ISO : 2013 Changes to ISO 21747: 2006
|
|
|
- Roger Tate
- 6 years ago
- Views:
Transcription
1 ISO : 2013 Changes to ISO 21747: 2006
2 ISO : 2013 Changes to ISO 21747: /17 Content Purpose of the document... 2 Part I - main content of ISO : Time-dependent distribution models... 3 Process performance indices... 4 Process performance index P p... 4 pper process performance index P pk... 5 ower process performance index P pk... 6 Minimum process performance index P pk... 7 Process capability indices... 8 Process capability index C p... 8 pper process capability index C pk... 9 ower process capability index C pk Minimum process capability index C pk Calculation methods of location (See ISO : 2013, table 3) Calculation methods of dispersion (See ISO : 2013, table 4) Application of different calculation methods Reporting performance and capability indices Part II - calculation methods for location and dispersion in Q-DAS products Calculation method settings in Q-DAS software products Settings for stable processes Settings for instable processes... 17
3 ISO : 2013 Changes to ISO 21747: /17 Purpose of the document The international standard ISO 21747: 2003 has been withdrawn and replaced by the standard ISO : In order to avoid confusion regarding compliance with ISO we provide information about the key content of ISO : This document is divided into two parts. Part I shows key content elements of ISO : 2013 with the main focus on calculation methods of process performance/capability indices. Part II provides recommendations regarding the settings for the evaluation strategy of Q-DAS software for compliance with ISO : These settings are related to: qs-stat: Process Capability module destra: Process Capability module procella: Process Capability module
4 ISO : 2013 Changes to ISO 21747: /17 Part I - main content of ISO : 2013 Time-dependent distribution models The following table lists all time-dependent distribution models in compliance with ISO : Characteristic Time-dependent distribution models (ISO : 2013) A1 A2 B C1 C2 C3 C4 D ocation c c c r r s s s Dispersion c c s/r c c c c s/r Short time distribution Resulting distribution nd 1m nd nd nd as as as nd 1m as nd 1m as as as Table 1: Time dependent distribution models (See ISO : 2013, table 2) c s r nd as 1m parameter remains constant parameter only changes systematically parameter only changes randomly normally distributed any shape not normally distributed, one mode only
5 density ISO : 2013 Changes to ISO 21747: /17 Process performance indices If a process is not considered to be in a state of statistical control, a process performance index can be assigned. Process performance index P p X % X % Specification = D = X % X % variable Figure 1: Process performance index Pp Δ dispersion of the distribution of the product characteristic lower specification limit Pp process performance index upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
6 density ISO : 2013 Changes to ISO 21747: /17 pper process performance index P pk X % X % D = X % variable Figure 2: pper process performance index P pk Δ Ppk difference between X 99,865 % and of the distribution of the product characteristic lower specification limit upper process performance index upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
7 density ISO : 2013 Changes to ISO 21747: /17 ower process performance index P pk X % X % D = X % variable Figure 3: ower process performance index P pk Δ Ppk difference between and X 0,135 % of the distribution of the product characteristic lower specification limit lower process performance index upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
8 density ISO : 2013 Changes to ISO 21747: /17 Minimum process performance index P pk X % X % D = X % D = X % variable Figure 4: Minimum process performance index P pk Δ Δ Ppk Ppk Ppk difference between and X 0,135 % of the distribution of the product characteristic difference between X 99,865 % and of the distribution of the product characteristic lower specification limit minimum process performance index lower process performance index upper process performance index upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
9 density ISO : 2013 Changes to ISO 21747: /17 Process capability indices If a process is considered to be in the state of statistical control, a capability index can be assigned. Process capability index C p X % X % Specification D = X % X % variable Figure 5: Process capability index C p Cp process capability index Δ dispersion of the distribution of the product characteristic lower specification limit upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
10 density ISO : 2013 Changes to ISO 21747: /17 pper process capability index C pk X % X % D = X % variable Figure 6: pper capability index C pk Cpk upper process capability index Δ difference between X 99,865 % and of the distribution of the product characteristic lower specification limit upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
