# Gage Studies for Continuous Data

Size: px
Start display at page:

## Transcription

1 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

2 Contents Contents Examples and Exercises Purpose Page Example 1 Fuel Injector Nozzle Diameters Example 2 Muffler Pipe Thickness Exercise A Assessing Consistency in Color Readings Exercise B Paper Breaking Strength Nested Gage R&R (destructive tests with small batch sizes) Example 3 Impact Testing of Stainless Steel Exercise C Improving the Measuring System Gage Linearity and Bias Study Example 4 Floor Tile Flatness Assess how the precision of a measurement system affects the variability of a measurement using a crossed gage R&R study. Design a gage R&R study to identify problems in a measurement system using a crossed gage R&R analysis and a gage run chart. Identify problems in a measurement system using a crossed gage R&R study. Determine the adequacy of a measurement system with measurements obtained from a destructive test using a crossed gage R&R study. Determine the adequacy of a measurement system with measurements obtained from a destructive test using a nested gage R&R study. Determine the adequacy of a measurement system with measurements obtained from a destructive test using a nested gage R&R study. Determine the linearity and bias of a measurement system using a gage linearity and bias study

3 Example 1 Fuel Injector Nozzle Diameters Problem A manufacturer of fuel injector nozzles installs a new digital measuring system. Investigators want to determine how well the new system measures the nozzles. Tools Gage R&R Study (Crossed) Data collection Technicians randomly sample, across all major sources of process variation (machine, time, shift, job change), 9 nozzles that represent those that are typically produced. They code the nozzles to identify the measurements taken on each nozzle. The first operator measures the 9 nozzles in random order. Then, the second operator measures the 9 nozzles in a different random order. Each operator repeats the process twice, for a total of 36 measurements. Variable Nozzle Operator Run Order Diam Description Fuel injector nozzle measured Operator who measured Original run order of the experiment Measured diameter of nozzle (microns) Note For valid measurement system analyses, you must randomly sample and measure parts. The specification for the nozzle diameters is 9012 ± 4 microns. The tolerance is 8 microns. 1-3

4 Measurement systems analysis What is measurement systems analysis Measurement systems analysis assesses the adequacy of a measurement system for a given application. When measuring the output from a process, consider two sources of variation: Part-to-part variation Measurement system variation If measurement system variation is large compared to part-to-part variation, the measurements may not provide useful information. When to use measurement systems analysis Before you collect data from your process (for example, to analyze process control or capability), use measurement system analysis to confirm that the measurement system measures consistently and accurately, and adequately discriminates between parts. Why use measurement systems analysis Measurement systems analysis answers questions such as: Can the measurement system adequately discriminate between different parts? Is the measurement system stable over time? Is the measurement system accurate throughout the range of parts? For example: Can a viscometer adequately discriminate between the viscosity of several paint samples? Does a scale need to be periodically recalibrated to accurately measure the fill weight of bags of potato chips? Does a thermometer accurately measure the temperature for all heat settings that are used in the process? 1-4

5 Gage R&R study (crossed) What is a gage R&R study (crossed) A crossed gage R&R study estimates how much total process variation is caused by the measurement system. Total process variation consists of part-to-part variation plus measurement system variation. Measurement system variation consists of: Repeatability variation due to the measuring device, or the variation observed when the same operator measures the same part repeatedly with the same device Reproducibility variation due to the measuring system, or the variation observed when different operators measure the same part using the same device When you estimate repeatability, each operator measures each part at least twice. When you estimate reproducibility, at least two operators must measure the parts. Operators measure the parts in random order, and the selected parts represent the possible range of measurements. When to use a gage R&R study (crossed) Use gage R&R to evaluate a measurement system before using it to monitor or improve a process. Use the crossed analysis when each operator measures each part (or batch, for a destructive test) multiple times. Why use a gage R&R study (crossed) This study compares measurement system variation to total process variation or tolerance. If the measurement system variation is large in proportion to total variation, the system may not adequately distinguish between parts. A crossed gage R&R study can answer questions such as: Is the variability of a measurement system small compared with the manufacturing process variability? Is the variability of a measurement system small compared with the process specification limits? How much variability in a measurement system is caused by differences between operators? Is a measurement system capable of discriminating between parts? For example: How much of the variability in the measured diameter of a bearing is caused by the caliper? How much of the variability in the measured diameter of a bearing is caused by the operator? Can the measurement system discriminate between bearings of different size? 1-5

