Estimating Long and Short Run Effects in Static Panel Models

Abstract

This paper assesses the biases of four different estimators with respect to the short run and the long run parameters if a static panel model is used, although the data generating process is a dynamic error components model. We analytically derive the associated biases and provide a discussion of the determinants thereof. Our analytical and numerical results as well as Monte Carlo simulations illustrate that the asymptotic bias of both the within and the between parameter with respect to the short run and long run impact can be substantial, depending on the memory of the data generating process, the length of the time series and the importance of the cross-sectional variation in the explanatory variables.     

Average outgoing quality of CSP-C continuous sampling plan under short run production processes

A CSP-C continuous sampling plan is a new single-level continuous sampling procedure developed by Govindaraju & Kandasamy (2000) by incorporating the concept of acceptance number to the CSP-1 plan for the application of continuous production processes. In this new plan, the sampling inspection phase is characterized by a maximum allowable number of non-conforming units, c, and a constant sampling rate, f. Govindaraju & Kandasamy (2000) derived the performance measures such as average outgoing quality (AOQ), average fraction inspected (AFI) etc, of the CSP-C plan using a Markov chain model for long run production processes. Yang (1983) has observed that the AOQ and AFI, being long run average measures, are not satisfactory measures of performance for short run production processes. Hence, formulas are derived in this paper, using the renewal theory approach enabling one to compute AOQ and AFI for both long run and short run production processes. Numerical illustrations are also given. By simulation, the accuracy of the short run measures is studied.     

Short run spc based upon the second order dynamic linear model for trend detection

Recently, several new applications of control chart procedures for short production runs have been introduced. Bothe (1989) and Burr (1989) proposed the use of control chart statistics which are obtained by scaling the quality characteristic by target values or process estimates of a location and scale parameter. The performance of these control charts can be significantly affected by the use of incorrect scaling parameters, resulting in either an excessive "false alarm rate," or insensitivity to the detection of moderate shifts in the process. To correct for these deficiencies, Quesenberry (1990, 1991) has developed the Q-Chart which is formed from running process estimates of the sample mean and variance. For the case where both the process mean and variance are unknown, the Q-chaxt statistic is formed from the standard inverse Z-transformation of a t-statistic. Q-charts do not perform correctly, however, in the presence of special cause disturbances at process startup. This has recently been supported by results published by Del Castillo and Montgomery (1992), who recommend the use of an alternative control chart procedure which is based upon a first-order adaptive Kalman filter model Consistent with the recommendations by Castillo and Montgomery, we propose an alternative short run control chart procedure which is based upon the second order dynamic linear model (DLM). The control chart is shown to be useful for the early detection of unwanted process trends. Model and control chart parameters are updated sequentially in a Bayesian estimation framework, providing the greatest degree of flexibility in the level of prior information which is incorporated into the model. The result is a weighted moving average control chart statistic which can be used to provide running estimates of process capability. The average run length performance of the control chart is compared to the optimal performance of the exponentially weighted moving average (EWMA) chart, as reported by Gan (1991). Using a simulation approach, the second order DLM control chart is shown to provide better overall performance than the EWMA for short production run applications     

Globally applicable control chart for online monitoring of stability of process mean

The shape features of run chart patterns of the most recent m observations arising from stable and unstable processes are different. Using this fact, a new monitoring statistic is defined whose value for given m depends on the pattern parameters but not on the process parameters. A control chart for this statistic for given m, therefore, will be globally applicable to normal processes. The simulation study reveals that the proposed statistic approximately follows normal distribution. The performances of the globally applicable control chart in terms of average run lengths (ARLs) are evaluated and compared with the X chart. Both in-control ARL and out-of-control ARLs with respect to different abnormal process conditions are found to be larger than the X chart. However, the proposed concept is promising because it can eliminate the burden of designing separate control charts for different quality characteristics or processes in a manufacturing set-up.     

Identification of average marginal effects under misspecification when covariates are normal

A previously known result in the econometrics literature is that when covariates of an underlying data generating process are jointly normally distributed, estimates from a nonlinear model that is misspecified as linear can be interpreted as average marginal effects. This has been shown for models with exogenous covariates and separability between covariates and errors. In this paper, we extend this identification result to a variety of more general cases, in particular for combinations of separable and nonseparable models under both exogeneity and endogeneity. So long as the underlying model belongs to one of these large classes of data generating processes, our results show that nothing else must be known about the true DGP—beyond normality of observable data, a testable assumption—in order for linear estimators to be interpretable as average marginal effects. We use simulation to explore the performance of these estimators using a misspecified linear model and show they perform well when the data are normal but can perform poorly when this is not the case.     

