1 Statistical Process Control (SPC) Training Guide Rev X05, 09/2013
2 What is data? Data is factual information (as measurements or statistics) used as a basic for reasoning, discussion or calculation. (Merriam-Webster Dictionary, m-w.com) What does this mean? Data allows us to make educated decisions and take action!
3 Why is Data Important? If we don t collect data about a process then what? Without data we don t understand the process / product So what? Without understanding of the process / product we can t control the outcome Is it important to control the outcome? When you can t control the outcome you are dependent on chance. You may have a good outcome, you may not. Without data collection you may not know either way.
4 Use of Data I m not collecting data because its non value add. Without data collection there is no way to identify problems, continuously improve or ensure you are meeting the voice of the customer. I m collecting data, but not looking at it. Is that okay? No, the collection of data without analysis is a bigger waste than not collecting data in the first place. What should I be doing with the data?
5 DATA Statistics Information that can be understood and acted on.
6 What are Statistics? A branch of mathematics dealing with the collection, analysis, interpretation and presentation of masses of numerical data (Merriam-Webster Dictionary, m-w.com) What does this mean? Once data is collected we can use appropriate statistical methods to describe (understand) our process / product and control (predict) the process / product outcome
7 Statistics Allow us to Describe our process / product Control (predict) process / product outcomes Sample (125 Pieces) Population (All Product)
8 Important Notes 1. Statistical conclusions require useful data We need to measure the right thing Determining what data to collect and how to collect it are important steps in the APQP / continuous improvement process 2. We need to have confidence the data collected is accurate A good measurement system is required to collect data Be sure the measurement system analysis (MSA) is acceptable before collecting data There is a separate training available for MSA 3. Reduce / Eliminate Waste Data that doesn t provide useful information drives waste We want to gain the most useful information from the least amount of data possible!
9 Types of Data Variable Data (Continuous Data) Measurements on a continuous scale Examples Product Dimensions Weight Time Cost Process parameters (cutting speed, injection pressure, etc.) Attribute Data (Discrete Data) Data by counting Examples Count of defective parts from production Number of chips on a painted part
10 Types of Attribute Data Binomial Distribution Pass / Fail (PPM) Number of defective bezels Number of defective castings Poisson Distribution Number of defects (DPMO) Number of defects per bezel Number of defects per casting
11 Which Type of Data is Better? Variable Data Pros: Provides useful information with smaller sample sizes Can identify common cause concerns at low defect rates Can be used to predict product / process outcomes (trends) Very useful for continuous improvement activities (DOE, Regression analysis, etc.) Cons: Data collection can be more difficult, requiring specific gauges or measurement methods Analysis of data requires some knowledge of statistical methods (Control charting, Regression analysis, etc.) Attribute Data Pros: Very easy to obtain Calculations are simple Data is usually readily available Good for metrics reporting / management review Good for baseline performance Cons: Data collection can be more difficult, requiring specific gauges or measurement methods Analysis of data requires some knowledge of statistical methods (Control charting, Regression analysis, etc.)
12 Introduction to Statistics Goal: 1. Define basic statistical tools 2. Define types of distributions 3. Understand the Central Limit Theorem 4. Understand normal distributions
13 Definitions Population: A group of all possible objects Subgroup (Sample): One or more observations used to analyze the performance of a process. Distribution: A method of describing the output of a stable source of variation, where individual values as a group form a pattern that can be described in terms of its location, spread and shape.
14 Measures of Data Distribution Measures of Location Mean (Average) The sum of all data values divided by the number of data points Mode The most frequently occurring number in a data set Median (Midpoint) Measures of Spread Range The difference between the largest and smallest values of a data set Standard Deviation The square root of the squared distances of each data point from the mean, divided by the sample size. Also known as Sigma (σ)
15 Distribution Types Discrete Binomial Poisson Continuous Normal Exponential Weibull Uniform
16 Central Limit Theorem The Central Limit Theorem is the basis for sampling and control charting (of averages). There are 3 properties associated with the CLT; 1. The distribution of the sample means will approximate a normal distribution as the sample size increases, even if the population is non-normal 2. The average of the sample means will be the same as the population mean 3. The distribution of the sample means will be narrower than the distribution of the individuals by a factor of 1, where n is the sample size. n
17 CLT Property 1 Population Population Population Population The distribution of the sample means of any population will approximate a normal distribution as the sample size increases, even if the population is non-normal. Because of this property control charts (for averages) is based on the normal distribution. Distribution of sample means from any population
20 Process Capability Goal Understand process capability and specification limits Understand the procedure of calculating process capability Understand C p, C pk, P p and P pk indices Estimating percentage of process beyond specification limits Understanding non-normal data Example capability calculation
21 Specification Limits Individual features (dimensions) on a product are assigned specification limits. How do we determine a process is able to produce a part that meets specification limits? Process Capability! LSL USL
22 Process Capability and Specification Limits Process capability is the ability of a process to meet customer requirements. LSL USL LSL USL Acceptable capability Product outside of spec limits
23 Calculating Process Capability
24 Determine Stability All sample means and ranges and in control and do not indicate obvious trends
25 Determine Normality Placing all data in a histogram may be used to help determine normality. If the data represents a normal curve.