6 Measurement system error Measurement system errors can be classified into two categories: Accuracy the difference between the part s measured and actual value Precision the variation when the same part is measured repeatedly with the same device Errors of one or both of these categories may occur within any measurement system. For example, a device may measure parts precisely (little variation in the measurements) but not accurately. Or a device may be accurate (the average of the measurements is very close to the master value), but not precise (the measurements have large variance). Or a device may be neither accurate nor precise. Accuracy The accuracy of a measurement system has three components: Bias a measure of the inaccuracy in the measurement system; the difference between the observed average measurement and a master value Linearity a measure of how the size of the part affects the bias of the measurement system; the difference in the observed bias values through the expected range of measurements Stability a measure of how well the system performs over time; the total variation obtained with a particular device, on the same part, when measuring a single characteristic over time Precision accurate and precise inaccurate but precise accurate but imprecise inaccurate and imprecise Precision, or measurement variation, has two components: Repeatability variation due to the measuring device, or the variation observed when the same operator measures the same part repeatedly with the same device Reproducibility variation due to the measuring system, or the variation observed when different operators measure the same part using the same device 1-6

7 Assessing the measurement system Use a Gage R&R study (crossed) to assess: How well the measuring system can distinguish between parts Whether the operators measure consistently Tolerance The specification limits for the nozzle diameters are 9012 ± 4 microns. In other words, the nozzle diameter is allowed to vary by as much as 4 microns in either direction. The tolerance is the difference between the specification limits: = 8 microns. By entering a value in Process tolerance, you can estimate what proportion of the tolerance is taken up by the variation in the measurement system. Gage R&R Study (Crossed) 1 Choose Stat Quality Tools Gage Study Gage R&R Study (Crossed). 2 Complete the dialog box as shown below. 3 Click Options. 4 Under Process tolerance, choose Upper spec - Lower spec and type 8. 5 Check Draw graphs on separate graphs, one graph per page. 6 Click OK in each dialog box. 1-7

8 Analysis of variance tables Minitab uses the analysis of variance (ANOVA) procedure to calculate variance components, and then uses those components to estimate the percent variation due to the measuring system. The percent variation appears in the gage R&R table. The two-way ANOVA table includes terms for the part (Nozzle), operator (Operator), and operator-by-part interaction (Nozzle Operator). If the p-value for the operator-by-part interaction is 0.25, Minitab generates a second ANOVA table that omits the interaction term from the model. To alter the default Type I error rate of 0.25, click Options in the main dialog box. In Alpha to remove interaction term, type a new value (for example, 0.3). Here, the p-value for Nozzle Operator is Therefore, Minitab removes the interaction term from the model and generates a second ANOVA table. Gage R&R Study - ANOVA Method Two-Way ANOVA Table With Interaction Source DF SS MS F P Nozzle Operator Nozzle * Operator Repeatability Total Alpha to remove interaction term = 0.25 Two-Way ANOVA Table Without Interaction Source DF SS MS F P Nozzle Operator Repeatability Total

9 Variance components Minitab also calculates a column of variance components (VarComp) and uses the values to calculate %Gage R&R with the ANOVA method. The gage R&R table breaks down the sources of total variability: Total Gage R&R consists of: Repeatability the variability from repeated measurements by the same operator. Reproducibility the variability when the same part is measured by different operators. (This can be further divided into operator and operator-by-part components.) Part-to-Part the variability in measurements across different parts. Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Why use variance components? Use variance components to assess the amount of variation that each source of measurement error and the part-to-part differences contribute to the total variation. Ideally, differences between parts should account for most of the variability; variability from repeatability and reproducibility should be very small. 1-9

