Basic Quality Tools 1
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X-Bar Charts
NCSS Statistical Software NCSS.com Chapter 244 X-bar Charts Introduction This procedure generates X-bar control charts for variables. The format of the control charts is fully customizable. The data for the subgroups can be in a single column or in multiple columns. This procedure permits the defining of stages. The center line can be entered directly or estimated from the data, or a sub-set of the data. Sigma may be estimated from the data or a standard sigma value may be entered. A list of out-of-control points can be produced in the output, if desired, and means may be stored to the spreadsheet. X-bar Control Charts X-bar charts are used to monitor the mean of a process based on samples taken from the process at given times (hours, shifts, days, weeks, months, etc.). The measurements of the samples at a given time constitute a subgroup. Typically, an initial series of subgroups is used to estimate the mean and standard deviation of a process. The mean and standard deviation are then used to produce control limits for the mean of each subgroup. During this initial phase, the process should be in control. If points are out-of-control during the initial (estimation) phase, the assignable cause should be determined and the subgroup should be removed from estimation. Determining the process capability (see R & R Study and Capability Analysis procedures) may also be useful at this phase. Once the control limits have been established of the X-bar charts, these limits may be used to monitor the mean of the process going forward. -
Image Segmentation Based on Histogram Analysis Utilizing the Cloud Model
Computers and Mathematics with Applications 62 (2011) 2824–2833 Contents lists available at SciVerse ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa Image segmentation based on histogram analysis utilizing the cloud model Kun Qin a,∗, Kai Xu a, Feilong Liu b, Deyi Li c a School of Remote Sensing Information Engineering, Wuhan University, Wuhan, 430079, China b Bahee International, Pleasant Hill, CA 94523, USA c Beijing Institute of Electronic System Engineering, Beijing, 100039, China article info a b s t r a c t Keywords: Both the cloud model and type-2 fuzzy sets deal with the uncertainty of membership Image segmentation which traditional type-1 fuzzy sets do not consider. Type-2 fuzzy sets consider the Histogram analysis fuzziness of the membership degrees. The cloud model considers fuzziness, randomness, Cloud model Type-2 fuzzy sets and the association between them. Based on the cloud model, the paper proposes an Probability to possibility transformations image segmentation approach which considers the fuzziness and randomness in histogram analysis. For the proposed method, first, the image histogram is generated. Second, the histogram is transformed into discrete concepts expressed by cloud models. Finally, the image is segmented into corresponding regions based on these cloud models. Segmentation experiments by images with bimodal and multimodal histograms are used to compare the proposed method with some related segmentation methods, including Otsu threshold, type-2 fuzzy threshold, fuzzy C-means clustering, and Gaussian mixture models. The comparison experiments validate the proposed method. ' 2011 Elsevier Ltd. All rights reserved. 1. Introduction In order to deal with the uncertainty of image segmentation, fuzzy sets were introduced into the field of image segmentation, and some methods were proposed in the literature. -
Permutation Tests
Permutation tests Ken Rice Thomas Lumley UW Biostatistics Seattle, June 2008 Overview • Permutation tests • A mean • Smallest p-value across multiple models • Cautionary notes Testing In testing a null hypothesis we need a test statistic that will have different values under the null hypothesis and the alternatives we care about (eg a relative risk of diabetes) We then need to compute the sampling distribution of the test statistic when the null hypothesis is true. For some test statistics and some null hypotheses this can be done analytically. The p- value for the is the probability that the test statistic would be at least as extreme as we observed, if the null hypothesis is true. A permutation test gives a simple way to compute the sampling distribution for any test statistic, under the strong null hypothesis that a set of genetic variants has absolutely no effect on the outcome. Permutations To estimate the sampling distribution of the test statistic we need many samples generated under the strong null hypothesis. If the null hypothesis is true, changing the exposure would have no effect on the outcome. By randomly shuffling the exposures we can make up as many data sets as we like. If the null hypothesis is true the shuffled data sets should look like the real data, otherwise they should look different from the real data. The ranking of the real test statistic among the shuffled test statistics gives a p-value Example: null is true Data Shuffling outcomes Shuffling outcomes (ordered) gender outcome gender outcome gender outcome Example: null is false Data Shuffling outcomes Shuffling outcomes (ordered) gender outcome gender outcome gender outcome Means Our first example is a difference in mean outcome in a dominant model for a single SNP ## make up some `true' data carrier<-rep(c(0,1), c(100,200)) null.y<-rnorm(300) alt.y<-rnorm(300, mean=carrier/2) In this case we know from theory the distribution of a difference in means and we could just do a t-test. -
