Skew Correction Research Articles

Comparing Confidence Intervals for the Mean of Symmetric and Skewed Distributions

In context-aware decision analysis, mean can be an important measure, even when the distribution is skewed. Previous comparative studies showed that it is a real challenge to construct a confidence interval that performs well for highly skewed data. In this study, we propose new confidence intervals for the population mean based on Edgeworth expansion that include both skewness and kurtosis corrections. We compared existing and newly proposed confidence intervals for a range of samples from symmetric and skewed distributions of varying levels of kurtosis. Using Monte Carlo simulations, we evaluated the performance of these intervals based on the coverage probability, mean length, and standard deviation of the length. The proposed bootstrap Edgeworth-based confidence interval outperformed other confidence intervals in terms of coverage probability for both symmetric and skewed distributions and can be recommended for general use in practice.

A Robust Design for the Omnibus SPRT Control Chart Under Skewed Data Distributions

Control charts are widely used in manufacturing industries to ensure that production levels are stable and satisfactory. Recently, the omnibus sequential probability ratio test (OSPRT) control chart was developed for the purpose of monitoring the mean and variability of a process simultaneously. As the OSPRT chart was proposed for the first time in literature, its development relied entirely on the assumption that data follow the Normal distribution. Nonetheless, researchers are frequently reminded that the quality characteristics of manufacturing processes do not necessarily follow the Normal distribution, e.g., strengths of glass fibres, and lifetimes of products. In this paper, we investigate the extent to which the performances of the OSPRT chart designed for the Normal model deteriorate, in situations where the data distributions are Gamma and Lognormal. Results show that the in-control average run length (ARL) and standard deviation of the run length of the OSPRT chart designed for the Normal distribution deteriorate rapidly as skewness increases. To address this issue, we propose a robust design for the OSPRT chart by adjusting its control limits, known as the skewness correction method. It is shown that the skewness-corrected OSPRT chart enjoys a guaranteed in-control ARL, with a justifiable degradation in its out-of-control performances. Besides, we also show some insights into selecting the charting parameters for the skewness-corrected OSPRT chart in order to achieve an optimum out-of-control ARL performance over various shift sizes. The paper wraps up with an illustrative example of the skewness-corrected OSPRT chart for monitoring the weights of radial tyres.

Control Charts for a Novel Exponent Power Rayleigh Distribution

Abstract: In this Paper, we presented the distribution as A Novel Exponent Power Rayleigh (NovEPRD) probability density function, Distribution, and Survival and Hazard functions introduced by Bharathi et al (2022) and A Novel Exponent Power Rayleigh (NovEPR) distribution Properties and its Applications studied by Bharathi et al (2022) and then here we derived the Weighted Variance (WV), Weighted Standard Deviation (WSD) and Correction Factor (CF) for existed A Novel Exponent Power Rayleigh (NovEPR) distribution , this paper obtains the parameters of the control lines X̅ and R drawn from the A Novel Exponent Power Rayleigh (NovEPR) distribution. These methods are compared with Newton Raphson’s simulations. For these control charts, Type I risk is compared with different groups of A Novel Exponent Power Rayleigh (NovEPR) distribution. Simulation results show that the Skewness Correction (SC) method of Type I carries less risk than other methods. When the distribution is approximately equal, the type I risk of the Shewhart, W V, WSD and SC X̅ plans is comparable, while the type I risk of the SC R plan is smaller

Incorporating plan complexity into the statistical process control of volumetric modulated arc therapy pre-treatment verifications.