10 Percent contribution %Contribution is based on the estimates of the variance components. Each value in VarComp is divided by the Total Variation, and then multiplied by 100. For example, to calculate the %Contribution for Part-to-Part, divide the VarComp for Part-to-Part by the Total Variation and multiply by 100: ( / ) Therefore, 99.2% of the total variation in the measurements is due to the differences between parts. This high %Contribution is considered very good. When %Contribution for Part-to-Part is high, the system can distinguish between parts. Using variance versus standard deviation Because %Contribution is based on the total variance, the column of values adds up to 100%. Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Process tolerance = 8 Study Var %Study Var %Tolerance Source StdDev (SD) (6 * SD) (%SV) (SV/Toler) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Number of Distinct Categories = 15 Minitab also displays columns with percentages based on the standard deviation (or square root of variance) of each term. These columns, labeled %StudyVar and %Tolerance, typically do not add up to 100%. Because the standard deviation uses the same units as the part measurements and the tolerance, it allows for meaningful comparisons. Note Minitab displays the column %Process if you enter a historical standard deviation in Options. 1-10

11 Percent study variation Use %StudyVar to compare the measurement system variation to the total variation. Minitab calculates %StudyVar by dividing each value in StudyVar by Total Variation and then multiplying by 100. %StudyVar for gage R&R is ( / ) %. Minitab calculates StudyVar as 6 times the standard deviation for each source. Gage R&R Study Var %Study Var %Tolerance Source StdDev (SD) (6 * SD) (%SV) (SV/Toler) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Number of Distinct Categories = 15 6s process variation Typically, process variation is defined as 6s, where s is the standard deviation, as an estimate of σ. When data are normally distributed, approximately 99.73% of the data fall within 6 standard deviations (± 3 standard deviations from the mean), and approximately 99% of the data fall within 5.15 standard deviations (± standard deviations from the mean). Note The Automotive Industry Action Group (AIAG) recommends the use of 6s in gage R&R studies. 1-11

12 Percent tolerance Comparing the measurement system variation with the tolerance is often informative. If you enter the tolerance, Minitab calculates %Tolerance, which compares measurement system variation to specifications. %Tolerance is the percentage of the tolerance taken up by the measurement system variability. Note If you do not enter a tolerance, the %Tolerance column does not appear in the output. If your measurement specification is single-sided, you do not have a tolerance range for the analysis. Gage R&R Study Var %Study Var %Tolerance Source StdDev (SD) (6 * SD) (%SV) (SV/Toler) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Number of Distinct Categories = 15 Minitab divides the measurement system variation (6 SD for Total Gage R&R) by the tolerance. Minitab multiplies the resulting proportion by 100 and reports it as %Tolerance. %Tolerance for gage R&R is ( /8) % Which metric to use Use %Tolerance or %StudyVar to evaluate the measuring system, depending on the measuring system. If the measurement system is used for process improvement (reducing part-to-part variation), %StudyVar is a better estimate of measurement precision. If the measurement system evaluates parts relative to specifications, %Tolerance is a more appropriate metric. 1-12

13 Total Gage R&R The %Study Var results indicate that the measurement system accounts for less than 10% of the overall variation in this study. The %Tolerance results indicate that the measurement system variation is less than 10% of the tolerance width. Total Gage R&R: %Study Var 8.97 %Tolerance 8.10 Remember that Minitab uses different divisors to calculate %Tolerance and %Study Var. Because the range for tolerance (8) is greater than the total study variation ( ) in this example, the %Tolerance is lower. Gage R&R Study Var %Study Var %Tolerance Source StdDev (SD) (6 * SD) (%SV) (SV/Toler) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Number of Distinct Categories =

14 Number of distinct categories The Number of Distinct Categories value estimates how many separate groups of parts the system can distinguish. Minitab calculates the number of distinct categories that can be reliably observed by: S part S measuring system Minitab truncates this value to the integer except when the value calculated is less than 1. In that case, Minitab sets the number of distinct categories equal to 1. Number of categories Means < 2 The system cannot discriminate between parts. = 2 Parts can be divided into high and low groups, as in attributes data. 5 The system is acceptable (according to the AIAG) and can distinguish between parts. Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Process tolerance = 8 Study Var %Study Var %Tolerance Source StdDev (SD) (6 * SD) (%SV) (SV/Toler) Total Gage R&R Repeatability Reproducibility Operator Part-To-Part Total Variation Number of Distinct Categories = 15 Here, the number of distinct categories is 15, which indicates the system can distinguish between parts extremely well. Note The AIAG recommends that the number of distinct categories be 5 or more. See [1] in the reference list. 1-14