A Guide to Creating and Interpreting Run and Control Charts Turning Data Into Information for Improvement Using This Guide
Institute for Innovation and Improvement A guide to creating and interpreting run and control charts Turning Data into Information for Improvement Using this guide The NHS Institute has developed this guide as a reminder to commissioners how to create and analyse time-series data as part of their improvement work. It should help you ask the right questions and to better assess whether a change has led to an improvement. Contents The importance of time based measurements .........................................4 Run Charts ...............................................6 Control Charts .......................................12 Process Changes ....................................26 Recommended Reading .........................29 The Improving immunisation rates importance Before and after the implementation of a new recall system This example shows yearly figures for immunisation rates of time-based before and after a new system was introduced. The aggregated measurements data seems to indicate the change was a success. 90 Wow! A “significant improvement” from 86% 79% to 86% -up % take 79% 75 Time 1 Time 2 Conclusion - The change was a success! 4 Improving immunisation rates Before and after the implementation of a new recall system However, viewing how the rates have changed within the two periods tells a 100 very different story. Here New system implemented here we see that immunisation rates were actually improving until the new 86% – system was introduced. X They then became worse. 79% – Seeing this more detailed X 75 time based picture prompts a different response. % take-up Now what do you conclude about the impact of the new system? 50 24 Months 5 Run Charts Elements of a run chart A run chart shows a measurement on the y-axis plotted over time (on the x-axis). -
Shinyitemanalysis for Psychometric Training and to Enforce Routine Analysis of Educational Tests
ShinyItemAnalysis for Psychometric Training and to Enforce Routine Analysis of Educational Tests Patrícia Martinková Dept. of Statistical Modelling, Institute of Computer Science, Czech Academy of Sciences College of Education, Charles University in Prague R meetup Warsaw, May 24, 2018 R meetup Warsaw, 2018 1/35 Introduction ShinyItemAnalysis Teaching psychometrics Routine analysis of tests Discussion Announcement 1: Save the date for Psychoco 2019! International Workshop on Psychometric Computing Psychoco 2019 February 21 - 22, 2019 Charles University & Czech Academy of Sciences, Prague www.psychoco.org Since 2008, the international Psychoco workshops aim at bringing together researchers working on modern techniques for the analysis of data from psychology and the social sciences (especially in R). Patrícia Martinková ShinyItemAnalysis for Psychometric Training and Test Validation R meetup Warsaw, 2018 2/35 Introduction ShinyItemAnalysis Teaching psychometrics Routine analysis of tests Discussion Announcement 2: Job offers Job offers at Institute of Computer Science: CAS-ICS Postdoctoral position (deadline: August 30) ICS Doctoral position (deadline: June 30) ICS Fellowship for junior researchers (deadline: June 30) ... further possibilities to participate on grants E-mail at [email protected] if interested in position in the area of Computational psychometrics Interdisciplinary statistics Other related disciplines Patrícia Martinková ShinyItemAnalysis for Psychometric Training and Test Validation R meetup Warsaw, 2018 3/35 Outline 1. Introduction 2. ShinyItemAnalysis 3. Teaching psychometrics 4. Routine analysis of tests 5. Discussion Introduction ShinyItemAnalysis Teaching psychometrics Routine analysis of tests Discussion Motivation To teach psychometric concepts and methods Graduate courses "IRT models", "Selected topics in psychometrics" Workshops for admission test developers Active learning approach w/ hands-on examples To enforce routine analyses of educational tests Admission tests to Czech Universities Physiology concept inventories .. -
Lecture 8 Sample Mean and Variance, Histogram, Empirical Distribution Function Sample Mean and Variance
Lecture 8 Sample Mean and Variance, Histogram, Empirical Distribution Function Sample Mean and Variance Consider a random sample , where is the = , , … sample size (number of elements in ). Then, the sample mean is given by 1 = . Sample Mean and Variance The sample mean is an unbiased estimator of the expected value of a random variable the sample is generated from: . The sample mean is the sample statistic, and is itself a random variable. Sample Mean and Variance In many practical situations, the true variance of a population is not known a priori and must be computed somehow. When dealing with extremely large populations, it is not possible to count every object in the population, so the computation must be performed on a sample of the population. Sample Mean and Variance Sample variance can also be applied to the estimation of the variance of a continuous distribution from a sample of that distribution. Sample Mean and Variance Consider a random sample of size . Then, = , , … we can define the sample variance as 1 = − , where is the sample mean. Sample Mean and Variance However, gives an estimate of the population variance that is biased by a factor of . For this reason, is referred to as the biased sample variance . Correcting for this bias yields the unbiased sample variance : 1 = = − . − 1 − 1 Sample Mean and Variance While is an unbiased estimator for the variance, is still a biased estimator for the standard deviation, though markedly less biased than the uncorrected sample standard deviation . This estimator is commonly used and generally known simply as the "sample standard deviation". -