Statistical process control (SPC) is a powerful statistical tool for process monitoring that has been highly recommended in healthcare applications, including radiation therapy quality assurance (QA). The AAPM TG-218 report described the clinical implementation of SPC for Volumetric Modulated Arc Therapy (VMAT) pre-treatment verifications, pointing out the need to adjust tolerance limits based on plan complexity. However, the quantification of plan complexity and its integration into SPC remains an unresolvedchallenge. The primary aim of this study is to investigate the incorporation of plan complexity into the SPC framework for VMAT pre-treatment verifications. The study explores and evaluates various strategies for this incorporation, discussing their merits and limitations, and provides recommendations for clinicalapplication. A retrospective analysis was conducted on 309 VMAT plans from diverse anatomical sites using the PTW OCTAVIUS 4D device for QA measurements. Gamma Passing Rates (GPR) were obtained, and lower control limits were computed using both the conventional Shewhart method and three heuristic methods (scaled weighted variance, weighted standard deviations, and skewness correction) to accommodate non-normal data distributions. The 'Identify-Eliminate-Recalculate' method was employed for robust analysis. Eight complexity metrics were analyzed and two distinct strategies for incorporating plan complexity into SPC were assessed. The first strategy focused on establishing control limits for different treatment sites, while the second was based on the determination of control limits as a function of individual plan complexity. The study extensively examines the correlation between control limits and plan complexity and assesses the impact of complexity metrics on the controlprocess. The control limits established using SPC were strongly influenced by the complexity of treatment plans. In the first strategy, a clear correlation was found between control limits and average plan complexity for each site. The second approach derived control limits based on individual plan complexity metrics, enabling tailored tolerance limits. In both strategies, tolerance limits inversely correlated with plan complexity, resulting in all highly complex plans being classified as in control. In contrast, when plans were collectively analyzed without considering complexity, all the out-of-control plans were highlycomplex. Incorporating plan complexity into SPC for VMAT verifications requires meticulous and comprehensive analysis. To ensure overall process control, we advocate for stringent control and minimization of plan complexity during treatment planning, especially when control limits are adjusted based on plancomplexity.

Efficient Corrections for Standardized Person-Fit Statistics.

Many popular person-fit statistics belong to the class of standardized person-fit statistics, T, and are assumed to have a standard normal null distribution. However, in practice, this assumption is incorrect since T is computed using (a) an estimated ability parameter and (b) a finite number of items. Snijders (Psychometrika 66(3):331-342, 2001) developed mean and variance corrections for T to account for the use of an estimated ability parameter. Bedrick (Psychometrika 62(2):191-199, 1997) and Molenaar and Hoijtink (Psychometrika 55(1):75-106, 1990) developed skewness corrections for T to account for the use of a finite number of items. In this paper, we combine these two lines of research and propose three new corrections for T that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The new corrections are efficient in that they only require the analysis of the original data set and do not require the simulation or analysis of any additional data sets. We conducted a detailed simulation study and found that the new corrections are able to control the Type I error rate while also maintaining reasonable levels of power. A real data example is also included.

Concomitant Skew and Phase Correction (CSPC) for Industry 5.0 Enabler Pervasive Distributed Computing Systems

Concomitant Skew and Phase Correction (CSPC) for Industry 5.0 Enabler Pervasive Distributed Computing Systems

Recognition of Off-Line Handwritten Kannada Words Using Enhanced Skew Detection and Correction Method

Handwritten character image is taken as dataset for this method. In the proposed system, extracting text lines, word, charactersand skew correction are done based on Enhanced Skew Detection and Correction for Words algorithm for estimating and correcting skew lines. The algorithm will be used for finding the height andwidth of the entire handwritten word. In case of no skew, minimum valuewill be considered for the height of the wordand maximum value will be considered for the width of the word. Once skew is corrected with approximateskew angle repetition of the same process, only busy zone is considered for performing precise skewcorrection. The recommended approach has tested roughly 3364 Kannada items and achieved the best performance of 97.05 percent.

Resource-Limited Skew Estimation and Correction (RLSEC) for Edge Devices in Delay Non-Tolerant Networks

Resource-Limited Skew Estimation and Correction (RLSEC) for Edge Devices in Delay Non-Tolerant Networks

Evaluating the Efficiency of Skew Correction Factors in Sediment Rating Curve and Comparison with Intelligent Models (Case Study: Jelogir Station, Khuzestan - Karkheh Catchment)

Evaluating the Efficiency of Skew Correction Factors in Sediment Rating Curve and Comparison with Intelligent Models (Case Study: Jelogir Station, Khuzestan - Karkheh Catchment)

Skew Correction and Image Cleaning Handwriting Recognition Using a Convolutional Neural Network

Handwriting recognition is a study of Optical Character Recognition (OCR) which has a high level of complexity. In addition, everyone has a unique and inconsistent handwriting style in writing characters upright, affecting recognition success. However, proper pre-processing and classification algorithms affect the success of pattern recognition systems. This paper proposes a pre-processing method for handwriting image recognition using a convolutional neural network (CNN). This study uses public datasets for training and private datasets for testing. This pre-processing consists of three processes: image cleaning, skew correction, and segmentation. These three processes aim to clean the image from unnecessary ink streaks. In addition, to make angle corrections to characters in italics in their writing. The model testing process uses image test data of handwriting that are not straight. There are three images based on the inclination angle: less than 45 degrees, equal to 45 degrees, and more than 45 degrees. Picture cleaning removes unnecessary strokes (noise) from the image using a layer mask, whereas skew correction changes the handwriting to an upright posture based on the detected angle. The pre-processing model we propose worked optimally on handwriting with a skew angle of fewer than 45 degrees and 45 degrees. Our proposed model generally works well for handwriting with fewer than 45 degrees skew with an accuracy of 88,96%. Research with a similar scope can continue to improve optimization with a focus on algorithms related to analysis layout studies. Besides that, it can focus more on automation in the segmentation process of each character.