26 Determine Normality A more statistical method is to use the Anderson Darling test for normality In Minitab go to: Stat > Basic Statistics > Normality Test Select Anderson Darling and click ok
27 Interpreting Normality The p-value must be greater than or equal to 0.05 to match the normal distribution.
28 Process Indices Indices of process variation only, in regard to specification; C p and P p Indices of process variation and centering combined, in regard to specification; C pk and P pk
29 NOTE Before calculating capability or performance indices we need to make sure of a couple of things! 1. The process needs to be stable (in control) 2. The process needs to be normal 3. A completed MSA needs to prove the measurement system is acceptable If the above items are not met understand the results of the capability studies may be inaccurate. Also, per the AIAG PPAP manual (4 th Edition) if the above items are not met corrective actions may be required prior to PPAP submittal.
30 C p Overview C p = Potential Process Capability = Tolerance Width of Distribution = Voice of Customer Voice of Process This index indicates potential process capability. Cp is not impacted by the process location and can only be calculated for bilateral tolerance.
31 C p Calculation C p = Where: USL LSL 6σ c = USL LSL 6 R d 2 USL = Upper specification limit LSL = Lower specification limit R = Average Range = a constant value based on subgroup sample size d 2 Subgroup Size d
32 Interpreting C p Garage Door Width Car <1 1 2 LSL USL Cp = Number of times the car (distribution) fits in the garage (specification limit)
33 C pk Overview C pk is a capability index. It takes the process location and the capability into account. C pk can be calculated for both single sided (unilateral) and two sided (bilateral) tolerances. For bilateral tolerances C pk is the minimum of CPU and CPL where: CPU = USL X 3σ c = USL X X LSL and CPL = 3 R 3σ c d 2 = X LSL 3 R d 2 Where: X = Process average USL = Upper specification limit LSL = Lower specification limit R = Average Range = a constant value based on subgroup sample size d 2 Note that R d 2 is an estimate of the standard deviation
34 C pk Example GHSP is provided a machined casting with a hole diameter of 16.5 ± 1.0mm. The supplier has collected 25 subgroups of 5 measurements and wants to determine the process capability. With a subgroup size of 5 d2 is (table to right). If the process average (X) is and the average range (R) is 0.561, then the C pk is calculated as follows: Subgroup Size d C pk = Minimum CPU = USL X 3σ c = USL X X LSL 3 R, CPL = 3σ c d 2 = X LSL 3 R d 2 = Minimum CPU = , CPL = = Minimum CPU = 1.372, CPL =1.392 = 1.372
35 C p / C pk Review C p indicates how many process distribution widths can fit within specification limits. It does not consider process location. Because of this it only indicates potential process capability, not actual process capability. C pk indicates actual process capability, taking into account both process location and the width of the process distribution.
36 P p Overview This index indicates potential process performance. It compares the maximum allowable variation as indicated by tolerance to the process performance P p is not impacted by the process location and can only be calculated for bilateral tolerance. P p must be used when reporting capability for PPAP P p = USL LSL 6σ p Where: σ = Standard deviation USL = Upper specification limit LSL = Lower specification limit
37 P p and C p P p C p C p takes into account within subgroup variation (average range) P p takes into account between subgroup variation
38 P pk Overview P pk is a performance index. It indicates actual process performance, taking into account both process location and overall process variation. P pk shows if a process is actually meeting customer requirements. P pk can be used for both unilateral and bilateral tolerances. P pk must be used when reporting capability for PPAP
39 P pk Calculation Ppk is the minimum of PPU and PPL where: PPU = USL X 3σ p X LSL and PPL = 3σ p Where: X = Process average USL = Upper specification limit LSL = Lower specification limit σ = Standard deviation
40 P p / P pk Review P p indicates how many process distribution widths can fit within specification limits. It does not consider process location. Because of this it only indicates potential process performance, not actual process performance. P pk indicates actual process performance, taking into account both process location and the width of the process distribution.