15 Components of variation The Components of Variation chart graphically represents the gage R&R table in the Session window output. Note In the Options subdialog box, you can choose to display these graphs on separate pages. Each cluster of bars represents a source of variation. By default, each cluster has two bars that correspond to %Contribution and %StudyVar. If you add a tolerance or historical standard deviation, a bar for %Tolerance or %Process appears. In a good measurement system, the largest component of variation is part-to-part variation. If, instead, large variation is attributed to the measurement system, the measurement system may need correcting. For the nozzle data, the difference in parts accounts for most of the variation. Note For the %Study and %Tolerance measures, the Repeat and Reprod bars may not add up to the Gage R&R bar because these percentages are based on standard deviations, not on variances. 1-15

16 R chart The R chart is a control chart of ranges that graphically displays operator consistency. An R chart consists of: Plotted points, which represent, for each operator, the difference between the largest and smallest measurements of each part. If the measurements are the same, the range = 0. Minitab plots the points by operator so that you can compare the consistency of each operator. Center line, which is the grand average of the ranges (the average of all the subgroup ranges). Control limits (UCL and LCL) for the subgroup ranges. Minitab uses the within-subgroup variation to calculate these limits. If any points on the R-chart fall above the upper control limit (UCL), the operator is not consistently measuring the parts. The UCL takes into account the number of times each operator measures a part. If operators measure consistently, the ranges are small relative to the data and the points fall within the control limits. Note Minitab displays an R chart when the number of replicates is less than 9; otherwise, Minitab displays an S chart. 1-16

17 Xbar chart The Xbar chart compares the part-to-part variation to the repeatability component. The Xbar chart consists of: Plotted points, which represent, for each operator, the average measurement of each part. Center line, which is the overall average for all part measurements by all operators. Control limits (UCL and LCL), which are based on the number of measurements in each average and the repeatability estimate. Because the parts chosen for a Gage R&R study should represent the entire range of possible parts, this graph ideally shows lack-of-control. It is desirable to observe more variation between part averages than what is expected from repeatability variation alone. For these data, many points are above or below the control limits. These results indicate that part-to-part variation is much greater than measurement device variation. 1-17

18 Operator by part interaction The Operator Nozzle Interaction plot displays the average measurements by each operator for each part. Each line connects the averages for a single operator. Ideally, the lines are virtually identical and the part averages vary enough so that differences between parts are clear. This pattern Lines are virtually identical. One line is consistently higher or lower than the others. Lines are not parallel, or they cross. Indicates Operators are measuring the parts similarly. One operator is measuring parts consistently higher or lower than the other operators. An operator s ability to measure a part depends on which part is being measured (an interaction exists between Operator and Part). Here, the lines follow one another closely, and the differences between parts are clear. The operators seem to be measuring parts similarly. Note The significance of this interaction effect was shown in the ANOVA table on page 1-8. The p-value for the interaction is 0.707, so the interaction is not significant at the α = 0.05 level. 1-18

19 Measurements by operator The By Operator plot can help you to determine whether measurements and variability are consistent across operators. The By Operator graph shows all of the study measurements, arranged by operator. When there are nine or fewer measurements for each operator, dots represent the measurements. When there are more than nine measurements for each operator, Minitab displays a boxplot. For both types of graphs, black circles represent the means, and a line connects them. Asterisks indicate potential outliers. If the line is Parallel to the x-axis Not parallel to the x-axis Then The operators are measuring the parts similarly, on average. The operators are measuring the parts differently, on average. Also use this graph to assess whether the overall variability in part measurements for each operator is the same: Is the spread in the measurements similar? Do one operator s measures vary more than the others? Here, the operators appear to be measuring the parts consistently, with approximately the same variation. 1-19

20 Measurements by part The By Nozzle plot shows all of the measurements in the study arranged by part. Minitab represents the measurements by empty circles and the means by solid circles. The line connects the average measurements for each part. Ideally: Multiple measurements for each part show little variation (the empty circles for each part are close together). Averages vary enough so that differences between parts are clear. 1-20