Probability‐type, Shewhart‐type and EWMA control charts for individual observations from the two‐parameter Lindley distribution

AbstractLindley distribution is a continuous distribution with various applications some of which are in medicine, genetics, epidemiology, biology, finance and actuarial sciences, ecology, meteorology, sociology, demography, agriculture, hydrology, geosciences, reliability and engineering, life testing and survival analysis, airborne systems and communications, environmental studies and modeling and describing of human mistakes, strikes, accidents, behavioural and emotional or IQ test scores and waiting times of customers in queues until service, etc. Due to its variety of applications, it appears to be important that control charts for detected shifts in a process should be constructed under the assumption that the quality characteristic of interest follows a Lindley‐related distribution. Here, we construct probability‐type, Shewhart‐type and EWMA control charts (and deal with the optimal choice of its parameters) for individual observations from the two‐parameter Lindley distribution, investigate and compare their performance and illustrate them using examples with both simulated and real data. The whole analysis reveals the superiority of using skewness correction for the construction of the control charts against not using it.

A study on the performance of the probability-limit control charts based on the geometric and negative binomial distributions

The Shewhart-type control chart based on the geometric distribution is widely used to monitor the number of normal events between two consecutive appearances of adverse events, but this control chart relies on the normality assumption and may thus result in unsatisfactory performance due to the high skewness of the geometric distribution. Thus, one can consider the probability-limit control chart based on the geometric distribution to correct the skewness, whereas the average run length or the false alarm rate of this control chart has been shown to be seriously biased despite of the skewness correction. In this paper, we first illustrate that the biased issue is mainly due to discreteness of the geometric distribution and then advocate the use of the control chart based on the negative binomial distribution. Numerical results from extensive Monte Carlo simulations clearly show that the control chart based on the negative binomial not only reduces the bias, but also outperforms the one based on the geometric control chart in a sense of smaller bias and high alarm rate.

Guaranteed performance of individual control chart used in gamma passing rate-based patient-specific quality assurance

PurposeTo assess the effect of sampling variability on the performance of individual charts (I-charts) for PSQA and provide a robust and reliable method for unknown PSQA processes. Materials and methodsA total of 1327 pretreatment PSQAs were analyzed. Different datasets with samples in the range of 20–1000 were used to estimate the lower control limit (LCL). Based on the iterative “Identify-Eliminate-Recalculate” and direct calculation without any outlier filtering procedures, five I-charts methods, namely the Shewhart, quantile, scaled weighted variance (SWV), weighted standard deviation (WSD), and skewness correction (SC) method, were used to compute the LCL. The average run length (ARL0) and false alarm rate (FAR0) were calculated to evaluate the performance of LCL. ResultsThe ground truth of the values of LCL, FAR0, and ARL0 obtained via in-control PSQAs were 92.31%, 0.135%, and 740.7, respectively. Further, for in-control PSQAs, the width of the 95% confidence interval of LCL values for all methods tended to decrease with the increase in sample size. In all sample ranges of in-control PSQAs, only the median LCL and ARL0 values obtained via WSD and SWV methods were close to the ground truth. For the actual unknown PSQAs, based on the “Identify-Eliminate-Recalculate” procedure, only the median LCL values obtained by the WSD method were closest to the ground truth. ConclusionsSampling variability seriously affected the I-chart performance in PSQA processes, particularly for small samples. For unknown PSQAs, the WSD method based on the implementation of the iterative “Identify-Eliminate-Recalculate” procedure exhibited sufficient robustness and reliability.