CUSUM control schemes for Gaussian processes

A CUSUM control scheme for detecting a change point in a Gaussian process is derived. An upper and a lower bound for the distribution of the run length and for its moments is given. In a Monte Carlo study the average run length (ARL) of this chart is compared with the ARL of two other CUSUM procedures which are based on approximations to the sequential probability ratio, and, moreover, with EWMA schemes for autocorrelated data. Results on the optimal choice of the reference value are presented. Furthermore it is investigated how these charts behave if the model parameters are estimated.     

A new nonparametric synthetic EWMA control chart for monitoring process mean

The exponentially weighted moving average (EWMA) control charts are widely used in chemical and process industries because of their excellent speed in catching small to moderate shifts in the process target. In usual practice, many data come from a process where the monitoring statistic is non-normally distributed or it follows an unknown probability distribution. This necessitates the use of distribution-free/nonparametric control charts for monitoring the deviations from the process target. In this paper, we integrate the existing EWMA sign chart with the conforming run length chart to propose a new synthetic EWMA (SynEWMA) sign chart for monitoring the process mean. The SynEWMA sign chart encompasses the synthetic sign and EWMA sign charts. Monte Carlo simulations are used to compute the run length profiles of the SynEWMA sign chart. Based on a comprehensive comparison, it turns out that the SynEWMA sign chart is able to perform substantially better than the existing EWMA sign chart. Both real and simulated data sets are used to explain the working and implementation of existing and proposed control charts.     

On designing new optimal synthetic Tukey’s control charts

Tukey’s control chart is generally used for monitoring the processes where the measurement process physically damages the product. It is based on single observation and robust to outliers. In this paper, two optimal synthetic Tukey’s control charts are proposed by integrating the conforming run length chart with the Tukey’s control chart and its modification. The performance comparison of the proposed charts with the existing Tukey’s control charts is made by using out-of-control average run length and extra quadratic loss as performance metrics. The proposed charts offer better protection against the process shifts as compare to the existing Tukey’s control charts when the underlying process distribution is symmetric or asymmetric. Simulation studies also establish the supremacy of the proposed control charts over the existing Tukey’s control charts. In the end, an illustrative example based on a real data set of the combined cycle power plant is provided for practical implementation.     

Generalized run tests for statistical process control

ABSTRACT

In a sequence of elements, a run is defined as a maximal subsequence of like elements. The number of runs or the length of the longest run has been widely used to test the randomness of an ordered sequence. Based on two different sampling methods and two types of test statistics used, run tests can be classified into one of four cases. Numerous researchers have derived the probability distributions in many different ways, treating each case separately. In the paper, we propose a unified approach which is based on recurrence arguments of two mutually exclusive sub-sequences. We also consider the sequence of nominal data that has more than two classes. Thus, the traditional run tests for a binary sequence are special cases of our generalized run tests. We finally show that the generalized run tests can be applied to many quality management areas, such as testing changes in process variation, developing non-parametric multivariate control charts, and comparing the shapes and locations of more than two process distributions.     

The run length distributions of the R,s and s2 control charts when is estimated

R, s and s2 charts with estimated control limits are widely used in practice. Common practice in control-chart theory is to estimate the control limits using data from the process and, once the process is determined to be in control, to treat the resulting control limits as though fixed. While there are empirical rules for setting up the control charts using past or trial data, little is known about the run length distributions of these charts when the fact that control limits are estimated is taken into account. In this paper, we derive and evaluate the run length distributions associated with the R, s and s2 charts when the process standard deviation a is estimated. The results are then used to discuss the appropriateness of the widely followed empirical rules for choosing the number m of samples and the sample size n.     

Poisson regression models with errors-in-variables: implication and treatment

Overdispersion has been a common phenomenon in count data and usually treated with the negative binomial model. This paper shows that measurement errors in covariates in general also lead to overdispersion on the observed data if the true data generating process is indeed the Poisson regression. This kind of overdispersion cannot be treated using the negative binomial model, as otherwise, biases will occur. To provide consistent estimates, we propose a new type of corrected score estimator assuming that the distribution of the latent variables is known. The consistency and asymptotic normality of the proposed estimator are established. Simulation results show that this estimator has good finite sample performance. We also illustrate that the Akaike information criterion and Bayesian information criterion work well for selecting the correct model if the true model is the errors-in-variables Poisson regression.     

Minimally changed run sequences in factorial experiments

Randomization of run sequences in factorial experiments may result in large number of changes in factor levels which will make the experimentation expensive, time-consuming and difficult. Experiments in which it is difficult to change the levels of factor(s) use of minimally changed run sequences may often be preferable to a random run sequence. In the present paper, we have developed method for obtaining minimally changed run sequences for factorial experiments. The general expression of factor-wise number of level changes for the developed minimally changed run sequences has also been obtained. A relationship has been established between the time count effect of a lower order factorial with minimally changed run sequences and that of a higher order factorial with minimally changed run sequences obtained through the lower order minimally changed run sequences. For providing a readymade solution to the end users, a SAS macro has also been developed for generating these minimally changed run sequences along with its parameters.     