Medians and the Individuals Control Chart the Individuals Control Chart
Medians and the Individuals Control Chart The individuals control chart is used quite often to monitor processes. It can be used in almost all cases, so it makes the art of deciding which control chart to use extremely easy at times. Not sure? Use the individuals control chart. The individuals control chart is composed of two charts: the X chart where the individual values are plotted and the moving range (mR) chart where the range between consecutive values are plotted. The averages and control limits are also part of the charts. The average moving range (R̅) is used to calculate the control limits on the X chart. If the mR chart has a lot of out of control points, the average moving range will be inflated leading to wider control limits on the X chart. This can lead to missed signals (out of control points) on the X chart. Is there anything you can do when the mR chart has many out of control points to help miss fewer signals on the X chart? Yes, there is. One method is to use the median moving range. The median moving range is impacted much less by large moving range values than the average. Another option is to use the median of the X values in place of the overall average on the X chart. This publication explores using median values for the centerlines on the X and mR charts. We will start with a review of the individuals control chart. Then, the individuals control charts using median values is introduced. The charts look the same – the only difference is the location of the centerlines and control limits. -
Phase I and Phase II - Control Charts for the Variance and Generalized Variance
Phase I and Phase II - Control Charts for the Variance and Generalized Variance R. van Zyl1, A.J. van der Merwe2 1Quintiles International, [email protected] 2University of the Free State 1 Abstract By extending the results of Human, Chakraborti, and Smit(2010), Phase I control charts are derived for the generalized variance when the mean vector and covariance matrix of multivariate normally distributed data are unknown and estimated from m independent samples, each of size n. In Phase II predictive distributions based on a Bayesian approach are used to construct Shewart-type control limits for the variance and generalized variance. The posterior distribution is obtained by combining the likelihood (the observed data in Phase I) and the uncertainty of the unknown parameters via the prior distribution. By using the posterior distribution the unconditional predictive density functions are derived. Keywords: Shewart-type Control Charts, Variance, Generalized Variance, Phase I, Phase II, Predictive Density 1 Introduction Quality control is a process which is used to maintain the standards of products produced or services delivered. It is nowadays commonly accepted by most statisticians that statistical processes should be implemented in two phases: 1. Phase I where the primary interest is to assess process stability; and 2. Phase II where online monitoring of the process is done. Bayarri and Garcia-Donato(2005) gave the following reasons for recommending Bayesian analysis for the determining of control chart limits: • Control charts are based on future observations and Bayesian methods are very natural for prediction. • Uncertainty in the estimation of the unknown parameters are adequately handled. -
Introduction to Using Control Charts Brought to You by NICHQ
Introduction to Using Control Charts Brought to you by NICHQ Control Chart Purpose A control chart is a statistical tool that can help users identify variation and use that knowledge to inform the development of changes for improvement. Control charts provide a method to distinguish between the two types of causes of variation in a measure: Common Causes - those causes that are inherent in the system over time, affect everyone working in the system, and affect all outcomes of the system. Using your morning commute as an example, it may take between 35-45 minutes to commute to work each morning. It does not take exactly 40 minutes each morning because there is variation in common causes, such as the number of red lights or traffic volume. Special Causes - those causes that are not part of the system all the time or do not affect everyone, but arise because of specific circumstances. For example, it may take you 2 hours to get to work one morning because of a special cause, such as a major accident. Variation in data is expected and the type of variation that affects your system will inform your course of action for making improvements. A stable system, or one that is in a state of statistical control, is a system that has only common causes affecting the outcomes (common cause variation only). A stable system implies that the variation is predictable within statistically established limits, but does not imply that the system is performing well. An unstable system is a system with both common and special causes affecting the outcomes. -
