Types Of Charts Research Articles

A proposed switching rule for variable sampling interval charts using moving average

Theoretical studies demonstrated that the variable sampling interval (VSI) charts give substantially faster detection of most process mean shifts than traditional charts. The standard VSI chart allows the long and short sampling intervals to be interchangeably used in the practical operation of the chart based on the information of the last sample mean. However, frequent switching between the long and short sampling intervals can be a complicating factor in the application of control charts. Some switching rules have been presented and studied in the literature to improve the situation of frequent switching. In the present paper, a switching rule based on moving average (MA) is proposed for the VSI chart. The advantages of moving average are not only to involve the recent several sample means, but also to consider the magnitude of deviation of these sample means from the centerline, which is not included by the switching rules in the literature. A computer simulation approach is applied to evaluate the performance of the proposed VSI chart with MA rule. From the simulation results, it can be seen that for a small process mean shift, the VSI chart with MA rule is always superior to the other types of VSI charts.

Statistical computation and analyses for attribute events

This article studies the monitoring of the attribute events based on statistical computation and analyses. The size of an attribute event is an integer rather than a continuous variable. For example, the detection of a product lot containing defectives is an attribute event, the size of which is the number of defectives found in this lot. While many control charts have been developed for monitoring the time interval ( T ) between the occurrences of an event, many other attribute charts may be employed to examine the size ( C ) of the event. However, these two types of control charts have been investigated and applied separately with limited syntheses in Statistical Process Control (SPC). This article presents a single SPC chart (called the rate chart for attribute, or rate chart in short) for simultaneously monitoring the time interval T and size C of an attribute event based on the ratio between C and T . Our studies show that the new chart is more effective for detecting the out-of-control status of the attribute event compared with an individual t chart or an individual c chart, as well as a combined t & c chart. More profound is that the rate chart performs more uniformly than other charts for detecting both T shift and C shift, as well as the joint shift in T and C . The rate chart has demonstrated its potential for both manufacturing systems and non-manufacturing sectors (e.g., supply chain management, office administration and health care industry), especially for the latter.

Intercept model errors and design of high sigma cause selecting control charts

In pedagogy, regression models assume an intercept term. But in real industry situations, there may be instances depicted by a no intercept model. In this work, the influence of intercept model errors in the design of high sigma cause selecting control charts for bivariate cascade processes have been discussed. A modified design flow has been proposed. It is also established that, for this type of control chart, when an intercept model is assumed as no intercept model the type II error or probability of missed signals is deflated. In the case of a no intercept model, assumed as an intercept model, the type II error is inflated.

A Comparison of Performances of Three Types of Control Charts for Skewed Distributions

This paper compares three different types of control charting methods used in the and gamma distributions while the control charts for skewed distributions studied are the weighted variance chart `WV − chart´ , weighted standard deviation chart `WSD − chart´ and skewness correction chart (SC − chart). These charts will be evaluated based on their in-control average run length (ARL0) performances. ARL is defined as the average number of sample points that must be plotted on a control chart before the first point plots beyond the control limits. Since these charts are designed based on the three standard deviation width, ARL0 ~ 370 is considered when the underlying distribution of a process is normal. A good chart has a large ARL0 value when the process follows a skewed distribution. A performance comparison based on a simulation study using the Statistical Analysis System (SAS) version 9 program shows that the SC − and WSD − charts have better ARL0 performances than the WV − chart. The SC − and WSD − charts have about the same ARL0 performances. Keywords: Control chart; skewed distribution; weighted variance (WV); weighted standard deviation (WSD); skewness correction (SC); average run length (ARL); process mean.