11 density ISO : 2013 Changes to ISO 21747: /17 ower process capability index C pk X % X % D = X % variable Figure 7: ower process capability index C pk Cpk lower process capability index Δ Ppk difference between and X 0,135 % of the distribution of the product characteristic lower specification limit lower process performance index upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
12 density ISO : 2013 Changes to ISO 21747: /17 Minimum process capability index C pk X % X % D = X % D = X % variable Figure 8: Minimum capability index C pk Cpk minimum process capability index Cpk lower process capability index Cpk upper process capability index Δ Δ difference between and X 0,135 % of the distribution of the product characteristic difference between X 99,865 % and of the distribution of the product characteristic lower specification limit upper specification limit X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
13 ISO : 2013 Changes to ISO 21747: /17 Calculation methods of location (See ISO : 2013, table 3) ocation method label, l Calculation method of location / formula M l,d 1 X mid = x = 1 x kn i 2 X mid = x = { kn i=1 x ( n+1 2 ) ; n odd 1 2 [x ( n 2 )+x ( n 2 3 X mid = x = 1 k x i 4 X mid = x = 1 k x i i=1 Table 2: Calculation methods of process location (See ISO : 2013, table 3) +1)] ; n even k i=1 k k n M l,d number of subgroups size of the i-th subgroup (same size for each subgroup) Calculation methods with location method label l and dispersion method label d x ( n+1 2 ) sample value of rank [(n+1)/2] using n as the number of all individuals x ( n 2 ) sample value of rank (n/2) using n as the number of all individuals x ( n +1) sample value of rank (n/2+1) using n as the number of all individuals 2 x i x x i individual value of a subroup average of all subgroup medians median of the i-th subgroup x average of all subgroup averages x i average of the i-th subgroup Note: The calculation formulas for location estimators #3 and #4 given in ISO : 2013 were incorrect. We use the corrected versions of these formulas in this document.
14 ISO : 2013 Changes to ISO 21747: /17 Calculation methods of dispersion (See ISO : 2013, table 4) Dispersion method label, d 1 Calculation method of dispersion / formula M l,d Δ = X % X % Δ = X % ; Δ = X % 2 Δ = 6σ ; Δ = 3σ ; Δ = 3σ where σ = 1 k k i=1 s i 2 3 Δ = 6σ ; Δ = 3σ ; Δ = 3σ where σ = k i=1 s i kc 4 4 Δ = 6σ ; Δ = 3σ ; Δ = 3σ where σ = k i=1 R i kd 2 5 Δ = 6σ ; Δ = 3σ ; Δ = 3σ where σ = 1 n 1 n i=1 (x i x ) 2 Table 3: Calculation methods of process dispersion (See ISO : 2013, table 4) c 4 Δ Δ Δ d 2 k M l,d R i s i 2 s i σ x constant based on subgroup size n dispersion of the process difference between and X 0,135 % of the distribution of the product characteristic difference between X 99,865 % and of the distribution of the product characteristic constant based on subgroup size n number of subgroups of the same size n Calculation methods with location method label l and dispersion method label d range of the i-th subgroup standard deviation of the i-th subgroup variance of the i-th subgroup standard deviation, population average of sample distribution X 0,135 % 0,135 % distribution quantile X 99,865 % 99,865 % distribution quantile
15 ISO : 2013 Changes to ISO 21747: /17 Application of different calculation methods The following table provides information about the calculation methods for the respective timedependent distribution model. Calculation method ocation Dispersion Time model A1 A2 B C1 C2 C3 C4 D 1 a a 2 a a a a a a a a 3 a 4 a a a 1 a a a a a a a a 2 a 3 a 4 a 5 a a a a a Table 4: Calculation methods for process location and dispersion (See ISO : 2013, table 5) a = applicable Note #1: Dispersion estimators based on the inner dispersion of subgroups (dispersion estimators #2, #3 and #4) are only available for the time distribution model A1. Note #2: ocation estimator #2 and dispersion estimator #1 are the most general estimators. For this reason, they should be used preferably. Note #3: Dispersion calculation method #1 can also be applied to the empirical cumulative distribution function if the amount of data is large, e.g individuals. Reporting performance and capability indices If process performance/capability statistics are used for process qualification, they shall be reported in relation to ISO : Typical contents of such a report: Process performance/capability index Minimum process performance/capability index Applied calculation method Number of values included in the calculation Measurement uncertainty Time distribution model
16 ISO : 2013 Changes to ISO 21747: /17 Part II - calculation methods for location and dispersion in Q-DAS products The following table shows the changes of labels for calculation methods. ocation parameter l Dispersion parameter d ocation and dispersion calculation methods ISO 21747: 2006 ISO : 2013 distribution model 1 1 A1, B 2 2 A1, A2, B, C1, C2, C3, C4, D 3 2 A1, A2, B, C1, C2, C3, C4, D 4 3 A1 5 4 A1, A2, B 1 2 A1 2 3 A1 3 4 A1 4 5 A1, A2, B, C1, D A1, A2, B, C1, C2, C3, C4, D Table 5: Comparison of ISO and ISO labels for process location and dispersion estimators
