Optimal design of synthetic np control chart based on median run length

The synthetic np chart is a combination of the np sub-chart and the conforming run length sub-chart. A procedure for the optimal design of the synthetic np chart is provided by minimizing the out-of-control median run length (MRL). The comparative results show that the synthetic np chart performs better than the corresponding standard np chart for detecting process shifts in the fraction non conforming, in terms of the MRL. An example is given to illustrate the operation of the synthetic np chart.     

On the run length of the EWMA scheme: a monotonicity result for normal variables

We discuss the EWMA control chart for a stationary Gaussian process {X_t}. It is proved that in the in-control state the probability of no signal until a fixed time is a nondecreasing function in the autocorrelations of {X_t} provided that they satisfy a certain monotonicity assumption.     

Run length,average run length and false alarm rate of shewhart x-bar chart: exact derivations by conditioning

The effects of estimation of the control limits on the performance of the popular Shewhart X-bar chart are examined via the average run length and the probability of a false alarm, when one or both of the process mean and variance are unknown. Exact expressions for the run length, the average run length (ARL) and the false alarm rate are obtained, in each case, using expectation by conditioning. Applying Jensen's inequality, together with expectation by conditioning, a simple lower bound to the ARL is obtained. This could be useful in designing the charts. The expressions for the exact ARL and the exact probabilities of false alarm are evaluated, using simulations, for various numbers of subgroups and shift sizes. The calculations throw new light on the performance of the Shewhart X-bar chart. Some recommendations are given.     

Optimal designs of multivariate synthetic |S| control chart based on median run length

The multivariate synthetic generalized sample variance |S| (synthetic |S|) chart is a combination of the |S| sub-chart and the conforming run length sub-chart. A procedure for optimal designs of the synthetic |S| chart, based on the median run length (MRL), for both zero and steady-state modes are provided by minimizing the out-of-control MRL. The comparative results show that the synthetic |S| chart performs better than the standard |S| chart for detecting shifts in the covariance matrix of a multivariate normally distributed process, in terms of the MRL. An example is given to illustrate the operation of the synthetic |S| chart.     

Efficient run orders for a two-factor response surface experiment on a correlated process

The standard assumption in the design and analysis of response surface experiments is that the errors are uncorrelated with common variance. In practice however there may be serial dependence between the errors, in which case the efficiency of the design depends on the order in which the runs are carried out. We investigate the effect of run order on a two-factor response surface experiment when there is positive serial correlation, and recommend some particular run orders which are efficient under a wide range of conditions.     

The effect of Phase I sample size on the run length performance of control charts for autocorrelated data

Traditional control charts assume independence of observations obtained from the monitored process. However, if the observations are autocorrelated, these charts often do not perform as intended by the design requirements. Recently, several control charts have been proposed to deal with autocorrelated observations. The residual chart, modified Shewhart chart, EWMAST chart, and ARMA chart are such charts widely used for monitoring the occurrence of assignable causes in a process when the process exhibits inherent autocorrelation. Besides autocorrelation, one other issue is the unknown values of true process parameters to be used in the control chart design, which are often estimated from a reference sample of in-control observations. Performances of the above-mentioned control charts for autocorrelated processes are significantly affected by the sample size used in a Phase I study to estimate the control chart parameters. In this study, we investigate the effect of Phase I sample size on the run length performance of these four charts for monitoring the changes in the mean of an autocorrelated process, namely an AR(1) process. A discussion of the practical implications of the results and suggestions on the sample size requirements for effective process monitoring are provided.     

On a control chart for the Gini index with simulations

In this work we suggest the use of the Gini index on control charts. The asymptotic properties of Gini index are presented and the control charts based on appropriate confidence intervals are constructed. The suitability of the proposed charts are investigated by means of extensive simulations.     

Simulating the average run length for cusum schemes using variance reduction techniques

Some variance reduction techniques utilizing the total hazard are developed to estimate the average run lengths of the cumulative sum charts through simulation when the process follows a general probability distribution. Particularly, we propose the hazard estimator and the cycle estimator. Simulation results are shown for the exponential case and these estimators are compared with the raw simulation estimator. Applicability to multivariate CUSUM schemes is briefly discussed in the conclusion.     

Average run length comparison of multivariate control charts

In this paper we use Monte Carlo Simulation methodology to compare the effectiveness of five multivariate quality control methods, namely Hotelling T ², Multivariate Shewhart Char, Discriminant Analysis, Decomposition Method, and Multivariate Ridge Residual Chart-developed by Authors-, for controlling the mean vector in a multivariate process. P-dimensional multivariate normal data generated using different covariance structures. Various amount of shift in the mean vector is induced and the resulting Average Run Length (ARL) is computed. The effectiveness of each method with regard to ARL is discussed.     

