Standard Deviation Control Chart Research Articles

A robust standard deviation control chart based on square A estimator

AbstractThe estimates of a standard deviation deteriorate the detection ability of control charts by reason of its high biases when the contaminations are present. This study proposes two kinds of square A estimators based on different screenings and compares the values of their mean squared error with those of existing estimators in diffuse and localized disturbances. The effectiveness of Phase II control charts is evaluated when the estimators are contaminated in Phase I using two kinds of disturbances. The proposed estimators perform the best against disturbances, with their average run lengths and expected average run lengths being closer to those in normal cases compared to other estimators.

Variability in the unregulated opioid market in the context of extreme rates of overdose

Background: Drug checking uses analytical chemistry technologies to report on the composition of drugs from the unregulated market to reduce substance use-related risks, while additionally allowing for monitoring and reporting of the supply. In the context of an overdose crisis linked to fentanyl, we used drug checking data to examine variability within the illicit opioid supply.Methods: In this time-series analysis, data was collected from a drug checking service in Victoria, Canada from November 2020 to July 2021. Drugs reported as opioids by participants of the service (N = 454) were analyzed to determine sample composition and paper spray mass spectroscopy was used to quantify low-concentration actives. Interquartile and statistical process control (SPC) analysis, namely standard deviation control charts, were used to examine the degree of variability among samples.Results: Fentanyl was found in 96% of samples reported to be opioids, with a median concentration of 9%. Concentrations varied significantly, with a standard deviation of 7% for fentanyl and where nearly 20% of data points fell outside the control limits. Over half of the samples contained an additional and unexpected active, most commonly etizolam (43% of samples). Etizolam also showed a large level of variability, uncorrelated to that of fentanyl.Conclusions: Based on our chemical quantification and SPC analysis, a high degree of variability was found in opioid samples from the unregulated market in both the drugs detected and the concentrations of those drugs. This demonstrated the opioid crisis to be less attributable to a bad batch of drugs but rather the general variability found in the unregulated market.

Design and analysis of exponentially weighted moving average control charts for monitoring the variability of log‐normal processes with estimated parameters

AbstractIn statistical process control (SPC), the control chart is a quite popular technique to monitor the process efficacy. From a statistical point of view, the control chart is considered superior if it has an effective structure withholding property of the resistance against infrequent situations in a practical environment. The current study is designed for the same purpose for observing the dispersion parameter of log‐normal distribution by using the structure of an exponentially weighted moving average (EWMA) chart. For the extensive study, EWMA range, EWMA standard deviation, EWMA EWMA EWMA mean absolute deviation, and EWMA transform standard deviation control charts are proposed. Properties of the run‐length profile of the proposed designed structures based on different existing estimators as well as a newly transformed dispersion estimator for log‐normal standard deviation are evaluated. The results indicate that the newly developed scheme outperforms the competitors when the dispersion parameter of the log‐normal distribution attains a large value. A real‐life application is also provided to validate how the developed design can be used in practice.

The effect of parameter estimation on control charts for the lognormal distribution

Statistical process control (SPC) is a method of monitoring, controlling and improving a process through statistical analysis. In real applications, many industrial process data may follow a positively-skewed distribution such as the lognormal distribution. In this article, under lognormal process, we study the performance of three control charts, Shewhart control chart, weighted variance control chart and weighted standard deviation control chart, based on the in-control expected average run length (AARL). The standard deviation of ARL (SDARL) metric is used to evaluate the performance for various amounts of phase I data. A formula to approximate the ARL by the normal approximation method is established in this study. The in-control and out-of-control performance of the three control charts are compared based on the normal approximation and simulation.

Instant detection of porosity in gas metal arc welding by using probability density distribution and control chart

A novel porosity detection technique from the voltage and current transients is introduced in this paper. An online weld monitoring that detects the porosity at an earlier stage is much demanding in the industry due to their adverse effects on structural integrity. In this research work, control chart and probability density distribution have been employed as tools to detect arc instability and weld porosity. The results showed that the pattern of probability density distribution changes for the defect and defect-free welds significantly. The mean and standard deviation control charts plotted with voltage clearly distinguished the quality of the weld based on sample points spread within or outside the control limits. For minute internal porosities, the sample points at the corresponding region in the standard deviation control chart were outside the limits whereas it is well within the control limits in the mean control chart. Inspector can predict the presence and near location of porosity using these tools by simple mathematical calculations easily and instantly. The results proved that the developed approach is successful and promising for the weld inspection.

Using the Control Chart Approach to Evaluate Hardness Tester Performance

Abstract The control chart data analysis approach is an ideal method to evaluate the quality of test data using a specific tester, such as a microindentation hardness tester, over a period of usage time. The method described in ASTM E2554 was used for this work. This analysis is done by plotting a Mean s and a standard deviation control chart of the weekly/periodic verification data obtained with certified hardness test blocks at a specific test force and a specific hardness level. The method is illustrated using a Knoop hardness test block certified at a test force of 500 gf and with a long diagonal length of 116.18 μm (527.1 HK). From this data, one can easily calculate the uncertainty of the measurements.

Quality Quandaries: How to Set Up a Robust Shewhart Control Chart for Dispersion?