Uniformity of Visual Acuity Measures in Published Studies

To investigate the methods used in contemporary ophthalmic literature to designate visual acuity (VA). Papers in all 2005 editions of five ophthalmic journals were considered. Papers were included if (1) VA, vision, or visual function was mentioned in the abstract and (2) if the study involved age-related macular degeneration, cataract, or refractive surgery. If a paper was selected on the basis of its abstract, the full text of the paper was examined for information on the method of refractive correction during VA testing, type of chart used to measure VA, specifics concerning chart features, testing protocols, and data analysis and means of expressing VA in results. One hundred twenty-eight papers were included. The most common type of charts used were described as logMAR-based. Although most (89.8%) of the studies reported on the method of refractive correction during VA testing, only 58.6% gave the chart design, and less than 12% gave any information whatsoever on chart features or measurement procedures used. The methods used and the approach to analysis were rarely described in sufficient detail to allow others to replicate the study being reported. Sufficient detail should be given on VA measurement to enable others to duplicate the research. The authors suggest that charts adhering to Bailey-Lovie design principles always be used to measure vision in prospective studies and their use encouraged in clinical settings. The distinction between the terms logMAR, an acuity notation, and Bailey-Lovie or ETDRS as chart types should be adhered to more strictly.

Group inspection of dependent binary processes

AbstractWe consider serially dependent binary processes, how they occur in several fields of practice. If such a process cannot be monitored continuously, because of process speed for instance, then one can analyze connected segments instead, where two successive segments have a sufficiently large time‐lag. Nevertheless, the serial dependence has to be considered at least within the segments, i.e. the distribution of the segment sums is not binomial anymore. We propose the Markov binomial distribution to approximate the true distribution of the segment sums. Based on this distribution, we develop a Markov np chart and a Markov exponentially weighted moving average (EWMA) chart. We show how average run lengths (ARLs) can be computed exactly for both types of chart. Based on such ARL computations, we derive recommendations for chart design and investigate the out‐of‐control performance. A real‐data example illustrates the application of these charts in practice. Copyright © 2008 John Wiley & Sons, Ltd.

Speaking Stata: Spineplots and their Kin

The term spineplot has been applied over the last decade or so to a type of bar chart used particularly for showing frequencies, proportions, or percentages of two cross-classified categorical variables. The principle is that the areas of rectangular tiles are proportional to the frequencies in the cells of a contingency table. Often both coarse and fine structure are easy to see, including departures from independence. The main idea has, in fact, been rediscovered repeatedly over at least the last 130 years. In its most general form, it has been widely publicized under the name mosaic plots. This column introduces, discusses, and exemplifies a Stata implementation of spineplots. It is noted that a restriction to two variables is more apparent than real, as either axis of a spineplot can show a composite variable defined by cross combinations of two or more variables.

Statistical process and measurement control for micro production

The core challenge of an industrially applicable and economic production of wear resistant micro components and systems is the establishment of both robust and flexible manufacturing process chains. In order to guarantee those stable process chains, manufacturing processes have to be controlled and continuously improved by an effective and fast interfering operational quality assurance that is adapted to the micro-specific framework. Since tolerances of micro-structured parts are in the micro- and sub-micrometer range, geometric measurement results have to meet high requirements in terms of precision and reliability. Therefore, in order to control manufacturing processes in micro production based on measurement data the increased importance of measurement uncertainty and measurement variation has to be considered. Measurement data show an interference of measurement and manufacturing distribution and can lead to wrong decisions when deciding whether the micro manufacturing process is in or out of control. Thus, the focus of the paper lies on continuously monitoring, controlling and separating measurement and manufacturing variation in a flexible, simple and reliable manner. Therefore, a new type of a multivariate μ-EWMA control chart developed at wbk is discussed and benchmarked with traditional control charts. The paper concludes with first results of the application of the multivariate μ-EWMA chart in micro production environment.

A decade later: Creating single-subject design graphs with Microsoft Excel 2007™.