Towards the implementation of a universal control chart and estimation of its average run length using a spreadsheet: An artificial neural network is employed to model the parameters in a special case

A control chart procedure has previously been proposed (Champ et al., 1991) for which the Shewhart X ¥ -chart, the cumulative sum chart, and the exponentially weighted moving average chart are special cases. The rapid and easy production of these charts, plus many others, is proposed using spreadsheets. In addition, for all these novel charts, the average run lengths are generated as a guide to their likely behaviour. The cumulative sum chart is widely employed in quality control and is considered in greater detail. Charts are designed to exhibit acceptable average run lengths both when the process is in and out of control. A functional technique for parameter selection for such a chart is introduced that results in target average run lengths. It employs the method of artificial neural networks to derive appropriate coefficients. This approach may be extended to any of the charts previously introduced.     

Towards the implementation of a universal control chart and estimation of its average run length using a spreadsheet: an artificial neural network is employed to model the parameters in a special case

A control chart procedure has previously been proposed (Champ et al., 1991) for which the Shewhart X ¯-chart, the cumulative sum chart, and the exponentially weighted moving average chart are special cases. The rapid and easy production of these charts, plus many others, is proposed using spreadsheets. In addition, for all these novel charts, the average run lengths are generated as a guide to their likely behaviour. The cumulative sum chart is widely employed in quality control and is considered in greater detail. Charts are designed to exhibit acceptable average run lengths both when the process is in and out of control. A functional technique for parameter selection for such a chart is introduced that results in target average run lengths. It employs the method of artificial neural networks to derive appropriate coefficients. This approach may be extended to any of the charts previously introduced.     

Multivariate models for correlated count data

In this study, we deal with the problem of overdispersion beyond extra zeros for a collection of counts that can be correlated. Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions have been considered. First, we propose a multivariate count model in which all counts follow the same distribution and are correlated. Then we extend this model in a sense that correlated counts may follow different distributions. To accommodate correlation among counts, we have considered correlated random effects for each individual in the mean structure, thus inducing dependency among common observations to an individual. The method is applied to real data to investigate variation in food resources use in a species of marsupial in a locality of the Brazilian Cerrado biome.     

Forecasting models for developing control scheme to improve furnace run length

In petrochemical industries, the gaseous feedstock like ethane and propane are cracked in furnaces to produce ethylene and propylene as main products and the inputs for the other plant in the downstream. A problem of low furnace run length (FRL) increases furnace decoking and reduces productivity along with the problem of reducing life of the coil. Coil pressure ratio (CPR) and tube metal temperature (TMT) are the two most important performance measures for the FRL to decide upon the need for furnace decoking. This article, therefore, makes an attempt to develop the prediction models for CPR and TMT based on the critical process parameters, which would lead to take the necessary control measures along with a prior indication for decoking. Regression-based time series and double exponential smoothing techniques are used to build up the models. The effective operating ranges of the critical process parameters are found using a simulation-based approach. The models are expected to be the guiding principles eventually to increase the average run length of furnace.     

Performance of and software for a modified mantel-haenszel statistic for correlated data

This paper presents the results of a small sample simulation study designed to evaluate the performance of a recently proposed test statistic for the analysis of correlated binary data. The new statistic is an adjusted Mantel-Haenszel test, which may be used in testing for association between a binary exposure and a binary outcome of interest across several fourfold tables when the data have been collected under a cluster sampling design. Al- though originally developed for the analysis of periodontal data, the proposed method may be applied to clustered binary data arising in a variety of settings, including longitu- dinal studies, family studies, and school-based research. The features of the simulation are intended to mimic those of a research study of periodontal health, in which a large number of observations is made on each of a relatively small number of patients. The simulation reveals that the adjusted test statistic performs well in finite samples, having empirical type I error rates close to nominal and empirical power similar to that of more complicated marginal regression methods. Software for computing the adjusted statistic is also provided.     

On detecting and modeling deterministic drift in long run sequences of tapping data

In tapping experiments, a subject attempts to tap continuously at a specified tempo. It is of interest to psychologists to study how well the subject can maintain the starting tempo, and in particular, whether the tempo tends to drift towards attractor tempos specified by a model suggested by rhythm researchers. This paper focuses on the analysis of a new data set of long run sequences of tapping data, applying rank tests to test tor drift specified by the attractor model, estimatingthe point at which the final tempo is achieved. and analyzing the amount and direction of drift.     

Robust likelihood inferences for multivariate correlated data

Multivariate normal, due to its well-established theories, is commonly utilized to analyze correlated data of various types. However, the validity of the resultant inference is, more often than not, erroneous if the model assumption fails. We present a modification for making the multivariate normal likelihood acclimatize itself to general correlated data. The modified likelihood is asymptotically legitimate for any true underlying joint distributions so long as they have finite second moments. One can, hence, acquire full likelihood inference without knowing the true random mechanisms underlying the data. Simulations and real data analysis are provided to demonstrate the merit of our proposed parametric robust method.