21 Final considerations Summary and conclusions The nozzle measuring system contributes very little to the overall variation, as confirmed by both the gage R&R table and graphs. The variation that is due to the measuring system, either as a percent of study variation or as a percent of tolerance, is less than 10%. According to AIAG guidelines, this system is acceptable. Additional considerations Graph patterns that show low measuring-system variation: Graph R-bar Xbar chart By part By operator Operator by part Pattern Small average range Narrow control limits and many points out of control Very similar measurements for each part across all operators, and clear differences between parts Straight horizontal line Overlaid lines AIAG guidelines for the gage R&R table are: %Tolerance, %StudyVar %Process Under 10% System is Acceptable 10% to 30% Potentially acceptable (depends on the criticality of the measurement, costs, risks, etc.) Over 30% Source: [1] in the reference list. Not acceptable Gage R&R (crossed) studies, like other measurement systems analysis (MSA) procedures, are designed experiments. For valid results, randomization and representative sampling are essential. 1-21

### Assessing Measurement System Variation

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

### Statistical Process Control (SPC) Training Guide

Statistical Process Control (SPC) Training Guide Rev X05, 09/2013 What is data? Data is factual information (as measurements or statistics) used as a basic for reasoning, discussion or calculation. (Merriam-Webster

### ABSORBENCY OF PAPER TOWELS

ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?

### Measurement System Analysis for Quality Improvement. U sing Gage R&R Study at Company XYZ. Bodin Singpai. A Research Paper

Measurement System Analysis for Quality Improvement U sing Gage R&R Study at Company XYZ By Bodin Singpai A Research Paper Submitted in Partial Fulfillment of the Requirements for the Master of Science

### Variables Control Charts

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

### Confidence Intervals for Cp

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

### Scatter Plots with Error Bars

Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each

### Confidence Intervals for One Standard Deviation Using Standard Deviation

Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from

### Analysis of Variance. MINITAB User s Guide 2 3-1

3 Analysis of Variance Analysis of Variance Overview, 3-2 One-Way Analysis of Variance, 3-5 Two-Way Analysis of Variance, 3-11 Analysis of Means, 3-13 Overview of Balanced ANOVA and GLM, 3-18 Balanced

### Instruction Manual for SPC for MS Excel V3.0

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

### THE PROCESS CAPABILITY ANALYSIS - A TOOL FOR PROCESS PERFORMANCE MEASURES AND METRICS - A CASE STUDY

International Journal for Quality Research 8(3) 399-416 ISSN 1800-6450 Yerriswamy Wooluru 1 Swamy D.R. P. Nagesh THE PROCESS CAPABILITY ANALYSIS - A TOOL FOR PROCESS PERFORMANCE MEASURES AND METRICS -

### Chapter 2: Frequency Distributions and Graphs

Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct

### One-Way ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate

1 One-Way ANOVA using SPSS 11.0 This section covers steps for testing the difference between three or more group means using the SPSS ANOVA procedures found in the Compare Means analyses. Specifically,

### EXCEL Analysis TookPak [Statistical Analysis] 1. First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it:

EXCEL Analysis TookPak [Statistical Analysis] 1 First of all, check to make sure that the Analysis ToolPak is installed. Here is how you do it: a. From the Tools menu, choose Add-Ins b. Make sure Analysis

### Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

### Exercise 1.12 (Pg. 22-23)

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.

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### Describing, Exploring, and Comparing Data

24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

### Doing Multiple Regression with SPSS. In this case, we are interested in the Analyze options so we choose that menu. If gives us a number of choices:

Doing Multiple Regression with SPSS Multiple Regression for Data Already in Data Editor Next we want to specify a multiple regression analysis for these data. The menu bar for SPSS offers several options:

### Six Sigma Acronyms. 2-1 Do Not Reprint without permission of

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

### Confidence Intervals for Cpk

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

### MBA 611 STATISTICS AND QUANTITATIVE METHODS

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

### 1.5 Oneway Analysis of Variance

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

### STATISTICAL QUALITY CONTROL (SQC)

Statistical Quality Control 1 SQC consists of two major areas: STATISTICAL QUALITY CONTOL (SQC) - Acceptance Sampling - Process Control or Control Charts Both of these statistical techniques may be applied

### Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY

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

### Repeatability and Reproducibility

Repeatability and Reproducibility Copyright 1999 by Engineered Software, Inc. Repeatability is the variability of the measurements obtained by one person while measuring the same item repeatedly. This

### Diagrams and Graphs of Statistical Data

Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in

### 46.2. Quality Control. Introduction. Prerequisites. Learning Outcomes

Quality Control 46.2 Introduction Quality control via the use of statistical methods is a very large area of study in its own right and is central to success in modern industry with its emphasis on reducing

### Gestation Period as a function of Lifespan

This document will show a number of tricks that can be done in Minitab to make attractive graphs. We work first with the file X:\SOR\24\M\ANIMALS.MTP. This first picture was obtained through Graph Plot.