41 A Few Notes C pk will always be smaller than C p, unless the process is centered. If the process is centered the two value will be the same. P pk will always be smaller than P p, unless the process is centered. If the process is centered the two values will be the same. C p and P p cannot be calculated for unilateral tolerances. C pk and P pk can be calculated for both unilateral and bilateral tolerances. Often, short term capability will be calculated using C p and C pk. This is because these indices use R d 2 to estimate standard deviation, which is a calculation of within subgroup variation. This calculation tells us how good a process could potentially be at its best performance. Pp and Ppk uses the actual (overall or between subgroup) standard deviation to calculate performance. As such, when reporting capability use P p and P pk.
42 C pk and P pk Compared These two data sets contain the same data. The top data set is from an immature process that contains special cause variation. The bottom data set has the same within group variation, but has between group variation removed. The bottom data set shows a process that is in statistical control. This example may be found in the AIAG SPC (Second Edition) Manual on page 136
43 Process Indices Review Process Indices 1. Cp = 4.01, Cpk = 4.01 Pp = 4.00, Ppk = Cp = 0.27, Cpk = 0.26 Pp = 0.25, Ppk = Cp = 4.01, Cpk = Pp = 3.99, Ppk = Cp = 4.01, Cpk = 4.00 Pp = 2.01, Ppk = 2.00 Interpretation 1. This process is stable and produces almost all parts within specification 2. Significant common cause variation exists 3. Significant special cause variation exists 4. Improvement can be made by centering the process
44 LSL = 160 USL = Estimating Percent Out of Specification To estimate the percentage of product that falls outside of the specification limits we need to compute Z upper and Z lower For this example assume an average range of 8.4 from a stable process using a sample size of Z lower is the number of standard deviations between the average and the LSL Z upper is the number of standard deviations between the average and the A USL JSJ Business
45 LSL = 160 USL = Estimating Percent Out of Specification σ = R d 2 = = 3.6 Z upper = USL X σ Z upper = = 0.94 The LSL is 5.17σ from X The USL is 0.94σ from X Z lower = Z lower = X LSL σ = 5.17
46 LSL = 160 USL = Estimating Percent Out of Specification Next, we need to reference a z table. From the z table we find 0.94, which corresponds to a proportion of This convert to 17.36% defective or 173,600 PPM Z upper = 0.94
47 Understanding Non-Normal Data What happens when data used for capability is not normally distributed? C p and P p indices are robust in their accuracy with regards to non-normal data. C pk and P pk indices are not robust with regards to non-normal data. Calculating (and making decisions based on) P pk and C pk indices assuming normality with non-normal data can be misleading.
48 Understanding Non-Normal Data What do I do if my data is not normal? Gather more data This may or may not be an option given timing and cost. The Central Limit Theorem (covered earlier) states that all population means resemble the normal distribution with larger sample size Transform the data Using either the Box-Cox or Johnson transformations we can transform non-normal data to a near normal form This allows use to accurately calculate Cpk and Ppk indices and the proportion nonconforming Calculate capabilities based on different distributions
49 Box-Cox Transformation The goal of the Box-Cox transformation is to identify a Lambda value (λ). The Lambda value will then be used in the function X λ to transform the data (X) from a non-normal set into a normal data set. The formula for this transformation is W=X λ where: and -5 λ 5 λ = 0 for the natural log transformation λ = 0.5 for the square root transformation
50 Box-Cox in Practice The Box-Cox transformation can be used in Minitab s capability analysis of normal data. When running a capability study in Minitab select: Stat > Quality Tools > Capability Sixpack > Normal Then select Transform and check Box-Cox power Transformation
51 Johnson Transformation The Johnson Transformation uses a system of transformations that yield approximate normality. The Johnson Transformation covers: Bounded data Log normal data Unbounded data This system of transformations cover all possible unimodal distribution forms (skewness-kurtosis) This transformation can also be ran in Minitab
52 Johnson Transformation in Practice The Johnson Transformation can be used in Minitab s capability analysis of normal data. When running a capability study in Minitab select: Stat > Quality Tools > Capability Sixpack > Normal Then select Transform and check Box-Cox power Transformation
53 Example Process Capability Using the data below captured from an early preproduction run calculate initial process capability The process specification is / data points were collected (subgroup of 1)