17 ISO : 2013 Changes to ISO 21747: /17 Calculation method settings in Q-DAS software products Settings for stable processes The following figure shows all methods complying with ISO in a red frame. All other calculation methods are not defined in ISO and should therefore not be used if compliance to ISO is important. All labels of the calculation methods have been changed in ISO The following table shows what the new labels refer to. abel of Calculation Method ISO 21747: 2006 ISO : 2013 Applicable to time dependent distribution model M1 4,1 M 3,2 A1 M1 4,2 M 3,3 A1 M1 4,3 M 3,4 A1 M1 4,4 M 3,5 A1 M1 1, M1 2, M1 1,6 M 1,1 A1, B M1 3,6 M 2,1 A1, A2, B, C1, C2, C3, C4, D Table 6: Comparison of ISO and ISO labels for calculation methods of location and dispersion (stable)
18 ISO : 2013 Changes to ISO 21747: /17 Settings for instable processes The following shows all methods complying with ISO in a red frame. All other calculation methods are not defined in ISO and should therefore not be used if compliance to ISO is important. All labels of the calculation methods have been changed in ISO The following table shows what the new labels refer to. abel of Calculation Method ISO 21747: 2006 ISO 22514: 2013 Applicable to time dependent distribution model M1 4,4 M 3,5 A1* M1 1,6 M 1,1 A1*, B M1 3,6 M 2,1 (A1*, A2*), B, C1, C2, C3, C4, D Table 7: Comparison of ISO and ISO labels for calculation methods of location and dispersion (not stable) * If a process is not considered to be in a state of statistical control, this time distribution model should not be applied
Prob and Stats, Nov 7
Prob and Stats, Nov 7 The Standard Normal Distribution Book Sections: 7.1, 7.2 Essential Questions: What is the standard normal distribution, how is it related to all other normal distributions, and how
Notes 12.8: Normal Distribution
Notes 12.8: Normal Distribution For many populations, the distribution of events are relatively close to the average or mean. The further you go out both above and below the mean, there are fewer number
Copyright 2005 Pearson Education, Inc. Slide 6-1
Copyright 2005 Pearson Education, Inc. Slide 6-1 Chapter 6 Copyright 2005 Pearson Education, Inc. Measures of Center in a Distribution 6-A The mean is what we most commonly call the average value. It is
CSC Advanced Scientific Programming, Spring Descriptive Statistics
CSC 223 - Advanced Scientific Programming, Spring 2018 Descriptive Statistics Overview Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.
Statistics vs. statistics
Statistics vs. statistics Question: What is Statistics (with a capital S)? Definition: Statistics is the science of collecting, organizing, summarizing and interpreting data. Note: There are 2 main ways
Introduction to Statistics I
Introduction to Statistics I Keio University, Faculty of Economics Continuous random variables Simon Clinet (Keio University) Intro to Stats November 1, 2018 1 / 18 Definition (Continuous random variable)
As you draw random samples of size n, as n increases, the sample means tend to be normally distributed.
The Central Limit Theorem The central limit theorem (clt for short) is one of the most powerful and useful ideas in all of statistics. The clt says that if we collect samples of size n with a "large enough
Fundamentals of Statistics
CHAPTER 4 Fundamentals of Statistics Expected Outcomes Know the difference between a variable and an attribute. Perform mathematical calculations to the correct number of significant figures. Construct
Chapter Seven. The Normal Distribution
Chapter Seven The Normal Distribution 7-1 Introduction Many continuous variables have distributions that are bellshaped and are called approximately normally distributed variables, such as the heights
Lecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 6 Normal Probability Distributions 6-1 Overview 6-2 The Standard Normal Distribution
Chapter 3. Numerical Descriptive Measures. Copyright 2016 Pearson Education, Ltd. Chapter 3, Slide 1
Chapter 3 Numerical Descriptive Measures Copyright 2016 Pearson Education, Ltd. Chapter 3, Slide 1 Objectives In this chapter, you learn to: Describe the properties of central tendency, variation, and
Statistics for Managers Using Microsoft Excel/SPSS Chapter 6 The Normal Distribution And Other Continuous Distributions
Statistics for Managers Using Microsoft Excel/SPSS Chapter 6 The Normal Distribution And Other Continuous Distributions 1999 Prentice-Hall, Inc. Chap. 6-1 Chapter Topics The Normal Distribution The Standard
Chapter 3 Descriptive Statistics: Numerical Measures Part A
Slides Prepared by JOHN S. LOUCKS St. Edward s University Slide 1 Chapter 3 Descriptive Statistics: Numerical Measures Part A Measures of Location Measures of Variability Slide Measures of Location Mean
INF FALL NATURAL LANGUAGE PROCESSING. Jan Tore Lønning, Lecture 3, 1.9
1 INF5830 2015 FALL NATURAL LANGUAGE PROCESSING Jan Tore Lønning, Lecture 3, 1.9 Today: More statistics 2 Recap Probability distributions Categorical distributions Bernoulli trial Binomial distribution
Statistics for Managers Using Microsoft Excel 7 th Edition
Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 7 Sampling Distributions Statistics for Managers Using Microsoft Excel 7e Copyright 2014 Pearson Education, Inc. Chap 7-1 Learning Objectives
ME3620. Theory of Engineering Experimentation. Spring Chapter III. Random Variables and Probability Distributions.