In Carr and Burkholder's article (1998), they utilized the graphing guidelines recommended in the manuscript preparation checklist in the Journal of Applied Behavior Analysis, however, the most recent recommendations (2000) do not include all of the guidelines mentioned in the first article. Those which are included: Data points do not connect across experimental phase and the y-axis zero value is raised off the abscissa. Absent from the newer recommendations is the criteria that data points do not quite touch the lines between them. Its removal as a criterion indicates that it is no longer a requirement, and as such will be addressed, but indicated as optional, according to the 2000 guidelines. As Carr and Burkholder indicated, the utilization of a spreadsheet to enter, gather, and analyze data will prevent redundant data entry and save time on the part of the behavior analyst. In addition, Excel[TM] appears to be a widely accepted spreadsheet program. In the tradition that Carr and Burkholder began, this tutorial will provide very detailed and easy to follow instructions on how to graph reversal, multi-element, and multiple baseline designs; however, as in the 1998 article, rudimentary understanding of spreadsheet programs is necessary prior to starting. In this tutorial, there will be no need to prepare the toolbar as all instructions will be utilizing default settings of Excel 2007[TM]. Each action step will be followed by a sequence of keyboard shortcuts to illustrate and simplify implementation of the instruction for that step. The keyboard shortcuts consist of the names of the keys in brackets []. Two keys connected by a plus sign within the same bracket indicate that the initial key should be depressed while pressing the second key (e.g., [ALT+T] indicates that one should hold down the Alt button and press the T button). Two bracketed buttons joined by a dash should be pressed in succession (e.g., [ALT+T]-[T]-[P] would indicate that you should hold down the ALT key and press the T key. After releasing these, you should press the T key again, and then press the P key. Anything in braces (e.g.,{Axis Title}) indicate that you should input text. Thus, if you encounter [ALT]-[T]-{Name}-[ENTER], you should press ALT, then press T, then type in the name, then press the ENTER key. When you encounter a word written in all capital letters, that indicates that this is the name of a button, text, or icon you should click or press. CREATING A REVERSAL DESIGN GRAPH Entering Data into the Spreadsheet Data will be staggered across columns by phases. This will provide a means to prevent data connection across phases (without having to manually do this phase by phase). In addition, it will allow the use of Excel Functions individually per phase to create trend lines. Once you have Excel 2007[TM] open, complete the following steps to enter your data. 1. Enter the data for the first phase (e.g., Baseline1) in the first column and click on the cell in the following row. Repeat until all data for this phase has been entered. {data}-[ENTER] 2. For each new phase (such as intervention, intervention 2, return to baseline, etc.), enter the data on the next row and in the column to the right of the previous column. Repeat for each phase. [[right arrow]]-{data}. Creating the Graph 1. Once all the data has been entered, drag your mouse pointer from the top left cell to the very bottom and right of the data series just entered. 2. Click the INSERT tab on the Ribbon, then the LINE graph icon (8th icon to the right). [ALT]-[I]-[H] 3. A menu of different types of charts will appear. Click on the LINE WITH MARKERS (hover over each picture of graph and it will display the type). [L]-[ENTER] 4. A new graph will appear on the same sheet as the data as well as a new part of the ribbon labeled CHART TOOLS. …

The design, selection, and performance of statistical control charts for healthcare process improvement

Although the value of Statistical Process Control (SPC) charts to monitor and improve healthcare processes has received growing interest, several important implementation and theoretical issues are largely not understood. SPC charts are chronological graphs of process data that are used in many other industries to help control and improve quality and, while based in statistical theory, are easy for practitioners to use and interpret. This article provides an overview of the use of SPC in healthcare process improvement and Six Sigma activities, including the process of selecting and using the appropriate type of control chart, their statistical performance, and the guidelines for determining the appropriate sample sizes. The operating characteristics are computed and tabulated for a wide range of scenarios in order to aid practitioners in designing control charts with the desired statistical properties.

Deterministic and reliability-based design: veneer cover soil stability

A design chart is a graphical tool that provides solutions to different scenarios of a system. In this paper, two types of design chart are developed based on deterministic and reliability-based analyses for determining the interface shear strength required for stability of a cover system to achieve a target safety factor of 1.5 and failure probability of 1 × 10−2. The deterministic design chart assists in the selection of different types of geosynthetic for lining materials based on the required interface shear strength for stability, and the reliability-based design chart enhances decision-making by taking into account the uncertainties in the design parameters, such as the variability of interface shear strength parameters. Additionally, the latter chart can also be used to determine the optimum slope angle for a containment facility that will satisfy both the target factor of safety and acceptable failure probability. Examples are provided to illustrate the use of the design charts in estimating the minimum required interface shear strength and their allowable variability for a given veneer cover, and the optimum slope inclination corresponding to different interface shear strengths and their associated variability.