54 Is the data stable?
55 Is the data normal?
56 Calculate Capability
57 Analyze Results Process Stable? Yes! Data set normal? Yes! Capability Acceptable? Yes!
58 SPC STATISTICAL PROCESS CONTROL The organization Listens and reacts The process talks through the control chart -Root cause -Learning (Understanding) -Corrective Action -Share knowledge The process responds
59 Why do we need process control? Why prevention instead of detection? Detection tolerates waste, Prevention avoids it.
60 Variation There are two types of variation 1. Common Cause The many factors that result in variation that is consistently acting on a process. If only common causes are present in a process it is considered stable and in control. If only common cause variation is present in a process the process outcome is predictable. 2. Special Cause Also known as assignable causes, special causes are factors that result in variation that only affect some of the process output. Special cause variation results in one or more points outside of controls limits and / or non-random patterns of points within control limits. Special cause variation is not predictable and, if present in a process, results in instability and out of control conditions.
61 Common Cause Variation If only common cause variation is present in a process it will result in an output that is stable over time and predictable Prediction Size Common cause variation can result in, for example, slight variation in the size of a bolt (exaggerated visual)
1 Gage Studies for Continuous Data Objectives Determine the adequacy of measurement systems. Calculate statistics to assess the linearity and bias of a measurement system. 1-1 Contents Contents Examples
Statistical Process Control Basics 70 GLEN ROAD, CRANSTON, RI 02920 T: 401-461-1118 F: 401-461-1119 www.tedco-inc.com What is Statistical Process Control? Statistical Process Control (SPC) is an industrystandard
Assessing Measurement System Variation Example 1: Fuel Injector Nozzle Diameters Problem A manufacturer of fuel injector nozzles installs a new digital measuring system. Investigators want to determine
Frequency Business Process Improvement 281-304-9504 20314 Lakeland Falls www.spcforexcel.com Cypress, TX 77433 Instruction Manual for SPC for MS Excel V3.0 35 30 25 LSL=60 Nominal=70 Capability Analysis
Chapter 297 Confidence Intervals for Cpk Introduction This routine calculates the sample size needed to obtain a specified width of a Cpk confidence interval at a stated confidence level. Cpk is a process
TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY Before we begin: Turn on the sound on your computer. There is audio to accompany this presentation. Audio will accompany most of the online
STATISTICAL REASON FOR THE 1.5σ SHIFT Davis R. Bothe INTRODUCTION Motorola Inc. introduced its 6σ quality initiative to the world in the 1980s. Almost since that time quality practitioners have questioned
INTRO-1 (1) THE SIX SIGMA BLACK BELT PRIMER by Quality Council of Indiana - All rights reserved Fourth Edition - September, 2014 Quality Council of Indiana 602 West Paris Avenue West Terre Haute, IN 47885
Six Sigma Breakthrough Strategy or Your Worse Nightmare? Jeffrey T. Gotro, Ph.D. Director of Research & Development Ablestik Laboratories Agenda What is Six Sigma? What are the challenges? What are the
Production Part Approval Process AIAG PPAP 4 th Edition Supplier Production Part approval process GHSP 11/24/2014 What is PPAP? Defines generic requirements for production parts approval, including production
BODY OF KNOWLEDGE CERTIFIED SIX SIGMA YELLOW BELT The topics in this Body of Knowledge include additional detail in the form of subtext explanations and the cognitive level at which test questions will
Chapter 296 Confidence Intervals for Cp Introduction This routine calculates the sample size needed to obtain a specified width of a Cp confidence interval at a stated confidence level. Cp is a process
Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques
THE INTERNATIONAL JOURNAL OF BUSINESS & MANAGEMENT Process Performance Analysis in the Production Process of Medical Bottles Dr. Kabaday Nihan Research Asistant, Department of Production Management, Business
Statistical Process Control OPRE 6364 1 Statistical QA Approaches Statistical process control (SPC) Monitors production process to prevent poor quality Acceptance sampling Inspects random sample of product
Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,
Certified Six Sigma Yellow Belt Quality excellence to enhance your career and boost your organization s bottom line asq.org/cert The Global Voice of Quality TM Certification from ASQ is considered a mark
Control Charts for Variables X-R, X-S charts, non-random patterns, process capability estimation. 1 Control Chart for X and R Often, there are two things that might go wrong in a process; its mean or its
Measures of Central Tendency and Variability: Summarizing your Data for Others 1 I. Measures of Central Tendency: -Allow us to summarize an entire data set with a single value (the midpoint). 1. Mode :