ME3620 Theory of Engineering Experimentation Chapter III. Random Variables and Probability Distributions Chapter III 1 3.2 Random Variables In an experiment, a measurement is usually denoted by a variable
If the distribution of a random variable x is approximately normal, then
Confidence Intervals for the Mean (σ unknown) In many real life situations, the standard deviation is unknown. In order to construct a confidence interval for a random variable that is normally distributed
Normal Distribution. Notes. Normal Distribution. Standard Normal. Sums of Normal Random Variables. Normal. approximation of Binomial.
Lecture 21,22, 23 Text: A Course in Probability by Weiss 8.5 STAT 225 Introduction to Probability Models March 31, 2014 Standard Sums of Whitney Huang Purdue University 21,22, 23.1 Agenda 1 2 Standard
MAS1403. Quantitative Methods for Business Management. Semester 1, Module leader: Dr. David Walshaw
MAS1403 Quantitative Methods for Business Management Semester 1, 2018 2019 Module leader: Dr. David Walshaw Additional lecturers: Dr. James Waldren and Dr. Stuart Hall Announcements: Written assignment
2017 Fall QMS102 Tip Sheet 2
Chapter 5: Basic Probability 2017 Fall QMS102 Tip Sheet 2 (Covering Chapters 5 to 8) EVENTS -- Each possible outcome of a variable is an event, including 3 types. 1. Simple event = Described by a single
( ) P = = =
1. On a lunch counter, there are 5 oranges and 6 apples. If 3 pieces of fruit are selected, find the probability that 1 orange and apples are selected. Order does not matter Combinations: 5C1 (1 ) 6C P
Contents Part I Descriptive Statistics 1 Introduction and Framework Population, Sample, and Observations Variables Quali
Part I Descriptive Statistics 1 Introduction and Framework... 3 1.1 Population, Sample, and Observations... 3 1.2 Variables.... 4 1.2.1 Qualitative and Quantitative Variables.... 5 1.2.2 Discrete and Continuous
Numerical Descriptions of Data
Numerical Descriptions of Data Measures of Center Mean x = x i n Excel: = average ( ) Weighted mean x = (x i w i ) w i x = data values x i = i th data value w i = weight of the i th data value Median =
UNIT 4 MATHEMATICAL METHODS
UNIT 4 MATHEMATICAL METHODS PROBABILITY Section 1: Introductory Probability Basic Probability Facts Probabilities of Simple Events Overview of Set Language Venn Diagrams Probabilities of Compound Events
2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 4 Random Variables & Probability Distributions Content 1. Two Types of Random Variables 2. Probability Distributions for Discrete Random Variables 3. The Binomial
Chapter 7. Confidence Intervals and Sample Sizes. Definition. Definition. Definition. Definition. Confidence Interval : CI. Point Estimate.
