L Berkley Davis Copyright 2009 MER301: Engineering Reliability1 LECTURE 2: Chapter 1: Role of Statistics in Engineering Chapter 2: Data Summary and Presentation

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 2 Summary of Lecture 2 Topics  Summary of Chapter 1 Topics Engineering Method Statistics in Engineering Collection of Engineering Data Observing Processes over Time  Summary of Chapter 2 Topics Populations and Samples Data Displays  Dot Diagrams  Histograms  Box and Whisker Plots  Scatter plots Central Point and Spread  Median,Quartiles,Interquartile range  Means, Variances and Standard Deviations

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 3 Engineering Method  Successful design and introduction of a new product is dependent on a rigorous engineering process that is executed with discipline and attention to detail  Design for Six Sigma is one such process that allows the designer to explicitly account for the effects of variation

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 4

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 5 Critical to Quality Variables(CTQ’s)  Products/Processes have measures of performance, operational flexibility, reliability, and cost that are directly seen by the end customer These are called CTQ variables(Big Y’s) and are the ultimate measurement of an engineered product or process Big Y’s are functions of other variables that the engineer must control in the design(control variables) or allow to be uncontrolled(noise) The Designer must understand Product and Process CTQ’s

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 6 Measurement System Errors…  Total Error in a measurement is defined as the difference between the True Value and the Measured Value of Y Accuracy of Measurement System is defined as the difference between a Standard Reference and the Average Observed Measurement  Two general categories of error – Bias or Accuracy Error and Precision Error (excluding gross blunders)  Total Error = Bias Error + Precision Error for independent random variables  Measurement System Error is described by Average Bias Error (Mean Shift)and a statistical estimate of the Precision Error (Variance) Measurement System Analysis is a Fundamental Part of Every Experiment

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 7 Not Accurate, Not PreciseAccurate, Not Precise Not Accurate, PreciseAccurate, Precise Experimental Gage R&R - Precision and Accuracy

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 8 Engineering Models  Mathematical Model:Quantitative description of a system/event with descriptive equations Physics Based(Mechanistic) Models built from first principles Empirical Models built from Data and Engineering Knowledge Both Physics Based and Empirical Models can be either Deterministic or Statistical/Probabilistic  Deterministic For Y=fn(x’s), model does not explicitly account for variation  Probabilistic/Statistical Accounts for variation in x’s, by letting each x be described by a mean value and a variation

L Berkley Davis Copyright 2009 Engineering Models

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 10 Statistics in Engineering…  Engineers work with data sets and need methods and tools to summarize data and draw conclusions Descriptive statistics to present data in an understandable manner Measures of central points and variation to characterize and data  Engineers deal with variation in all of their work. Variation arises from: Real variation caused by parts tolerance, materials property variations or operational differences Apparent or Gage R&R variation from measurement system error  A consequence of variation is that engineers must deal with probability in product assembly, product performance, and product reliability  Statistical Design Methods are needed to deal with probabilistic design

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 11 Statistical Methods/Tools…  Probability –The Laws of Chance  Descriptive Statistics- Analytical and graphical methods that allow us to describe or picture a data set  Inferential Statistics- Methods by which conclusions can be drawn about a large group of objects based on observing only a portion of the objects  Model Building- Development of prediction equations(transfer functions) from experimental data

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 12 Uses of Statistical Tools  Establishing design targets from CTQ’s  Data collection(sampling,gage R&R,DOE) Sampling strategy Analysis of data(means,variances, generation of transfer functions, descriptive statistics) Statistical Inference/hypothesis testing  Model Building/Optimization/Validation  Statistical Design/Process Control

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 13 Collection of Engineering Data

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 14 Designed Factorial Experiments  Several process variables(factors) and their ranges are identified as being significant in a Factorial Study

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 15 Observing Processes over Time

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 16 Summary of Chapter 2 Topics  Populations and Samples  Data Displays Dot Diagrams Histograms Box and Whisker Plots Scatter plots  Central Point and Spread Median,Quartiles,Interquartile range Means, Variances and Standard Deviations

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 17 Populations and Samples  Population- entire group of objects being studied  Sample- collection of objects from which data are actually gathered Sample may be all or part of the entire population Sample Data are used to make predictions about the Population Validity of the predictions depends on how the Sample is taken and how big it is…  Both Populations and Samples are characterized by the Central Point and the Spread of the variables being studied Populations are what we want to know about- Sample data are what we get …..

L Berkley Davis Copyright 2009 Data Displays  Dot Diagrams  Histograms  Box and Whisker  Scatter Plots MER301: Engineering Reliability Lecture 2 18

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 19 Pareto Charts  Widely used in process analysis to identify the most frequent failures

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 20 Measures of Central Point and Spread  Percentile Ordered ranking of Data  Median – measure of central tendency Not sensitive to Outliers  Quartiles – divides data into 4 equal parts First or lower, second, third or upper  Interquartile Range – measure of Spread

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 21 Central point-Population Mean  For a population of size N….

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 22 What is Variance?  Variance is a quantitative measure of the square of the difference between each measurement in a sample and the mean of the sample.  Comparison of the(square root of)variance to the mean gives information as to how well a process is controlled

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 23 Spread-Population Variance  Measure of variation in the population

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 24 Central Point-Sample Mean  n observations in a sample are denoted by x 1, x 2, …, x n,

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 25 Central Point-Sample Median  n observations in a sample are denoted by x 1, x 2, …, x n,

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 26 Spread-Sample Variance  Measure of variation in the sample  Note n-1 rather than N as divisor

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 27 Sample Mean and Variance…Rank Order Median..Histogram and Box Plot…

L Berkley Davis Copyright 2009 MER301: Engineering Reliability Lecture 2 28 Summary of Lecture 2 Topics  Summary of Chapter 1 Topics Engineering Method Statistics in Engineering Collection of Engineering Data Observing Processes over Time  Summary of Chapter 2 Topics Populations and Samples Data Displays  Dot Diagrams  Histograms  Box and Whisker Plots  Scatter plots Central Point and Spread  Median,Quartiles,Interquartile range  Means, Variances and Standard Deviations