Assessment of Hemoglobin Level of Pregnant Women Before and After Iron Deficiency Treatment Using Nonparametric Statistics M. Abdollahian *, S. Ahmad *, S. Nuryani #, + D. Anggraini * School of Mathematical
Probability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #15 Special Distributions-VI Today, I am going to introduce
IE 408: Quality Assurance Helicopter Project TPR 3 5/6/2015 John Balzani, Aloysia Beaulieu, Chris Diaz, Kyle Jiron, Nick Kreuter Work Instruction: Purpose: The purpose of this section of the project is
Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research
Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about
Six Sigma Acronyms $k Thousands of dollars $M Millions of dollars % R & R Gauge % Repeatability and Reproducibility ANOVA Analysis of Variance AOP Annual Operating Plan BB Black Belt C & E Cause and Effects
American Journal of Theoretical and Applied Statistics 2014; 3(4): 90-95 Published online July 20, 2014 (http://www.sciencepublishinggroup.com/j/ajtas) doi: 10.11648/j.ajtas.20140304.12 ISSN: 2326-8999
www.arpapress.com/volumes/vol4issue2/ijrras_4_2_05.pdf CONTROL CHARTS FOR IMPROVING THE PROCESS PERFORMANCE OF SOFTWARE DEVELOPMENT LIFE CYCLE S. Selva Arul Pandian & P. Puthiyanayagam Department of mathematics,
Control Charts - SigmaXL Version 6.1 Control Charts: Overview Summary Report on Test for Special Causes Individuals & Moving Range Charts Use Historical Groups to Display Before VS After Improvement X-Bar
4. Continuous Random Variables, the Pareto and Normal Distributions A continuous random variable X can take any value in a given range (e.g. height, weight, age). The distribution of a continuous random
Hilary Emmett, 22 August 2007 Improve the quality of your critical business decisions Agenda Simulation and Lean Six Sigma What is Monte Carlo Simulation? Loan Process Example Inventory Optimization Example
Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to
Lecture 5 : The Poisson Distribution Jonathan Marchini November 10, 2008 1 Introduction Many experimental situations occur in which we observe the counts of events within a set unit of time, area, volume,
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
Exploratory Data Analysis Johannes Schauer email@example.com Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction
THE CERTIFIED SIX SIGMA BLACK BELT HANDBOOK SECOND EDITION T. M. Kubiak Donald W. Benbow ASQ Quality Press Milwaukee, Wisconsin Table of Contents list of Figures and Tables Preface to the Second Edition
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
Quality Improvement The Six Sigma Way Mala Murugappan and Gargi Keeni Tata Consultancy Services Abstract Six Sigma provides an effective mechanism to focus on customer requirements, through improvement
A Multi-Stream Process Capability Assessment Using a Nonconformity Ratio Based Desirability Function Thesis for the Acquisition of the Degree of a Doctor in Natural Sciences of the University of Dortmund
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
General Lean Six Sigma Defined UN Describe Nature and purpose of Lean Six Sigma Integration of Lean and Six Sigma UN Compare and contrast focus and approaches (Process Velocity and Quality) Y=f(X) Input
Notes on Continuous Random Variables Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes
METALLURGY AND FOUNDRY ENGINEERING Vol. 38, 2012, No. 1 http://dx.doi.org/10.7494/mafe.2012.38.1.25 Andrzej Czarski*, Piotr Matusiewicz* INFLUENCE OF MEASUREMENT SYSTEM QUALITY ON THE EVALUATION OF PROCESS
THE USE OF STATISTICAL PROCESS CONTROL IN PHARMACEUTICALS INDUSTRY Alexandru-Mihnea SPIRIDONICĂ 1 E-mail: firstname.lastname@example.org Abstract The use of statistical process control has gained a major
2014 by Minitab Inc. All rights reserved. Minitab, Quality. Analysis. Results. and the Minitab logo are registered trademarks of Minitab, Inc., in the United States and other countries. Additional trademarks
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
rev 12 Six Sigma Project Charter Name of project: Reduce the time of producing admissions dashboard reports Green belt: Yes Submitted by: Xingming Yu e-mail: email@example.com Date submitted: May 21, 212
Universally Accepted Lean Six Sigma Body of Knowledge for Green Belts The IASSC Certified Green Belt Exam was developed and constructed based on the topics within the body of knowledge listed here. Questions
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Variables
Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. firstname.lastname@example.org
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number
Certified Quality Process Analyst Quality excellence to enhance your career and boost your organization s bottom line asq.org/certification The Global Voice of Quality TM Certification from ASQ is considered
Plastic Threads Technical University of Gabrovo Yordanka Atanasova Threads in plastic products can be produced in three ways: a) by direct moulding with thread punch or die; b) by placing a threaded metal
Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.