Chapter 7 Confidence Intervals and Sample Sizes 7. Estimating a Proportion p 7.3 Estimating a Mean µ (σ known) 7.4 Estimating a Mean µ (σ unknown) 7.5 Estimating a Standard Deviation σ In a recent poll,
Lecture 23. STAT 225 Introduction to Probability Models April 4, Whitney Huang Purdue University. Normal approximation to Binomial
Lecture 23 STAT 225 Introduction to Probability Models April 4, 2014 approximation Whitney Huang Purdue University 23.1 Agenda 1 approximation 2 approximation 23.2 Characteristics of the random variable:
AP STATISTICS FALL SEMESTSER FINAL EXAM STUDY GUIDE
AP STATISTICS Name: FALL SEMESTSER FINAL EXAM STUDY GUIDE Period: *Go over Vocabulary Notecards! *This is not a comprehensive review you still should look over your past notes, homework/practice, Quizzes,
STATS DOESN T SUCK! ~ CHAPTER 4
CHAPTER 4 QUESTION 1 The Geometric Mean Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year. During the second year, however, the investment suffers a 50%
AP Stats Review. Mrs. Daniel Alonzo & Tracy Mourning Sr. High
AP Stats Review Mrs. Daniel Alonzo & Tracy Mourning Sr. High sdaniel@dadeschools.net Agenda 1. AP Stats Exam Overview 2. AP FRQ Scoring & FRQ: 2016 #1 3. Distributions Review 4. FRQ: 2015 #6 5. Distribution
Descriptive Statistics
Petra Petrovics Descriptive Statistics 2 nd seminar DESCRIPTIVE STATISTICS Definition: Descriptive statistics is concerned only with collecting and describing data Methods: - statistical tables and graphs
Unit2: Probabilityanddistributions. 3. Normal and binomial distributions
Announcements Unit2: Probabilityanddistributions 3. Normal and binomial distributions Sta 101 - Fall 2017 Duke University, Department of Statistical Science Formatting of problem set submissions: Bad:
Statistics Class 15 3/21/2012
Statistics Class 15 3/21/2012 Quiz 1. Cans of regular Pepsi are labeled to indicate that they contain 12 oz. Data Set 17 in Appendix B lists measured amounts for a sample of Pepsi cans. The same statistics
Chapter Seven: Confidence Intervals and Sample Size
Chapter Seven: Confidence Intervals and Sample Size A point estimate is: The best point estimate of the population mean µ is the sample mean X. Three Properties of a Good Estimator 1. Unbiased 2. Consistent
Data Distributions and Normality
Data Distributions and Normality Definition (Non)Parametric Parametric statistics assume that data come from a normal distribution, and make inferences about parameters of that distribution. These statistical
Normal Probability Distributions
Normal Probability Distributions Properties of Normal Distributions The most important probability distribution in statistics is the normal distribution. Normal curve A normal distribution is a continuous
Sampling and sampling distribution
Sampling and sampling distribution September 12, 2017 STAT 101 Class 5 Slide 1 Outline of Topics 1 Sampling 2 Sampling distribution of a mean 3 Sampling distribution of a proportion STAT 101 Class 5 Slide
Unit2: Probabilityanddistributions. 3. Normal and binomial distributions
Announcements Unit2: Probabilityanddistributions 3. Normal and binomial distributions Sta 101 - Summer 2017 Duke University, Department of Statistical Science PS: Explain your reasoning + show your work
3.1 Measures of Central Tendency
3.1 Measures of Central Tendency n Summation Notation x i or x Sum observation on the variable that appears to the right of the summation symbol. Example 1 Suppose the variable x i is used to represent
The Normal Distribution
5.1 Introduction to Normal Distributions and the Standard Normal Distribution Section Learning objectives: 1. How to interpret graphs of normal probability distributions 2. How to find areas under the
Lecture 18 Section Mon, Feb 16, 2009
The s the Lecture 18 Section 5.3.4 Hampden-Sydney College Mon, Feb 16, 2009 Outline The s the 1 2 3 The 4 s 5 the 6 The s the Exercise 5.12, page 333. The five-number summary for the distribution of income
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a Announcements: There are some office hour changes for Nov 5, 8, 9 on website Week 5 quiz begins after class today and ends at
Statistics 511 Supplemental Materials
Gaussian (or Normal) Random Variable In this section we introduce the Gaussian Random Variable, which is more commonly referred to as the Normal Random Variable. This is a random variable that has a bellshaped
Quantitative Methods for Economics, Finance and Management (A86050 F86050)
