Statistics Statistical Process Control & Control Charting
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1 Statistics Statistical Process Control & Control Charting Cayman Systems International 1/22/98 1
2 Recommended Statistical Course Attendance Basic Business Office, Staff, & Management Advanced Business Selected Staff, & Management Statistical Process Control Production Floor, Production Staff & Management, All of Quality & Engineering Measurement System Analysis Production Staff & Management, All of Quality & Engineering Design of Experiment Specific Production Staff, Quality Engineers& QA Manager & Product Engineering *Your APQP Team should attend as many classes as time will allow Cayman Systems International 1/22/98 2
3 Basic Definitions Statistics: the science of collecting, analyzing, interpreting and presenting data. A Statistic is a single characteristic taken from this process. Cayman Systems International 1/22/98 3
4 Universe, Populations & Samples Universe: the collection of all elements Population: the set of objects of interest Sample: a subset of objects taken from the population Randam Sample: all possible samples of the same size have an equal chance of occuring. Cayman Systems International 1/22/98 4
5 Statistical Methodology Statistical methods are procedures for drawing conclusions about populations utilizing information provided by random samples. Regression Analysis Correlation Analysis Predictive Statistics Data Collection Statistical Methodology Organization & presentation Frequency Distribution Histograms Experimental Design Statistical Inference Descriptive Measures Central Tendency Hypothesis Testing Dispersion Cayman Systems International 1/22/98 5
6 Classification of Statistics: Descriptive statistics: the methodology of efficiently collecting, organizing, and describing data. To: Inductive Statistics: the process of drawing conclusions about unknown characteristics of a population usually based from a sample taken from the population Predictive Statistics: the process of predicting future values based on historical data. Tomorrow we will produce 5000 parts, based off of last weeks production of : 5250; 5500; 4500; 4750; 5000 Cayman Systems International 1/22/98 6
7 Four Levels of Measurements Nominal: Objects are classified into simple attributable categories with no quantitative difference between them, (Yes/No, Good/Bad). Ordinal: Objects are able to be arranged, ranked, or ordered into a meaningful attributable arrangement with no real measurement. (Yellow/Blue/Green, Square/Round/Triangle) Interval: observations are able to be ranked into exact differences between any two observations, measurements with no natural origin or zero, 80 degrees is not twice as hot as 40 degrees. A one unit scale change corresponds to a one unit change on the object being studied. Ratio: contains all the properties of interval but has a natural origin. Having a natural origin allows 25 to behalf of 50. Note that each successive level has all the properties of the previous. Cayman Systems International 1/22/98 7
8 SPC is Concerned With: Regression Analysis Correlation Analysis Predictive Statistics Data Collection Statistical Methodology Organization & presentation Frequency Distribution Histograms Experimental Design Statistical Inference Descriptive Measures Central Tendency Hypothesis Testing Dispersion Cayman Systems International 1/22/98 8
9 Data Collection Cayman Systems International 1/22/98 9
10 A SET (A) Collection of Distinct Objects Having Some Attribute in Common This is an example of a Null or Empty Set UNIVERSAL SET The Total Set of Elements of Interest Venn Diagrams A b A a Elements distinct objects in a set {a, b} SUBSET (A) portion of the set defined in some unambiguous way A b Cayman Systems International 1/22/98 10 A b a A A B A c B a c d Intersect (A B) U Common Elements of sets {a,c} f A a b d B c d MUTUALLY EXCLUSIVE Subsets A & B have no elements in common Union (A U B) Component Elements of sets {a,b,c,d} Complement ( )is the inverse of the specific set called out Complement of set A is A or { 0 } subset A = {c,d,f} f f
11 Events A Sample Space (S) is the set of all possible outcomes. An Event is any subset of a sample space. A Simple Event is any subset of the sample space to include a single outcome. S = {H, T} A Compound Event is any subset of the sample space which consists of two or more simple events. S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Cayman Systems International 1/22/98 11 Heads Tails Heads Tails Heads Tails Heads A set of Events is said to be Collectively Exhaustive if all simple events are included, (like the equation above). Tails Mutually Exclusive HHH HHT HTH HTT THH THT TTH TTT
12 Putting it all Together When gathering data for a process, we must realize that Cayman Systems International 1/22/98 12
13 Organizing Data Cayman Systems International 1/22/98 13
14 Presenting Data Cayman Systems International 1/22/98 14
15 Descriptive Measurement Cayman Systems International 1/22/98 15
16 Statistical Process Control Cayman Systems International 1/22/98 16
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