### Control Charts for Variables. Control Chart for X and R

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

### Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data

Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable

### CALCULATIONS & STATISTICS

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

### SPSS Manual for Introductory Applied Statistics: A Variable Approach

SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All

### Appendix 2.1 Tabular and Graphical Methods Using Excel

Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.

### LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### Process Capability Analysis Using MINITAB (I)

Process Capability Analysis Using MINITAB (I) By Keith M. Bower, M.S. Abstract The use of capability indices such as C p, C pk, and Sigma values is widespread in industry. It is important to emphasize

### SPSS/Excel Workshop 3 Summer Semester, 2010

SPSS/Excel Workshop 3 Summer Semester, 2010 In Assignment 3 of STATS 10x you may want to use Excel to perform some calculations in Questions 1 and 2 such as: finding P-values finding t-multipliers and/or

### Confidence Intervals for the Difference Between Two Means

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

### Chapter 7. One-way ANOVA

Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

### An Honest Gauge R&R Study

006 ASQ/ASA Fall Technical Conference Manuscript No. 189 An Honest Gauge R&R Study Donald J. Wheeler January 009 Revision In a 1994 paper Stanley Deming reported that when he did his literature search

### 12: Analysis of Variance. Introduction

1: Analysis of Variance Introduction EDA Hypothesis Test Introduction In Chapter 8 and again in Chapter 11 we compared means from two independent groups. In this chapter we extend the procedure to consider

### Content Sheet 7-1: Overview of Quality Control for Quantitative Tests

Content Sheet 7-1: Overview of Quality Control for Quantitative Tests Role in quality management system Quality Control (QC) is a component of process control, and is a major element of the quality management

### 2 Sample t-test (unequal sample sizes and unequal variances)

Variations of the t-test: Sample tail Sample t-test (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing

### SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS

SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing

### Statistical Process Control OPRE 6364 1

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

### Six Sigma Workshop Fallstudie och praktisk övning

Six Sigma Workshop Fallstudie och praktisk övning 0-fels LEAN-konferens, Folkets Hus 05-NOV-2013 Lars Öst GE business segments Technology Infrastructure Energy Infrastructure GE Capital NBC Universal Healthcare

### Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk

Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:

### Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

### Method Validation/Verification. CAP/CLIA regulated methods at Texas Department of State Health Services Laboratory

Method Validation/Verification CAP/CLIA regulated methods at Texas Department of State Health Services Laboratory References Westgard J. O.: Basic Method Validation, Westgard Quality Corporation Sarewitz

### The Chi-Square Test. STAT E-50 Introduction to Statistics

STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

### Probability Distributions

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

### Minitab 17 Statistical Software

Minitab 17 Statistical Software Contents Part 1. Introduction to Minitab 17 Part 2. New Features in 17.2 Part 3. Problems Resolved in Minitab 17.2 Part 4. New Features in 17.3 Part 5. Problems Resolved

Table of Contents Introduction to Minitab...2 Example 1 One-Way ANOVA...3 Determining Sample Size in One-way ANOVA...8 Example 2 Two-factor Factorial Design...9 Example 3: Randomized Complete Block Design...14

### THE OPEN SOURCE SOFTWARE R IN THE STATISTICAL QUALITY CONTROL

1. Miriam ANDREJIOVÁ, 2. Zuzana KIMÁKOVÁ THE OPEN SOURCE SOFTWARE R IN THE STATISTICAL QUALITY CONTROL 1,2 TECHNICAL UNIVERSITY IN KOŠICE, FACULTY OF MECHANICAL ENGINEERING, KOŠICE, DEPARTMENT OF APPLIED

### SPC Response Variable

SPC Response Variable This procedure creates control charts for data in the form of continuous variables. Such charts are widely used to monitor manufacturing processes, where the data often represent

### STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI

STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members

### Main Effects and Interactions

Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly

### Final Exam Practice Problem Answers

Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### What Are the Differences?