Single-Timestamp Skew Correction (STSC) in V2X Networks

Modern vehicles nowadays have many capabilities apart from the basic function of driving. These are now intelligent, smart, and can communicate over the Internet. A vehicle-to-everything (V2X) wireless network represents a network where vehicles communicate vital sensor data with other vehicles, pedestrians, and fixed infrastructure over the internet. There are various challenges in V2X communication that may affect the efficiency of autonomous devices, systems, and infrastructure. Of the many challenges, time synchronization among many devices in V2X networks is a key challenge. In a V2X network, all nodes within the network need to be time-synchronized; this is essential for task scheduling, computation off-loading, event sequencing, resource sharing, and efficient utilization of resources in the network. In recent works, many researchers have addressed time synchronization in V2X networks by considering multiple timestamps in order to estimate the time skew offset with varying results. In this paper, we consider a skew-based approach, namely, a single-timestamp skew correction (STSC) for time synchronization in V2X networks. The proposed method needs a single timestamp to estimate time skew at the hardware level with the help of physical-layer time synchronization using symbol timing recovery. Implementation results prove that the STSC accurately synchronizes the nodes in phase and frequency, therefore resulting in a greater accuracy and better energy savings in the V2X networks.

Prediction of BRAF V600E variant from cancer gene expression data

BRAF inhibitors have been approved for the treatment of melanoma, non-small cell lung cancer, and colon cancer. Real-time polymerase chain reaction or next-generation sequencing were clinically used for BRAF variant detection to select who responds to BRAF inhibitors. The prediction of BRAF variants using gene expression data might be an alternative test when the direct variant sequencing test is not feasible. In this study, we built a prediction model to detect BRAF V600 variants with mRNA gene expression data in various cancer types. We adopted a penalized logistic regression for the BRAF V600E variants prediction model. Ten times bootstrap resampling was done with a combined target variable and cancer type stratification. Data preprocessing included knnimputation for missing value imputation, YeoJohnson transformation for skewness correction, center, and scale for standardization, synthetic minority over-sampling technique for class imbalance. Hyperparameter optimization with a grid search was undertaken for model selection in terms of area under the precision-recall. The area under the curve of the receiver operating characteristic curve on the test set was 0.98 in thyroid carcinoma, 0.90 in colon adenocarcinoma, and 0.85 in cutaneous melanoma. The area under the precision-recall of the test set was 0.98 in thyroid carcinoma, 0.71 in colon adenocarcinoma, and 0.65 in cutaneous melanoma. Our penalized logistic regression model can predict BRAF V600E variants with good performance in thyroid carcinoma, cutaneous melanoma, and colon adenocarcinoma.

Mean control chart based on ranked set schemes for unknown skewed probability distribution and parameters

SummarySeveral structures of mean control chart based on ranked set schemes are available in literature. These structures involve assumptions, that is, process distribution is known and sufficient amount of samples is available in estimating unknown parameters. It is a fact that the restricted assumptions do not fulfill in several processes. In such situation, the actual false alarm rate of mean control chart under ranked set schemes is deviated from true level. This issue has taken as one of the motivations of present study. In this study, we have designed a skewness correction mean control chart for managing the situations where skewed probability distribution and process parameters are unknown. The proposed skewness correction mean control chart depends on known skewness level of a process characteristics rather than the restricted assumption of known probability distribution. Furthermore, proposed skewness correction and usual mean control charts are assessed using actual false alarm rate. The outcomes revealed that actual false alarm rate of proposed skewness correction mean control chart remains close to true level when assumption(s) is violated compared to usual mean control chart. To explain the implementation procedure as well as advantages of the proposed control chart over usual, simulated and real data examples are considered. The real data example from agriculture field is included in which proposed control chart is implemented to monitor calcium + magnesium contents of irrigation water.