In this article, the authors have outlined procedures to construct Phase I and Phase II standard deviation control charts.

Probabilidade do erro do tipo I nas cartas X e S de Shewhart sob não normalidade

O objetivo deste artigo é verificar o comportamento das cartas de média e desvio padrão de Shewhart em relação à probabilidade do erro do tipo I quando da violação da suposição de normalidade. Foi realizada a simulação de uma série de 500.000 amostras (subgrupos) de tamanho n = 3, 5, 7, 10, 15, 20 e 25. As amostras foram simuladas a partir das distribuições normal, t de Student, exponencial, qui-quadrado, gamma e Weibull. Verificou-se em dados não normais o aumento na probabilidade de erro do tipo I na carta de médias em todas as distribuições simuladas. O mínimo tamanho da amostra necessário está relacionado ao grau de assimetria da distribuição dos dados, sendo que, em alguns casos, nem mesmo n = 25 apresentou resultados satisfatórios. No gráfico S, o aumento da probabilidade de erro do tipo I é significativamente superior em quase todas as distribuições simuladas e seu comportamento é influenciado não só pelo tipo de distribuição, mas também pelo tamanho da amostra.

A Robust Standard Deviation Control Chart

This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse disturbances, that is, outliers spread over the subgroups, or localized disturbances, which affect an entire subgroup. In this article, we compare various robust standard deviation estimators and propose an algorithm that is robust against both types of disturbances. The algorithm is intuitive and is the best estimator in terms of overall performance. We also study the effect of using robust estimators from Phase I on Phase II control chart performance. Additional results for this article are available online as Supplementary Material.

Design and Analysis of Control Charts for Standard Deviation with Estimated Parameters

This paper concerns the design and analysis of the standard deviation control chart with estimated limits. We consider an extensive range of statistics to estimate the in-control standard deviation (Phase I) and design the control chart for real-time process monitoring (Phase II) by determining the factors for the control limits. The Phase II performance of the design schemes is assessed when the Phase I data are uncontaminated and normally distributed as well as when the Phase I data are contaminated. We propose a robust estimation method based on the mean absolute deviation from the median supplemented with a simple screening method. It turns out that this approach is efficient under normality and performs substantially better than the traditional estimators and several robust proposals when contaminations are present.

Statistical Control and Investigation of Capability of Process and Machine in Wire Cut Edm Process of Gas Turbine Blade Airfoil Tip

Statistical process control (spc), as one of the quality devices, can be help manufacturers improve the quality of their products in today’s competitive world. This research examines the statistical method of wire-cut electric discharge machining (WEDM) process of the turbine blade airfoil tip for control and consistency of the process. For this purpose, the standard deviation control chart, S, and the average data, , which are applied for identifying the acquired factors, have been used. Next, regarding the plan features, the manufacturing process is assessed to determine whether the products meet quality and the customer requirements or not. Therefore, the coefficients Cpk is applied which indicate the capability of the manufacturing process. Then, in order to produce high quality blades within the tolerance range, the capability of WEDM machine is examined, using coefficients CM. Finally, it is shown that in order to produce the desired product, the process can be controlled and fixed by using the statistical process control devices and inspecting the standard deviation of data and investigation of capability of process and machine.

Statistical process control for quality improvement

Statistical process control - a brief overview acceptance-rejection statistical process control the development of mean and standard deviation control charts sequential approaches exploratory techniques for preliminary analysis optimization approaches multivariate approaches. Appendices: a brief introduction to linear algebra a brief introduction to stochastics statistical tables.

An Approach to Controlling Process Variability

The design of statistical procedures to monitor and control the variability of production processed has received comparatively little attention in the literature. This paper considers the use of a standard deviation Control Chart for this purpose.The d..

A proposed method to use electronic spreadsheets to develop quality control charts

The combination of the personal computer and spreadsheet software provide an inexpensive and accurate capability to use control charts for the quality contol average and standard deviation. The popular spreadsheet program, Lotus 17ndash;2–3, is limited to graphing six variables. Eight are needed to graph both the average and standard deviation control charts on a single screen. This article examines several methods to overcome this limitation. All calculation needed are performed and a series of charts are drawn for the readers examination.

Graphical Analysis of Process Variation Studies

Graphical procedures for analyzing the results of nested sampling studies are presented and illustrated with examples. It is shown that a standard deviation control chart analysis will detect atypical results and nonhomogeneous variances that can greatl..

ANALYSIS OF SOME SAMPLING DISTRIBUTIONS FOR QUALITY CONTROL OF FOODS

ABSTRACTThe sampling distributions of aflatoxin in fresh and roasted pecans, visible mycelium in fresh pecans and total plate count in ground beef were examined using the chi‐square and Kolmogorov‐Smirnov tests. The Kolmogorov‐Smirnov test was found to be more conservative than the chi‐square test and a powerful technique for rejection of null hypotheses. The results indicated that many sampling distributions used in quality control of foods deviate significantly from the normal distribution. The sampling distribution for total plate count in ground beef and the distribution of sample means were determined. A critical sample size of at least 5 was found to be necessary to approximate the normal distribution for the sample means. The average and standard deviation control charts utilizing the sample size of 5 were established to illustrate the detection of out‐of‐control samples.