Comparison between the MSA manual and VDA Volume 5 What Are the Differences? MSA is short for Measurement Systems Analysis. This document was first published by the Automotive Industry Action Group (AIAG)

### Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

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

### Chapter 4 and 5 solutions

Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,

### Section 13, Part 1 ANOVA. Analysis Of Variance

Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability

### 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

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

### TI-Inspire manual 1. Instructions. Ti-Inspire for statistics. General Introduction

TI-Inspire manual 1 General Introduction Instructions Ti-Inspire for statistics TI-Inspire manual 2 TI-Inspire manual 3 Press the On, Off button to go to Home page TI-Inspire manual 4 Use the to navigate

### Statistics courses often teach the two-sample t-test, linear regression, and analysis of variance

2 Making Connections: The Two-Sample t-test, Regression, and ANOVA In theory, there s no difference between theory and practice. In practice, there is. Yogi Berra 1 Statistics courses often teach the two-sample

### Exploratory data analysis (Chapter 2) Fall 2011

Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,

### Using SPSS, Chapter 2: Descriptive Statistics

1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,

### Common Tools for Displaying and Communicating Data for Process Improvement

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

### Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)

Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume

### Chapter 5 Analysis of variance SPSS Analysis of variance

Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,

### Drawing a histogram using Excel

Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

### Individual Moving Range (I-MR) Charts. The Swiss Army Knife of Process Charts

Individual Moving Range (I-MR) Charts The Swiss Army Knife of Process Charts SPC Selection Process Choose Appropriate Control Chart ATTRIBUTE type of data CONTINUOUS DEFECTS type of attribute data DEFECTIVES

### Lean Six Sigma Black Belt-EngineRoom

Lean Six Sigma Black Belt-EngineRoom Course Content and Outline Total Estimated Hours: 140.65 *Course includes choice of software: EngineRoom (included for free), Minitab (must purchase separately) or

### Northumberland Knowledge

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

### Mixed 2 x 3 ANOVA. Notes

Mixed 2 x 3 ANOVA This section explains how to perform an ANOVA when one of the variables takes the form of repeated measures and the other variable is between-subjects that is, independent groups of participants

### Statistical Process Control Basics. 70 GLEN ROAD, CRANSTON, RI 02920 T: 401-461-1118 F: 401-461-1119 www.tedco-inc.com

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

### Descriptive Statistics

Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web

### SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)

Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer

### IBM SPSS Direct Marketing 23

IBM SPSS Direct Marketing 23 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 23, release

### Measurement with Ratios

Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

### Process Quality. BIZ2121-04 Production & Operations Management. Sung Joo Bae, Assistant Professor. Yonsei University School of Business

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

### Consider a study in which. How many subjects? The importance of sample size calculations. An insignificant effect: two possibilities.

Consider a study in which How many subjects? The importance of sample size calculations Office of Research Protections Brown Bag Series KB Boomer, Ph.D. Director, boomer@stat.psu.edu A researcher conducts

### How To Run Statistical Tests in Excel

How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting

### UNDERSTANDING THE TWO-WAY ANOVA

UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables

### IBM SPSS Direct Marketing 22

IBM SPSS Direct Marketing 22 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 22, release

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application

### 1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

### FREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5

Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities

### EXPERIMENTAL ERROR AND DATA ANALYSIS

EXPERIMENTAL ERROR AND DATA ANALYSIS 1. INTRODUCTION: Laboratory experiments involve taking measurements of physical quantities. No measurement of any physical quantity is ever perfectly accurate, except

### Chapter 2: Descriptive Statistics

Chapter 2: Descriptive Statistics **This chapter corresponds to chapters 2 ( Means to an End ) and 3 ( Vive la Difference ) of your book. What it is: Descriptive statistics are values that describe the

### There are six different windows that can be opened when using SPSS. The following will give a description of each of them.

SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet

### University of Arkansas Libraries ArcGIS Desktop Tutorial. Section 2: Manipulating Display Parameters in ArcMap. Symbolizing Features and Rasters:

: Manipulating Display Parameters in ArcMap Symbolizing Features and Rasters: Data sets that are added to ArcMap a default symbology. The user can change the default symbology for their features (point,