Asymptotics for minimal overlapping patterns for generalized Euler permutations, standard tableaux of rectangular shape, and column strict arrays

A permutation $\tau$ in the symmetric group $S_j$ is minimally overlapping if any two consecutive occurrences of $\tau$ in a permutation $\sigma$ can share at most one element. B\'ona \cite{B} showed that the proportion of minimal overlapping patterns in $S_j$ is at least $3 -e$. Given a permutation $\sigma$, we let $\text{Des}(\sigma)$ denote the set of descents of $\sigma$. We study the class of permutations $\sigma \in S_{kn}$ whose descent set is contained in the set $\{k,2k, \ldots (n-1)k\}$. For example, up-down permutations in $S_{2n}$ are the set of permutations whose descent equal $\sigma$ such that $\text{Des}(\sigma) = \{2,4, \ldots, 2n-2\}$. There are natural analogues of the minimal overlapping permutations for such classes of permutations and we study the proportion of minimal overlapping patterns for each such class. We show that the proportion of minimal overlapping permutations in such classes approaches $1$ as $k$ goes to infinity. We also study the proportion of minimal overlapping patterns in standard Young tableaux of shape $(n^k)$.Comment: Accepted by Discrete Math and Theoretical Computer Science. Thank referees' for their suggestion

Constructing SPC Charts by Cumulative Square and Cumulative Variance Methodologies

The authors discuss the methodologies for constructing quality control charts by cumulative square and cumulative variance methodologies. These methodologies correspond to the EWMS and EWMV methods proposed by MacGregor and Harris (1993). Based on the distributions of the quality control chart statistics, we focus on the average (mean) cumulative square and average (mean) cumulative variance schemes to arrive at control limits appearing as parallel lines seen in stand Shewhart control charts. Last , we utilize the Box quadratic form and approximation to deal with the complexities of cumulative variance where means vary over time

The Multivariate EWMA Model and Health Care Monitoring

We introduce the construction of MEWMA (Multivariate exponentially weighted movingaverage) process control in the field of bio surveillance. Such introduction will both improve the reliability of data collected in bio surveillance, better interpretation of the results,improvement in the quality of results and standardization of results when more than two variables are involved. We propose sensitivity ratios as a measure of the effects of the mean shift and dispersion shift in processes under study. Using these sensitivity measures, we designed the optimal exponential weighting factor, which is consistent to results reported in control chart applications. Although ARL (average run length) is the usual measure for control chart performance in multivariate process control, it is by no means the only criterion, however, at the moment it is most widely used criterion for decision making. We suggest addition study of other criteria. For example Medial Run Length, Days to Completion, Direction of Eorrors and others

Using Golden Ratio Search to Improve Paired Construction of Quality Control Charts

Our purpose is to indicate a new method for determining the control limits of univariate control charts to show the effectiveness of golden ratios search. We examine a solution to a problem when signals from mean and variance charts differ. Lack of concordance in the signals from mean and variance (or standard deviation) control charts bring confusion to Quality Contro managers which in turn may lead to sub optimal management quality practices. To achieve better quality management practice, we provide a solution to the problem of finding different decision signals for in-control processes for quality control charts for mean and variability. We construct the control charts in experimental conditions for in-control average run length using the methods of simulation. Finally, we employ the golden ratio search method to identify the control limit parameters which differ from standard methods for constructing quality control charts. Last, we minimize the length of time in computation in the construction of these new quality control charts

Estimating σ and Improving Control Limits with RWAV for Normal and Nonnormal Processes

In this article, we compare the statistical properties of , , and RWAV methods for estimation of variance of a process for quality control purposes. We investigate effects of non-normality for different estimators. Our results indicate that RWAV gives the best estimates of the standard deviations for both normal and non-normal processes. We recommend the construction of control charts with RWAV

Multivariate Ewma Models and Monitoring Health Surveillance during a Pandemic

We examine a common problem is biological analytics and surveillance in health care. These methods can improve greatly the process of monitoring health data to assess changes in the likelihood of Pandemics and disease incidence in a world where medical knowledge is still largely in an embryonic period. Based on an illustration, we suggest that multivariate exponential moving-average (MEWMA) control charts are suitable in many cases where detection and inspection of several or more variables over a lengthy period of testing provide for the best analysis of data leading to pre-­diagnostic and diagnostic therapy. Though these methods came from the control of quality and continuous improvement in lean manufacturing and service operations, these methods are useful if not a vital application in the analysis of health care and therapeutic data. The indications from this study corroborate earlier findings by others that MEWMA methods fit the diagnostic activity under study. Unfortunately Pandemic Analysis is using oversimplified techniques in analyzing data secure by diagnostic tests which can easily be improved especially in the use modern day analytics based on quality control methods used in other disciplines

A Reference Point Theory of Mergers and Acquisitions

The use of judgmental anchors or reference points in valuing corporations affects several basic aspects of merger and acquisition activity including offer prices, deal success, market reaction, and merger waves. Offer prices are biased toward the 52-week high, a highly salient but largely irrelevant past price, and the modal offer price is exactly that reference price. An offer’s probability of acceptance discontinuously increases when the offer exceeds the 52-week high; conversely, bidder shareholders react increasingly negatively as the offer price is pulled upward toward that price. Merger waves occur when high recent returns on the stock market and on likely targets make it easier for bidders to offer the 52-week high