Poisson GWMA Control Chart

A generally weighted moving average (GWMA) control chart for monitoring Poisson observations is introduced. Using simulation, its average run lengths and standard deviations of run lengths are compared with those of other control charts for Poisson data. It is shown that the Poisson GWMA chart outperforms other control charts, especially when the process shift is small.     

A Multivariate Adaptive Exponentially Weighted Moving Average Control Chart

A multivariate extension of the adaptive exponentially weighted moving average (AEWMA) control chart is proposed. The new multivariate scheme can detect small and large shifts in the process mean vector effectively. The proposed scheme can be viewed as a smooth combination of a multivariate exponentially weighted moving average (MEWMA) chart and a Shewhart χ²-chart. The optimal design of the proposed chart is given according to a pre-specified in-control average run length and two shift sizes; a small and large shift each measured in terms of the non centrality parameter. The signal resistance of the newly proposed multivariate chart is also given. Comparisons among the new chart, the MEWMA chart, and the combined Shewhart-MEWMA (S-MEWMA) chart in terms of the standard and worst-case average run length profiles are presented. In addition, the three charts are compared with respect to their worst-case signal resistance values. The proposed chart gives somewhat better worst-case ARL and signal resistance values than the competing charts. It also gives better standard ARL performance especially for moderate and large shifts. The effectiveness of our proposed chart is illustrated through an example with simulated data set.     

The Robustness of the MaxEWMA Chart to Non-normality

Abstract

The MaxEWMA chart has recently been introduced as an improvement over the standard EWMA chart for detecting changes in the mean and/or standard deviation of a normally distributed process. Although this chart was originally developed for normally distributed process data, its robustness to violations of the normality assumption is the central theme of this study. For data distributions with heavy tails or displaying strong skewness, the in-control average run lengths (ARLs) for the MaxEWMA chart are shown to be significantly shorter than expected. On the other hand, out-of-control ARLs are comparable to normal theory values for a variety of symmetric non-normal distributions. The MaxEWMA chart is not robust to skewness.     

Designing of a control chart using belief statistic for exponential distribution

A new control chart is proposed by using the belief statistic for the exponential distribution. The structure of the proposed control chart is given to measure the average run length for the shifted process. The comparison of the proposed chart is given with the existing charts in terms of the average run lengths, which shows the outperformance of the proposed chart. The performance of the proposed control chart is also discussed with the help of simulated data.     

Improving the performance of the zone control chart

A general model for the zone control chart is presented. Using this model, it is shown that there are score vectors for zone control charts which result in superior average run length performance in comparison to Shewhart charts with common runs rules.

A fast initial response (FIR) feature for the zone control chart is also proposed. Average run lengths of the zone control chart with this feature are calculated. It is shown that the FIR feature improves zone control chart performance by providing significantly earlier signals when the process is out of control.     

Control chart for monitoring multivariate COM-Poisson attributes

Statistical process control of multi-attribute count data has received much attention with modern data-acquisition equipment and online computers. The multivariate Poisson distribution is often used to monitor multivariate attributes count data. However, little work has been done so far on under- or over-dispersed multivariate count data, which is common in many industrial processes, with positive or negative correlation. In this study, a Shewhart-type multivariate control chart is constructed to monitor such kind of data, namely the multivariate COM-Poisson (MCP) chart, based on the MCP distribution. The performance of the MCP chart is evaluated by the average run length in simulation. The proposed chart generalizes some existing multivariate attribute charts as its special cases. A real-life bivariate process and a simulated trivariate Poisson process are used to illustrate the application of the MCP chart.     

Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL

Statistical design is applied to a multivariate exponentially weighted moving average (MEWMA) control chart. The chart parameters are control limit H and smoothing constant r. The choices of the parameters depend on the number of variables p and the size of the process mean shift δ. The MEWMA statistic is modeled as a Markov chain and the Markov chain approach is used to determine the properties of the chart. Although average run length has become a traditional measure of the performance of control schemes, some authors have suggested other measures, such as median and other percentiles of the run length distribution to explain run length properties of a control scheme. This will allow a thorough study of the performance of the control scheme. Consequently, conclusions based on these measures would provide a better and comprehensive understanding of a scheme. In this article, we present the performance of the MEWMA control chart as measured by the average run length and median run length. Graphs are given so that the chart parameters of an optimal MEWMA chart can be determined easily.