Unit 23: Control Charts
Unit 23: Control Charts Prerequisites Unit 22, Sampling Distributions, is a prerequisite for this unit. Students need to have an understanding of the sampling distribution of the sample mean. Students should be familiar with normal distributions and the 68-95-99.7% Rule (Unit 7: Normal Curves, and Unit 8: Normal Calculations). They should know how to calculate sample means (Unit 4: Measures of Center). Additional Topic Coverage Additional coverage of this topic can be found in The Basic Practice of Statistics, Chapter 27, Statistical Process Control. Activity Description This activity should be used at the end of the unit and could serve as an assessment of x charts. For this activity students will use the Control Chart tool from the Interactive Tools menu. Students can either work individually or in pairs. Materials Access to the Control Chart tool. Graph paper (optional). For the Control Chart tool, students select a mean and standard deviation for the process (from when the process is in control), and then decide on a sample size. After students have determined and entered correct values for the upper and lower control limits, the Control Chart tool will draw the reference lines on the control chart. (Remind students to enter the values for the upper and lower control limits to four decimals.) At that point, students can use the Control Chart tool to generate sample data, compute the sample mean, and then plot the mean Unit 23: Control Charts | Faculty Guide | Page 1 against the sample number. After each sample mean has been plotted, students must decide either that the process is in control and thus should be allowed to continue or that the process is out of control and should be stopped. -
What Determines Which Numerical Measures of Center and Spread Are
Quiz 1 12pm Class Question: What determines which numerical measures of center and spread are appropriate for describing a given distribution of a quantitative variable? Which measures will you use in each case? Here are your answers in random order. See my comments. it must include a graphical display. A histogram would be a good method to give an appropriate description of a quantitative value. This does not answer the question. For the quantative variable, the "average" must make sense. The values of the variables are numbers and one value is larger than the other. This does not answer the question. IQR is what determines which numerical measures of center and spread are appropriate for describing a given distribution of a quantitative variable. The min, Q1, M, Q3, max are the measures I will use in this case. No, IQR does not determine which measure to use. the overall pattern of the quantitative variable is described by its shape, pattern and spread. A description of the distribution of a quantitative variable must include a graphical display, which is the histogram,and also a more precise numerical description of the center and spread of the distribution. The two main numerical measures are the mean and the median. This is all true, but does not answer the question. The two main numerical measures for the center of a distribution are the mean and the median. the three main measures of spread are range, inter-quartile range, and standard deviation. This is all true, but does not answer the question. When examining the distribution of a quantitative variable, one should describe the overall pattern of the data (shape, center, spread), and any deviations from the pattern (outliers). -
Understanding Statistical Process Control (SPC) Charts Introduction
Understanding Statistical Process Control (SPC) Charts Introduction This guide is intended to provide an introduction to Statistic Process Control (SPC) charts. It can be used with the ‘AQuA SPC tool’ to produce, understand and interpret your own data. For guidance on using the tool see the ‘How to use the AQuA SPC Tool’ document. This introduction to SPC will cover: • Why SPC charts are useful • Understanding variation • The different types of SPC charts and when to use them • How to interpret SPC charts and what action should be subsequently taken 2 Why SPC charts are useful When used to visualise data, SPC techniques can be used to understand variation in a process and highlight areas that would benefit from further investigation. SPC techniques indicate areas of the process that could merit further investigation. However, it does not indicate that the process is right or wrong. SPC can help: • Recognise variation • Evaluate and improve the underlying process • Prove/disprove assumptions and (mis)conceptions • Help drive improvement • Use data to make predictions and help planning • Reduce data overload 3 Understanding variation In any process or system you will see variation (for example differences in output, outcome or quality) Variation in a process can occur from many difference sources, such as: • People - every person is different • Materials - each piece of material/item/tool is unique • Methods – doing things differently • Measurement - samples from certain areas etc can bias results • Environment - the effect of seasonality on admissions There are two types of variation that we are interested in when interpreting SPC charts - ‘common cause’ and ‘special cause’ variation.