Construction Skewness Correction the And R Control Chart under Non –Normality

Shewhart's charts are powerful tools in Statistical Process Control (SPC) and are widely used. Usually, Shewhart's charts are depending on the normality assumption. The control charts rely on normality assumptions, which is not always the case for industrial data. Skewness correction and an alternate technique of constructing non-normality control charts for persons The proposes of this paper is to use a skewness correction SC control chart to monitor or construct the control chart for the skewness distribution. The SC chart or the new control chart compared with the Shewhart and weighted variance (WV) control. The probability of exceeding out-of-control detections is also accomplished under a normal curve, the probability that a deviation from the means of the 3σ limit in both directions is 0.0027. Change with the sample size leads to an increase in skewness distribution, leading to a relative increase in the type-Ι error. Reference: M. A., Majed H. A S. (2016). SCALED WEIGHTED VARIANCE S CONTROL CHART FOR SKEWED POPULATIONS, 15th September 2016. Vol.91. No.1 M A.,Majed H. A.,Ali A. (2020). Enhancing R control Chart Performance in Monitoring Process Dispersion Using Scaled Weighted Varianceb Method for Skewed population .Medwell journal 2020 K. ,Berna.Y. ,(2005), The Individuals Control Chart In Case of Non-Normality, Vol. 5,Issue 2 I Li, Nan-C. Su ,(2014). Design of X And R Control Charts For Skew Normal Distributed Data Montegomery (2019). Introduction To Statistical Quality Control ,6th edition Lai K. C., Heng J.,C (2003). Skewness Correction X and R charts for Skewed Distributions, Wiley D. , Hamurkaroglu. C. (2012) , Control Charts for Skewed Distributions Weibull, Gamma and Lognormal, Vol.9, No 2 2012 Michael .B. C. Khoo, Zhang WU, (2008). A SYNTHETIC CONTROL CHART FOR MONITORING THE PROCESS MEAN OF SKEWED POPULATIONS BASED ON THE WEIGHTED VARIANCE METHOD, Vol 15, No 3, 2008. Mans E. (2008). A simulation method For Skewness Correction .Dec 2008 Mostapha A,(2020). EWMA Control Chart For Skewed Distribution, Graduate School of Science and Engineering of Hacettepe University as a Partial Fulfillment to the Requirements for the Award of the degree of Masters in Statistics. Osaman H.A.,Muhammad A.,(2018) ,A new Generalized Ra ng Control Chart for the Weibull Distribution,Wiley 2018. Rao R.S, Pushpa L. (2016). Skewness Corrected Control Charts For two Inverted CHPSS pecial Issue 10. Dec. 2016, han , Rashid M. Muhammad R.,(2015), On Efficient Skewnes Correction Charts Under Contamintion and Non-Normality,2015 John Willey Thomas P.,(2003). The Six Sigma Handbook, Revised and Expanded, McGraw –Hill.

A novel skew correction methodology for handwritten words in multilingual multi-oriented documents

Multi-oriented handwritten documents require additional preprocessing for segmentation and subsequent phases to work accurately in handwritten recognition systems. Skew correction is one such additional phase. Appearance of skew in multi-oriented Indian language based handwritten document is higher due to the presence of cursive nature. In the current work, we utilise a salient feature present in Indian scripts called $m\bar {a}$ tr $\bar {a}$ (also known as headline), extract a group of eligible pixels, and employ linear curve fitting for detecting and correcting skew in handwritten words. The proposed method is capable of correcting skew in four distinct Indian languages, viz. Bangla, Hindi, Marathi, and Punjabi. It is capable of efficiently handling skewed word images to an extent of ± 55∘ and delivers precise result even when the $m\bar {a}$ tr $\bar {a}$ is mostly absent or discontinuous.

Wrong skewness and finite sample correction in the normal-half normal stochastic frontier model

In parametric stochastic frontier models, the composed error is specified as the sum of a two-sided noise component and a one-sided inefficiency component, which is usually assumed to be half-normal, implying that the error distribution is skewed in one direction. In practice, however, estimation residuals may display skewness in the wrong direction. Model respecification or pulling a new sample is often prescribed. Since wrong skewness may manifest as a finite sample problem, this paper proposes a finite sample adjustment to existing estimators to obtain the desired direction of residual skewness. This provides an alternative empirical approach to deal with the wrong skewness problem that does not require respecification of the model.

Designing robust modified R control charts for asymmetric distributions under ranked set and median ranked set sampling

Presence of outliers or contamination in the process control affect the construction of quality control limits badly. Therefore, more attention is to paid robust methods describing the data majority. The main focus of this study is to construct robust R charts by using ranked set sampling (RSS) and median ranked set sampling (MRSS) designs under contaminated skewed distributions such as Marshall–Olkin bivarite Weibull and Bivarite Lognormal distributions. Three robust methods named as robust modified Shewhart, robust modified weighted variance and robust modified skewness correction methods are introduced. An extensive simulation study is presented in order to analyse the efficiency of different sampling designs and robust modified R charts on the charts’ performance. These methods are evaluated in terms of their Type I risks (p). The simulation study showed that, in the contamination case, Shewhart, weighted variance and skewness correction charts based on classic estimators are affected from outliers under simple random sampling and RSS designs and cause the increase of the p values in the process. However using MRSS design is not affected by outliers. In the case of contamination, proposed robust MSC method under MRSS has the best performance for all cases. Moreover a real data application is conducted to show the superiority of proposed methods.