Quantitative Methods for Economics, Finance and Management (A86050 F86050) Matteo Manera matteo.manera@unimib.it Marzio Galeotti marzio.galeotti@unimi.it 1 This material is taken and adapted from Guy Judge
Lecture 18 Section Mon, Sep 29, 2008
The s the Lecture 18 Section 5.3.4 Hampden-Sydney College Mon, Sep 29, 2008 Outline The s the 1 2 3 The 4 s 5 the 6 The s the Exercise 5.12, page 333. The five-number summary for the distribution of income
Statistics 431 Spring 2007 P. Shaman. Preliminaries
Statistics 4 Spring 007 P. Shaman The Binomial Distribution Preliminaries A binomial experiment is defined by the following conditions: A sequence of n trials is conducted, with each trial having two possible
Chapter 7 - Lecture 1 General concepts and criteria
Chapter 7 - Lecture 1 General concepts and criteria January 29th, 2010 Best estimator Mean Square error Unbiased estimators Example Unbiased estimators not unique Special case MVUE Bootstrap General Question
Model Paper Statistics Objective. Paper Code Time Allowed: 20 minutes
Model Paper Statistics Objective Intermediate Part I (11 th Class) Examination Session 2012-2013 and onward Total marks: 17 Paper Code Time Allowed: 20 minutes Note:- You have four choices for each objective
Measure of Variation
Measure of Variation Variation is the spread of a data set. The simplest measure is the range. Range the difference between the maximum and minimum data entries in the set. To find the range, the data
Continuous Probability Distributions & Normal Distribution
Mathematical Methods Units 3/4 Student Learning Plan Continuous Probability Distributions & Normal Distribution 7 lessons Notes: Students need practice in recognising whether a problem involves a discrete
Chapter 8: The Binomial and Geometric Distributions
Chapter 8: The Binomial and Geometric Distributions 8.1 Binomial Distributions 8.2 Geometric Distributions 1 Let me begin with an example My best friends from Kent School had three daughters. What is the
Homework: Due Wed, Feb 20 th. Chapter 8, # 60a + 62a (count together as 1), 74, 82
Announcements: Week 5 quiz begins at 4pm today and ends at 3pm on Wed If you take more than 20 minutes to complete your quiz, you will only receive partial credit. (It doesn t cut you off.) Today: Sections
6.2 Normal Distribution. Normal Distributions
6.2 Normal Distribution Normal Distributions 1 Homework Read Sec 6-1, and 6-2. Make sure you have a good feel for the normal curve. Do discussion question p302 2 3 Objective Identify Complete normal model
Measures of Variation. Section 2-5. Dotplots of Waiting Times. Waiting Times of Bank Customers at Different Banks in minutes. Bank of Providence
Measures of Variation Section -5 1 Waiting Times of Bank Customers at Different Banks in minutes Jefferson Valley Bank 6.5 6.6 6.7 6.8 7.1 7.3 7.4 Bank of Providence 4. 5.4 5.8 6. 6.7 8.5 9.3 10.0 Mean
Mean of a Discrete Random variable. Suppose that X is a discrete random variable whose distribution is : :
Dr. Kim s Note (December 17 th ) The values taken on by the random variable X are random, but the values follow the pattern given in the random variable table. What is a typical value of a random variable
Applications of Data Dispersions
1 Applications of Data Dispersions Key Definitions Standard Deviation: The standard deviation shows how far away each value is from the mean on average. Z-Scores: The distance between the mean and a given
AP Stats. Review. Mrs. Daniel Alonzo & Tracy Mourning Sr. High
AP Stats Review Mrs. Daniel Alonzo & Tracy Mourning Sr. High sdaniel@dadeschools.net Agenda 1. AP Stats Exam Overview 2. AP FRQ Scoring & FRQ: 2016 #1 3. Distributions Review 4. FRQ: 2015 #6 5. Distribution
Chapter 3. Descriptive Measures. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 3, Slide 1
Chapter 3 Descriptive Measures Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 3, Slide 1 Chapter 3 Descriptive Measures Mean, Median and Mode Copyright 2016, 2012, 2008 Pearson Education, Inc.
Confidence Intervals for the Mean. When σ is known
Confidence Intervals for the Mean When σ is known Objective Find the confidence interval for the mean when s is known. Intro Suppose a college president wishes to estimate the average age of students attending
Gamma Distribution Fitting
Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics
Data Analytics (CS40003) Practice Set IV (Topic: Probability and Sampling Distribution)
Data Analytics (CS40003) Practice Set IV (Topic: Probability and Sampling Distribution) I. Concept Questions 1. Give an example of a random variable in the context of Drawing a card from a deck of cards.
