Univariate And Multivariate Synthetic Control Charts For Monitoring The Process Mean Of Skewed Distributions

Alat yang paling berkuasa dalam Kawalan Kualiti Berstatistik (SQC) ialah carta kawalan. The most powerful tool in Statistical Quality Control (SQC) is the control chart. Control charts are now widely accepted and used in industries

The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts.It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts.This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained.The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the out-of-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes.By minimising the false positives, a sound judgement can be made for any clinical decision

The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts. It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts. This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained. The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the outof-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes. By minimising the false positives, a sound judgement can be made for any clinical decision

Robustification of CUSUM control structure for monitoring location shift of skewed distributions based on modified one-step M-estimator

Including three existing charts, a new approach employing a modified one-step M-estimator (MOM) with Cumulative Sum (CUSUM) control structure were evaluated and compared for their Phase II performances based on the average run length (ARL) under various skewed distributions. The primary focus was on the robustness of the CUSUM charts in two separate cases: (i) when the process parameters are known and (ii) when the process mean is unknown and estimated from an in-control Phase I sample. The simulation and real data analysis showed the proposed technique is comparable or sometimes better than the existing charts

Proposed X and S control charts for skewed distributions

This paper proposes a weighted variance method to compute the limits of the X and S charts for skewed distributions.The proposed charts extend the weighted variance X and R charts in by enabling a process from a skewed distribution with moderate and large sample sizes to be monitored efficiently, hence producing more favourable Type-I and Type-II error rates than the charts in.Note that the charts in are only intended to be used for small sample sizes. The Type-I and Type-II error rates computed show that the proposed charts outperform the existing heuristic charts, as well as those in for moderate and large sample sizes, involving cases with known and unknown parameters, when the distribution of a process is skewed

New X-bar control chart using skewness correction method for skewed distributions with application in healthcare

Control chart has been long-established among the highly reputable tools in statistical process control (SPC) with extensive industrial application. Shewhart chart is one of the most popular charts, but its reliability is arguable when dealing with skewed data, due to inflated false alarm rate (Type I error). In alleviating the problem, this study has developed a new X-bar control chart for monitoring of process mean using skewness correction (SC) method for skewed distributions, thus named as SC- control chart. The SC method is incorporated into the standard Shewhart’s X-bar chart, leading to the proposed univariate SC- to monitor the process mean of skewed data. It offers asymmetric control limits using the usual three sigma and the same known function of the skewness estimated from subgroups without assuming any distribution. The chart’s constants, and skewness correction factor are computed via numerical integration. To evaluate the strength and weakness of the charts, several conditions are created from different types of distributions and subgroup sizes. The SC- performance evaluation based on the false alarm rates (FAR) and probability of out-of-control (OOC) detection are accomplished using Monte Carlo simulation in SAS version 9.4. To illustrate its applicability, a real data on healthcare is employed. Its FAR performance is compared to the established charts: weighted variance X-bar R(WV- ); weighted variance X-bar S(WV- ); and standard X-bar S (ST- ). In aspect of the probability of OOC detection, the SC- is contended by the exact S chart. Extensive simulation study shows that the proposed SC- chart performs well in terms of FAR in almost all the degrees of skewness and sample sizes, n. In terms of the probability of OOC detection, it provides the closest values to those of the exact chart. It offers substantial enhancement over the established charts, and thus signifies as a preferred alternative especially in cases of skewed data

The impact of data anomaly on EWMA phase II performance

In applying control chart with estimated parameters for monitoring changes in a process, Phase I samples are typically assumed to be free of outliers or any other data anomaly. Naturally, the sample mean and the sample standard deviations are used as estimators, yielding efficient estimates for the chart. Nonetheless, when Phase I may be contaminated, this regular practice is no longer suitable as classical estimators are susceptible to the effect of outliers which in turn may affect control chart performance. This study shows that the effect is not trivial via. the application of EWMA control chart. Moreover, this study focuses on the effect using alternative and robust Phase I estimators on the EWMA when the chart is used to monitor changes in the process mean. In this study, an automatic trimmed mean estimator is used to provide estimate for the process mean. Meanwhile, for the standard deviation of the process, this study employs three different estimators including the corresponding robust scale estimator used in the trimming process of the location measure. Simulated data were used to test the performance of the EWMA control charts. The finding based on mean and percentiles of the run-length distribution shows quicker detection of out-of-control status when robust statistics were used to compute parameter estimates in Phase I of the EWMA chart upon contamination in the data set

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

An EWMA chart for sample range of Weibull data using weighted variance method

This article proposes new EWMA chart in observing process standard deviation or dispersion with sample range of Weibull data using weighted variance method (WV).This control chart, called Weighted Variance EWMA sample range WV-EWMASR chart hereafter.The proposed WV-EWMASR chart compared with standard EWMASR of [7], skewness correction R chart (SC-R) suggested by[3]and Weighted Variance R chart (WV-R) proposed by [2], in the case of Type I and Type II errors when the data generated from Weibull distribution. Optimal parameters λ and k of the proposed WV-EWMASR and standard EWMASR are obtained via simulation using SAS program 9.4.The proposed WV-EWMASR control chart reduces to the standard EWMASR control chart of [7] when the process follow symmetric distribution. The proposed WV-EWMASR control chart has less Type I error than the standard EWMASR, SC-R and WV-R control charts, for Weibull distribution data. In case of Type II error, the proposed WV-EWMASR control chart is closer to EWMA chart with the exact limits than the standard EWMASR in [7]