed in terms of the multivariate cointegration model given in the autoregressive and the moving average form. The basic results needed for the analysis of I(1) and 1(2)processes are reviewed and the results applied to Danish monetary data. The test procedures reveal that nominal money stock is essentially I(2). Long-run price homogeneity is supported by the data and imposed on the system. It is found that the bond rate is weakly exogenous for the long-run parameters and therefore act as a driving trend. Using the nonstationarity property of the data, “excess money” is estimated and its effect on the other determinants of the system is investigated. In particular, it is found that “excess money” has no effect on price inflation.     

A recursive approach to parameter estimation in regression and time series models

In this paper we discuss the recursive (or on line) estimation in (i) regression and (ii) autoregressive integrated moving average (ARIMA) time series models. The adopted approach uses Kalman filtering techniques to calculate estimates recursively. This approach is used for the estimation of constant as well as time varying parameters. In the first section of the paper we consider the linear regression model. We discuss recursive estimation both for constant and time varying parameters. For constant parameters, Kalman filtering specializes to recursive least squares. In general, we allow the parameters to vary according to an autoregressive integrated moving average process and update the parameter estimates recursively. Since the stochastic model for the parameter changes will "be rarely known, simplifying assumptions have to be made. In particular we assume a random walk model for the time varying parameters and show how to determine whether the parameters are changing over time. This is illustrated with an example.     

Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT

We propose inverse probability weighted estimators for the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient. When the (binary) instrument satisfies one-sided noncompliance, we propose a Durbin–Wu–Hausman-type test of whether treatment assignment is unconfounded conditional on some observables. The test is based on the fact that under one-sided noncompliance LATT coincides with the average treatment effect for the treated (ATT). We conduct Monte Carlo simulations to demonstrate, among other things, that part of the theoretical efficiency gain afforded by unconfoundedness in estimating ATT survives pretesting. We illustrate the implementation of the test on data from training programs administered under the Job Training Partnership Act in the United States. This article has online supplementary material.     

Properties and performance of one-sided cumulative count of conforming chart with parameter estimation in high-quality processes

The one-sided cumulative count of conforming (CCC) chart is a useful method to monitor nonconforming fraction in high-quality manufacturing processes. The nonconforming fraction parameter is assumed to be known when implementing a one-sided CCC chart. In this study, we investigated the impact of estimated nonconforming fraction, [pcirc] ₀, in a one-sided CCC chart. The run length distribution is derived as well as the conditional probability of a false alarm rate (CFAR), conditional average run length (CARL) and its standard deviation (CSDRL). Simulation results are conducted to evaluate the effect of [pcirc] ₀ in a one-sided CCC chart. The results show that values of CFAR, CARL and CSDRL are close to the nominal values for a large sample. The impact of estimation errors was also studied. We find that CFAR decreases for large [pcirc] ₀. Thus, a large value of [pcirc] ₀ is suggested for fewer false alarms.     

Control charts based on linear combinations of order statistics

The last 20 years have seen an increasing emphasis on statistical process control as a practical approach to reducing variability in industrial applications. Control charts are used to detect problems such as outliers or excess variability in subgroup means that may have a special cause. We describe an approach to the computation of control limits for exponentially weighted moving average control charts where the usual statistics in classical charts are replaced by linear combinations of order statistics; in particular, the trimmed mean and Gini's mean difference instead of the mean and range, respectively. Control limits are derived, and simulated average run length experiments show the trimmed control charts to be less influenced by extreme observations than their classical counterparts, and lead to tighter control limits. An example is given that illustrates the benefits of the proposed charts. parameters; see, for example, Hunter (1986) and Montgomery (1996). On the other hand, EWMA charts have been shown to be more efficient than Shewharttype charts in detecting small shifts in the process mean; see, for example, Ng & Case (1989), Crowder (1989), Lucas & Saccucci (1990), Amin & Searcy (1991) and Wetherill & Brown (1991). In fact, the EWMA control chart has become popular for monitoring a process mean; see Hunter (1986) for a good discussion. More recently, EWMA charts have been developed for monitoring process variability;     

A Double Moving Average Control Chart

The double exponentially weighted moving average (DEWMA) technique has been investigated in recent years for detecting shifts in the process mean and has been shown to be more efficient than the corresponding exponentially weighted moving average (EWMA) technique. In this article, we extend the DEWMA technique of performing exponential smoothing twice to the double moving average (DMA) technique by computing the moving average twice. Using simulation, we show that our proposed DMA chart improves upon the ARL performance of the moving average (MA) chart in detecting mean shifts of small to moderate magnitudes. It is also shown through simulation that, generally, the DMA charts with spans, w = 10 and 15 provide comparable average run length (ARL) performances to the EWMA and cumulative sum (CUSUM) charts, designed for detecting small shifts.