Recognition versus Resolution: a Comparison of Visual Acuity Results Using Two Alternative Test Chart Optotype

Purpose To quantify the difference between recognition (letter) and resolution (Landolt) visual acuity (VA) in a group of normally sighted subjects. Is it reasonable to assume that the two acuity measures are clinically equivalent? Methods A pair of 6 m acuity test charts was produced: one comprised letters and the other Landolt broken rings. Construction of both charts conformed to the logMAR design format. Monocular VA was determined for the dominant eye of 300 screened and normally sighted optometric patients aged 16 to 40, each wearing an optical refractive (spectacle) correction. Results Letter acuity was superior to Landolt acuity ( P≤0.0001). The mean paired acuity difference was -0.041 logMAR (standard deviation 0.034): the 95% limits of agreement were ±0.067 logMAR units or ±3.3 chart optotype. Repeatability was high and similar for each chart type (±2.1 and ±2.4 optotype for letter and Landolt, respectively). Gender, test sequence, and laterality of the dominant eye (left or right) were each non-statistically significant variables. Conclusions For normally sighted subjects wearing an optimal refractive correction, a bias was recorded in favour of recognition over resolution acuity: the clinical difference amounted to approximately 40% of one logMAR chart line, with similar high repeatability for either chart optotype. We conclude that the assumption of clinical equivalence between letter and Landolt acuity is reasonable under optimum test conditions.

Bayesian monitoring to detect a shift in process mean

AbstractA Bayesian analogue of the Shewhart X‐bar chart is defined and compared with cumulative sum charts. The comparison identifies types of production process where the Bayesian chart has better expected performance than the cumulative sum chart. Implementing the Bayesian chart requires more detailed knowledge of the process structure than is required by the best‐known types of charts, but acquiring this information can yield tangible benefits. Copyright © 2007 John Wiley & Sons, Ltd.

Bayesian Statistical Process Control

ABSTRACT This article presents a general Bayesian statistical process control chart. Most previous applications of Bayes' theorem to quality control have either been tied to a rigid optimization model or have used Bayes' theorem to infer the values of structural parameters of the monitored process. The methodology presented differs from both of these approaches. The result is a flexible tool that can be manipulated by decision makers, as is the case with other types of control charts. The Bayesian chart is demonstrated for joint monitoring of the mean and standard deviation of a normal random variable, and compared to both Shewhart and cumulative sum monitoring. The basis for comparison is the expected number of false alarms per expected time in control and the average out-of-control run length. The comparison identifies types of production process where the Bayesian chart has better expected performance than the other two charts and also shows that even though the Bayesian chart requires more detailed knowledge of process structure, acquiring this knowledge can yield real benefits. The article concludes with a practical example.

Using control charts to monitor quality of hospital care with administrative data

Nearly all hospital-specific comparative analyses, based on administrative data, are presented using cross-sectional displays. In this paper, we compare cross-sectional analyses with sequential monitoring using control charts. of administrative data to compare cross-sectional funnel plots with one type of control chart: the risk-adjusted, expected-minus-observed plot. Eighteen tertiary and base hospitals in Queensland, Australia, for the two financial years 2003-04 and 2004-05. Patients admitted with acute myocardial infarction. Risk-adjusted, 30-day, in-hospital, mortality rates. There were no outliers on the cross-sectional funnel plots for either of the 2 years using three-sigma limits and three low-outliers and one high-outlier using two-sigma limits. One reasonable interpretation of these plots is that most of the variations are due to statistical noise and there is little to be learnt by seeking to understand the reasons for variation across hospitals. In contrast, for the control charts, 28% of hospitals signalled for a relative increase of 75% above that for all hospitals combined. If the aim of clinical indicators based on administrative data is to provide a starting point for learning, then control charting provides potentially more useful information than the more commonly used cross-sectional analyses. Control charts provide an understandable and up-to-date overview that allows early detection of runs of good or bad outcomes that can help hospitals identify areas for more in-depth self-monitoring and learning.

