Zawar Hussain

Progressive Mean Control Chart for Monitoring Process Location Parameter

Control charts are widely used for process monitoring. They show whether the variation is due to common causes or whethersome of the variation is due to special causes. To detect large shifts in the process, Shewhart-type control charts are preferred.Cumulativesum(CUSUM)andexponentiallyweightedmovingaverage(EWMA)controlchartsaregenerallyusedtodetectsmalland moderate shifts. Shewhart-type control charts (without additional tests) use only current information to detect specialcauses, whereas CUSUM and EWMA control charts also use past information. In this article, we proposed a control chart calledprogressivemean(PM)controlchart,inwhichaPMisusedasaplottingstatistic.Theproposedchartisdesignedsuchthatitusesnot only the current information but also the past information. Therefore, the proposed chart is a natural competitor for theclassical CUSUM, the classical EWMA and some recent modifications of these two charts. The conclusion of this article is thatthe performanceofthe proposedPMchart issuperiortothe comparedonesfor small and moderateshifts, and its performancefor large shifts is better (in terms of the average run length). Copyright

Bayesian Estimation Using Warner's Randomized Response Model through Simple and Mixture Prior Distributions

Bayesian estimation of population proportion of a sensitive characteristic is proposed by adopting a simple beta distribution and a mixture of Beta distributions as quantification of prior information using simple random sampling with replacement. In the sequel application of the stratified random sampling is also studied in Bayesian scenario. It is assumed that data are collected through Warner (1965) randomized response technique. To study the performance of Bayesian estimators we have used Mean Squared Error (MSE) and/or Relative Efficiency (RE) as performance criterion. Further, comparison of the suggested estimator is made with Kim et al. (2006) stratified estimator and usual maximum likelihood estimator in case of stratified random sampling. It is observed that unlike the moment and maximum likelihood methods, proposed Bayesian estimation method is free of the problems of having an estimate of population proportion outside the interval (0, 1) and large variance when the sample proportion of yes responses is very low or very high.

An alternative to Ryu et al. randomized response model

Abstract The present study introduces an unbiased estimator of population mean of a sensitive quantitative variable. The proposed model is based on utilizing the Ryu et al. (2005) model and to have two responses in anticipation of getting more useful information. The relative efficiency of the proposed estimator with respect to Greenberg et al. (1971), Eichhorn and Hayre (1983), Gupta et al. (2002) and Ryu et al. (2005) is calculated.

Progressive Variance Control Charts for Monitoring Process Dispersion

In a process, the deviation from location or scale parameters affects the quality of the process and waste resources. So it is essential to monitor such processes for possible changes due to any assignable causes. Control charts are the most famous tool used to meet this intention. It is useless to monitor process location until the assurance that process dispersion is in-control. This study proposes some new two-sided memory control charts named as progressive variance (PV) control charts which are based on sample variance to monitor changes in process dispersion assuming normality of quality characteristic to be monitored. Simulation studies are made, and an example is discussed to evaluate the performance of the proposed charts. The comparison of the proposed chart is made with exponentially weighted moving average- and cumulative sum-type charts for process dispersion. The study shows that performance of the proposed charts are uniformly better than its competitors for detecting positive shifts while for detecting negative shift in the variance their performance is better for small shifts and reasonably good for moderated shifts.

Additive and subtractive scrambling in optional randomized response modeling.

This article considers unbiased estimation of mean, variance and sensitivity level of a sensitive variable via scrambled response modeling. In particular, we focus on estimation of the mean. The idea of using additive and subtractive scrambling has been suggested under a recent scrambled response model. Whether it is estimation of mean, variance or sensitivity level, the proposed scheme of estimation is shown relatively more efficient than that recent model. As far as the estimation of mean is concerned, the proposed estimators perform relatively better than the estimators based on recent additive scrambling models. Relative efficiency comparisons are also made in order to highlight the performance of proposed estimators under suggested scrambling technique.

Simultaneous Use of Runs Rules and Auxiliary Information With Exponentially Weighted Moving Average Control Charts

Quality has become a key determinant of success in all aspects of industry. Exponentially weighted moving average control chart is an important tool of statistical process control used to monitor and improve quality of industrial processes. To enhance the performance of control charts, there are many strategies including the choice of an efficient plotting statistic, the choice of an efficient sampling design, the application of runs rules, and the use auxiliary information among many others. In this study, we propose nine different signaling schemes to enhance the performance of an exponentially weighted moving average control chart for location parameter, which is based on the exploitation of auxiliary information. Performance evaluation of the proposed schemes is carried out in terms of average run length. Comparisons of proposals are made with the classical as well as the auxiliary based exponentially weighted moving average and cumulative sum charts, which indicate that the proposed schemes perform better than the comparative counterparts under discussion. Copyright

Improved randomized response models in additive scrambling

Abstract In this investigation, we consider the problem of procuring the reliable information on stigmatizing variable. Two optional randomized response models are proposed for efficient estimation of mean and sensitivity level. A comparison of proposed optional randomized response models (ORRMs) with Huang (2010) and Gupta et al. (2010) models have been made. It is found that the proposed strategies perform better than those of Huang (2010) and Gupta et al. (2010) models whether it is estimation of mean or sensitivity level. A comparison is also made among the Huang (2010), Gupta et al. (2010) and proposed ORRMs to identify the best one. Percentage relative efficiency comparisons are also made to study the performance of the proposed procedures.

Mean and sensitivity estimation of a sensitive variable through additive scrambling

Abstract This article focuses on reducing the additional variance due to randomization of the responses. The idea of additive scrambling and its inverse has been used along with (i) split sample approach and (ii) double response approach. Specifically, our proposal is based on Gupta et al. (2006) randomized response model. We selected this model for improvement because it provides estimator of mean and sensitivity level of a sensitive variable and is better than all of its competitors proposed earlier to it and even Gupta et al. (2006) sensitivity estimator is better than that of Gupta et al. (2010). Our suggested estimators are unbiased estimators and perform better than Gupta et al. (2006) estimator. The issue of privacy protection is also discussed.

A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework

To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simple models. This paper is about studying a 3-component mixture of the Rayleigh distributionsin Bayesian perspective. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different scenarios. In case the case that no or little prior information is available, elicitation of hyperparameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times. In addition, to highlight the practical significance, an illustrative example based on a real-life engineering data is also given.

An improved binary randomized response model using six decks of cards

ABSTRACT This article purposes the estimation of population proportion of a sensitive attribute through randomized response technique. An efficient estimator is suggested using six decks of cards to randomise the response. Many existing models can now be viewed as the special case of the proposed model. The superiority of the proposed procedure is established through numerical calculation of percentage relative efficiency with prominent competitors. The proposed procedure is also studied under stratified random sampling protocol. In addition, it is shown that, the proposed stratified estimator, performs better in term of efficiency than its only existing two deck stratified competitor.