Continuous random variables
Continuous random variables probability density function (f(x)) the probability distribution function of a continuous random variable (analogous to the probability mass function for a discrete random variable),
CHAPTERS 5 & 6: CONTINUOUS RANDOM VARIABLES
CHAPTERS 5 & 6: CONTINUOUS RANDOM VARIABLES DISCRETE RANDOM VARIABLE: Variable can take on only certain specified values. There are gaps between possible data values. Values may be counting numbers or
Key Objectives. Module 2: The Logic of Statistical Inference. Z-scores. SGSB Workshop: Using Statistical Data to Make Decisions
SGSB Workshop: Using Statistical Data to Make Decisions Module 2: The Logic of Statistical Inference Dr. Tom Ilvento January 2006 Dr. Mugdim Pašić Key Objectives Understand the logic of statistical inference
Continuous Probability Distributions
Continuous Probability Distributions Chapter 7 Learning Objectives List the characteristics of the uniform distribution. Compute probabilities using the uniform distribution List the characteristics of
Web Extension: Continuous Distributions and Estimating Beta with a Calculator
19878_02W_p001-008.qxd 3/10/06 9:51 AM Page 1 C H A P T E R 2 Web Extension: Continuous Distributions and Estimating Beta with a Calculator This extension explains continuous probability distributions
Technical Note: An Improved Range Chart for Normal and Long-Tailed Symmetrical Distributions
Technical Note: An Improved Range Chart for Normal and Long-Tailed Symmetrical Distributions Pandu Tadikamalla, 1 Mihai Banciu, 1 Dana Popescu 2 1 Joseph M. Katz Graduate School of Business, University
Chapter ! Bell Shaped
Chapter 6 6-1 Business Statistics: A First Course 5 th Edition Chapter 7 Continuous Probability Distributions Learning Objectives In this chapter, you learn:! To compute probabilities from the normal distribution!
Descriptive Statistics
Chapter 3 Descriptive Statistics Chapter 2 presented graphical techniques for organizing and displaying data. Even though such graphical techniques allow the researcher to make some general observations
1) 3 points Which of the following is NOT a measure of central tendency? a) Median b) Mode c) Mean d) Range
February 19, 2004 EXAM 1 : Page 1 All sections : Geaghan Read Carefully. Give an answer in the form of a number or numeric expression where possible. Show all calculations. Use a value of 0.05 for any
Standard Deviation. Lecture 18 Section Robb T. Koether. Hampden-Sydney College. Mon, Sep 26, 2011
Standard Deviation Lecture 18 Section 5.3.4 Robb T. Koether Hampden-Sydney College Mon, Sep 26, 2011 Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Sep 26, 2011 1 / 42 Outline 1 Variability
Process Capability. Karthik Iyer Senior Policy Advisor CDER/OC/OMPQ October 16 th, 2014 QbD/PAT
Karthik Iyer Senior Policy Advisor CDER/OC/OMPQ October 16 th, 201 QbD/PAT * This presentation reflects the views of the author and should not be construed to represent FDA s views or policies. WL Example
2. The sum of all the probabilities in the sample space must add up to 1
Continuous Random Variables and Continuous Probability Distributions Continuous Random Variable: A variable X that can take values on an interval; key feature remember is that the values of the variable
Sampling Distribution
MAT 2379 (Spring 2012) Sampling Distribution Definition : Let X 1,..., X n be a collection of random variables. We say that they are identically distributed if they have a common distribution. Definition
Statistics I Final Exam, 24 June Degrees in ADE, DER-ADE, ADE-INF, FICO, ECO, ECO-DER.
Statistics I Final Exam, June. Degrees in ADE, DER-ADE, ADE-INF, FICO, ECO, ECO-DER. EXAM RULES: Use separate booklets for each problem. Perform the calculations with at least two significant decimal places.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics. Convergent validity: the degree to which results/evidence from different tests/sources, converge on the same conclusion.
Uniform Probability Distribution. Continuous Random Variables &
Continuous Random Variables & What is a Random Variable? It is a quantity whose values are real numbers and are determined by the number of desired outcomes of an experiment. Is there any special Random
3.3-Measures of Variation
3.3-Measures of Variation Variation: Variation is a measure of the spread or dispersion of a set of data from its center. Common methods of measuring variation include: 1. Range. Standard Deviation 3.