Estimation of the Change Point in Monitoring the Process Mean and Variance

Knowing the time of a process change could lead to quicker identification of the special cause and less process down time, as well as help to reduce the probability of incorrectly identifying the special cause. In this article, we propose the maximum likelihood estimator (MLE) for the process change point when a control chart with the fixed sampling rate (FSR) scheme or the variable sampling rate (VSR) scheme is used in monitoring a process to detect changes in the process mean and/or variance of a normal quality variable. We investigate the performance of this estimator when it is used in various types of control charts.

Use of independent runs for the improvement of the response of Shewhart control charts

The paper deals with an extension of standard Shewhart charts witch provide independent runs of given length, or IR-charts, with the purpose of improving the performance of the former by allowing a faster detection of small and medium shifts in a process mean. The author purposely chooses to remain in the field of indipendent sample observations, which are much more frequently used in SPC compared to other types of charts due to their simplicity, and shows how careful choice of independent runs, formed by the same sample means used in a standard X-chart, can be adopted in order to reduce ARL values and, therefore, the expected time of detection of out-of-control situations. The result is obtained without the main drawback of dependent runs procedures as summarised in the Western Electric Company runs rules and others recalled in the paper, with lies in the fact that their in-control ARL is too low, thus providing a too short expected time before a false out-of control alarm occurs.

Tutorial on Monitoring Time to Next Medication Error

Alemi and colleagues in this issue of the journal have proposed that rare events can be monitored by shifting from frequency of the event to the examination of the time to the event. This article examines their claim with data obtained from an acute care hospital in the United States. We examined the data on medication omissions to see whether changes in underlying process can be detected through control charts. Medication errors are rare; the article examines medication errors due to omission, which makes the phenomena rarer. The empirical question was whether changes in process of care could be detected using control charts from data on medication omissions. Two different types of control chart, the XmR and Tukey charts, were used to analyze the data. The control chart with the tightest control limits was chosen for further interpretation. The XmR chart showed that there was sufficient power to detect unusual days in which the time to omission error was higher than historical norm. This article suggests that even rare events can be monitored through judicious use of time to the event. It shows the viability of safety teams using time to sentinel events to monitor progress in reducing frequency of sentinel events.

Plot and see! Maternal comprehension of growth charts worldwide

To evaluate maternal comprehension of growth charts used in growth monitoring and promotion (GMP), a worldwide programme with important budgets but contrasting results. Systematic literature review through MEDLINE, POPLINE, Global Health, ERIC and the Cochrane Library with the keywords 'growth monitoring' or 'growth chart' limited to the title/abstract field and to the 0-5 years age range. Twenty studies from Asia (8), Africa (8) and Latin America/Caribbean (3) were included in the review. The results of the 14 non-intervention, cross-sectional studies provide convincing evidence that a third to three-fourths of carers in developing countries do not understand the growth charts. Literacy had a strong effect on women's ability to interpret the cards. Appropriate training and educational activities also increased substantially maternal comprehension as demonstrated in five of the six intervention trials. Many carers have poor comprehension of growth charts, but their comprehension increases not only with literacy, but also with training. Activities aimed at improving communication skills of health staff and at empowering parents to practice responsive parenting could greatly improve GMP outcomes.

Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential Sampling

Traditional control charts for process monitoring are based on taking samples of fixed size at equally spaced sampling points. As an alternative to these traditional fixed sampling rate (FSR) control charts, variable sampling rate (VSR) control charts change the sampling rate as a function of the data from the process. With VSR control charts the sampling rate is increased whenever there is some indication of a problem with the process, and decreased when there is no indication of a problem. This paper investigates a type of VSR control chart based on sequential sampling in which the sample size used at a sampling point is a function of the data from the current and past sampling points. Sequential sampling is investigated in the context of simultaneously monitoring both the mean and variability of a multivariate normal process. Multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from the target are considered. When sequential sampling is used in a combination of the MEWMA charts based on sample means and on squared deviations from the target, the average performance is much better than that of the standard FSR multivariate control charts that have traditionally been used.