INDE 2333 ENGINEERING STATISTICS I LECTURE 1 University of Houston Dept. of Industrial Engineering Houston, TX (713)

AGENDA l Some statistics related quotes l Importance of Probability and Statistics l Basic Concepts l Treatment of data

SOME STATISTICS RELATED QUOTES l “Not all that can be counted counts, not all that counts can be counted” l In order to improve a process, you must first be able to measure it l Right the first time l There are three types of liars: n Liars, damn liars, and statisticians

IMPORTANCE OF PROBABILITY AND STATISTICS l Walter Shewhart, 1920’s l Japan’s manufacturing rise, 1950’s l U.S. Manufacturing Crisis, 1980’s n Crosby, “Quality is Free” n Juran n Deming, 14 points n Malcolm Baldridge Award n Tom Peters, Harley-Davidson l Tools n Ishikawa, Pareto, and SPC Charts n JIT n Benchmarking n 6 Sigma, Motorola

BASIC CONCEPTS l Unit n Single entity of interest n Different measures l Population n Set of all units of interest present l Sample n Subset of the population present n Measurements actually collected n Samples should random not be biased l Sample size n Number of units in the sample that are taken for measurement

EXAMPLE l Sample Mean n Average value of sample l Sample Standard Deviation n Measurement of spread or variation in measurements l Situation n Company uses automatic equipment to fill bottles n FDA requires that the bottles be filled a minimum amount n FDA fines company when bottles are not n Automatic filling processes has inherent variation

VODKA, KETCHUP, ETC ml observations FDA

TREATMENT OF DATA l General Concepts l Pareto and Dot Diagrams l Frequency Distributions l Graphs of Frequency Distributions l Descriptive Measures l Quartiles and Percentiles l X bar and s

GENERAL CONCEPTS l Raw statistical data from surveys, experiments, etc can be too overwhelming to understand l The data must be condensed and represented in a manner that is more easily understood l Graphically l Tabular or Numerical form

PARETO DIAGRAMS l Special bar chart l Based on the Pareto Principle l Ordered in descending order of interest l Allows attention to be directed on most important areas l Frequently include cost related data

PARETO CHART Gasket Ring Number Of Obs Hole Too Small Hole Too Large ChippedScratchedAll Others

PARETO CHART Gasket Ring Cost of Defects Hole Too Small Hole Too Large ChippedScratchedAll Others

DOT DIAGRAMS l Visually summarizes individual data l Check for unusual patterns l Easily identifies outliers l Differences in data sources n Machines n Personnel n Materials

DOT DIAGRAMS Deviation from nominal value in um Day Shift Night Shift

FREQUENCY DISTRIBUTIONS l Table of data l Divided in classes / categories / cells l Number of cells is usually related to the total obs l Class / category / cell limits l Class / category / cell frequencies

FREQUENCY DISTRIBUTIONS Class LimitsFrequency Total80

CUMULATIVE DISTRIBUTION l Total number of observations less than a given value

CUMULATIVE DISTRIBUTION Class LimitsCumulative Frequency Less than

GRAPHS OF FREQUENCY DISTRIBUTIONS l Histogram of cell observations l Horizontal or vertical l Size is based on observations in each cell

GRAPHS OF FREQUENCY DISTRIBUTIONS

OGIVE l Graph of cumulative distribution

OGIVE

STEM AND LEAF DISPLAYS l Smaller sets of data l Does not lose any information l Class, as well as, actually data values l Data values are listed to the right of the classes

STEM AND LEAF DISPLAY Class Limits

STEM AND LEAF DISPLAY Class Limits

DESCRIPTIVE MEASURES l Mean l Median l Mode l Minimum l Maximum l Range l Variance l Standard Deviation l Coefficient of variation

MEAN l X bar l Arithmetic average of all values l Sum of all values divided by number of values l Sample mean and population mean

MEDIAN l “Middle value” l Observations are ordered from smallest to largest l Median observation depends on number of obs l Odd number of observations n (n+1)/2 n For 5 observations, median is value of (5+1)/2=3 rd observation l Even number of observations n Median value is average of the two observations in positions n/2 and (n+2)/2 n For 6 observations, average values of 3 rd and 4 th observations

MODE l Most common value

MINIMUM l Smallest value

MAXIMUM l Largest value

RANGE l Method to measure the dispersion of the values l Largest value minus the smallest value l Can be misleading when outliers are present l Does not take into account the distribution of bunching of values l Simple and fast to calculate so commonly used in industry particularly with SPC charts

RANGE = Maximum value – minimum value

SAMPLE VARIANCE l Absolute measure of dispersion l When many values are away from the mean, the variance is large l When many values are close to the mean, the variance is small l Based on n Sample mean n Squared difference of observations from sample mean n Number of observations in sample

SAMPLE VARIANCE

SAMPLE STANDARD DEVIATION l Absolute measure of dispersion l Based on square root of variance

SAMPLE STANDARD DEVIATION

QUARTILES AND PERCENTILES l Quartiles n Groupings of 25% observations n 1 st, 2 nd, 3 rd, 4 th quartile l Percentiles n At least 100 p % are at or below value n At least 100 (1-p) % are at or above value

PROCEDURE FOR CALCULATING PERCENTILES l Order observations smallest to largest l Calculate n * p l Not an integer n Round up to next highest integer and find value l Integer n Calculate mean of kth and (k+1)th observations

BOX PLOT Minimum Maximum Median Q1 Q2