Statistics 6 th Edition
Statistics 6 th Edition Chapter 5 Discrete Probability Distributions Chap 5-1 Definitions Random Variables Random Variables Discrete Random Variable Continuous Random Variable Ch. 5 Ch. 6 Chap 5-2 Discrete
Statistics for Business and Economics
Statistics for Business and Economics Chapter 5 Continuous Random Variables and Probability Distributions Ch. 5-1 Probability Distributions Probability Distributions Ch. 4 Discrete Continuous Ch. 5 Probability
Asymmetric prediction intervals using half moment of distribution
Asymmetric prediction intervals using half moment of distribution Presentation at ISIR 2016, Budapest 23 rd August 2016 Lancaster Centre for Forecasting Asymmetric prediction intervals using half moment
Normal Model (Part 1)
Normal Model (Part 1) Formulas New Vocabulary The Standard Deviation as a Ruler The trick in comparing very different-looking values is to use standard deviations as our rulers. The standard deviation
10/1/2012. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1
PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Pivotal subject: distributions of statistics. Foundation linchpin important crucial You need sampling distributions to make inferences:
Chapter 3 Discrete Random Variables and Probability Distributions
Chapter 3 Discrete Random Variables and Probability Distributions Part 4: Special Discrete Random Variable Distributions Sections 3.7 & 3.8 Geometric, Negative Binomial, Hypergeometric NOTE: The discrete
Chapter 4 Variability
Chapter 4 Variability PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J Gravetter and Larry B. Wallnau Chapter 4 Learning Outcomes 1 2 3 4 5
UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions.
UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions. Random Variables 2 A random variable X is a numerical (integer, real, complex, vector etc.) summary of the outcome of the random experiment.
Some Characteristics of Data
Some Characteristics of Data Not all data is the same, and depending on some characteristics of a particular dataset, there are some limitations as to what can and cannot be done with that data. Some key
Shifting and rescaling data distributions
Shifting and rescaling data distributions It is useful to consider the effect of systematic alterations of all the values in a data set. The simplest such systematic effect is a shift by a fixed constant.
Data that can be any numerical value are called continuous. These are usually things that are measured, such as height, length, time, speed, etc.
Chapter 8 Measures of Center Data that can be any numerical value are called continuous. These are usually things that are measured, such as height, length, time, speed, etc. Data that can only be integer
Chapter 5. Continuous Random Variables and Probability Distributions. 5.1 Continuous Random Variables
Chapter 5 Continuous Random Variables and Probability Distributions 5.1 Continuous Random Variables 1 2CHAPTER 5. CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Probability Distributions Probability
Chapter 7 presents the beginning of inferential statistics. The two major activities of inferential statistics are
Chapter 7 presents the beginning of inferential statistics. Concept: Inferential Statistics The two major activities of inferential statistics are 1 to use sample data to estimate values of population
Exploring Data and Graphics
Exploring Data and Graphics Rick White Department of Statistics, UBC Graduate Pathways to Success Graduate & Postdoctoral Studies November 13, 2013 Outline Summarizing Data Types of Data Visualizing Data
Random Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES
Random Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES Essential Question How can I determine whether the conditions for using binomial random variables are met? Binomial Settings When the
Random variables. Contents
Random variables Contents 1 Random Variable 2 1.1 Discrete Random Variable............................ 3 1.2 Continuous Random Variable........................... 5 1.3 Measures of Location...............................
MAS187/AEF258. University of Newcastle upon Tyne
MAS187/AEF258 University of Newcastle upon Tyne 2005-6 Contents 1 Collecting and Presenting Data 5 1.1 Introduction...................................... 5 1.1.1 Examples...................................
The Normal Probability Distribution
1 The Normal Probability Distribution Key Definitions Probability Density Function: An equation used to compute probabilities for continuous random variables where the output value is greater than zero
INF FALL NATURAL LANGUAGE PROCESSING. Jan Tore Lønning, Lecture 3, 1.9
INF5830 015 FALL NATURAL LANGUAGE PROCESSING Jan Tore Lønning, Lecture 3, 1.9 Today: More statistics Binomial distribution Continuous random variables/distributions Normal distribution Sampling and sampling
Introduction to Computational Finance and Financial Econometrics Descriptive Statistics
You can t see this text! Introduction to Computational Finance and Financial Econometrics Descriptive Statistics Eric Zivot Summer 2015 Eric Zivot (Copyright 2015) Descriptive Statistics 1 / 28 Outline
Overview/Outline. Moving beyond raw data. PSY 464 Advanced Experimental Design. Describing and Exploring Data The Normal Distribution
PSY 464 Advanced Experimental Design Describing and Exploring Data The Normal Distribution 1 Overview/Outline Questions-problems? Exploring/Describing data Organizing/summarizing data Graphical presentations
Lean Six Sigma: Training/Certification Books and Resources
Lean Si Sigma Training/Certification Books and Resources Samples from MINITAB BOOK Quality and Si Sigma Tools using MINITAB Statistical Software A complete Guide to Si Sigma DMAIC Tools using MINITAB Prof.