BIZ2121-04 Production & Operations Management Process Quality Sung Joo Bae, Assistant Professor Yonsei University School of Business Disclaimer: Many slides in this presentation file are from the copyrighted
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
2 ESTIMATION Chapter 2 Estimation Objectives After studying this chapter you should be able to calculate confidence intervals for the mean of a normal distribution with unknown variance; be able to calculate
Statistical Quality Control CHAPTER 6 Before studying this chapter you should know or, if necessary, review 1. Quality as a competitive priority, Chapter 2, page 00. 2. Total quality management (TQM) concepts,
Software Quality Unit 2. Advanced techniques Index 1. Statistical techniques: Statistical process control, variable control charts and control chart for attributes. 2. Advanced techniques: Quality function
1 WHERE DOES THE 10% CONDITION COME FROM? The text has mentioned The 10% Condition (at least) twice so far: p. 407 Bernoulli trials must be independent. If that assumption is violated, it is still okay
Errata for ASM Exam C/4 Study Manual (Sixteenth Edition) Sorted by Page 1 Errata and updates for ASM Exam C/Exam 4 Manual (Sixteenth Edition) sorted by page Practice exam 1:9, 1:22, 1:29, 9:5, and 10:8
The normal approximation to the binomial The binomial probability function is not useful for calculating probabilities when the number of trials n is large, as it involves multiplying a potentially very
Process Capability and Six Sigma Methodology Including Fuzzy and Lean Approaches 9 Özlem Şenvar and Hakan Tozan Marmara University, Turkish Naval Academy Turkey 1. Introduction Process capability analysis
IE 3255. Statistical Quality Control 3.0 cr; prerequisite: Stat 3611, BSIE or BSME candidate, or Instructor Consent Statistical quality control in manufacturing; modeling, process quality, control charts,
t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. email@example.com www.excelmasterseries.com
SPI HS70 Remote Control of Multiple Lines with RMCworks Machine Status Monitoring It costs highly to post process analysis technicians for each production line. RMCworks provides solution that one technical
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
Data Transforms: atural Log and Square Roots 1 Data Transforms: atural Logarithms and Square Roots Parametric statistics in general are more powerful than non-parametric statistics as the former are based
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
Advanced Topics in Statistical Process Control The Power of Shewhart s Charts Second Edition Donald J. Wheeler SPC Press Knoxville, Tennessee Contents Preface to the Second Edition Preface The Shewhart
. Combining Control and Burndown Charts and Related Elements Discussion Document By Mark Crowther, Empirical Pragmatic Tester Introduction When following the Scrum approach a tool frequently used is the
290 Chapter 6 The Normal Distribution Figure 6 5 Areas Under a Normal Distribution Curve 34.13% 34.13% 2.28% 13.59% 13.59% 2.28% 3 2 1 + 1 + 2 + 3 About 68% About 95% About 99.7% 6 3 The Distribution Since
MATH 10: Elementary Statistics and Probability Chapter 5: Continuous Random Variables Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides,
Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot
Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.
Tip Sheet SPC Demonstration Tips Key Points to Cover When Demonstrating Ignition SPC Downtime In general, the SPC Module is designed with a great level of flexibility to support a wide variety of production
Some Essential Statistics The Lure of Statistics Data Mining Techniques, by M.J.A. Berry and G.S Linoff, 2004 Statistics vs. Data Mining..lie, damn lie, and statistics mining data to support preconceived
The Standard Normal distribution 21.2 Introduction Mass-produced items should conform to a specification. Usually, a mean is aimed for but due to random errors in the production process we set a tolerance
Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means
Supplier Quality Management Production Part Approval Process (PPAP) Manual February, 2009 Rev 6 Release Cooper Industries 600 Travis Suite 5600 Houston, TX 77002 Table of Contents TABLE OF CONTENTS...2
CHAPTER 7 INTRODUCTION TO SAMPLING DISTRIBUTIONS CENTRAL LIMIT THEOREM (SECTION 7.2 OF UNDERSTANDABLE STATISTICS) The Central Limit Theorem says that if x is a random variable with any distribution having