【正文】 Correlation Introduction  Used for quantitative variables (X’s and Y’s) For review: What is the focus of Six Sigma? Q. What does this equation represent? A. A mathematical model of a process Purpose of Regression: to predict Y from a setting of x Examples: Distance = f(acceleration, initial velocity, time) 中國(guó)最大的管 理 資料下載中心 (收集 \整理 . 大量免費(fèi)資源共享 ) 第 21 頁(yè) 共 67 頁(yè) Product yield = f(concentrations of reactants) Hardness = f(alloy, anneal temperature) ) ( x f Y = Remember, the focus of Six Sigma is to determine the defining equation of the process. It is to identify the important input variables, determine the relationship to the outputs, determine the optimum values of the critical inputs and then control the inputs at the optimum settings. To do this, the Black Belt must know the relationship between the inputs and the outputs. This module discusses linear modeling techniques for identifying the relationship between continuous variable inputs and continuous variable outputs. A Simple Linear Model Linear equations require continuous input and output variables. One other assumption is that the independent variable (input) is known and fixed and that all of the variation is in the dependent variable (output). This is not usually the case, but often the inputs are settings on dials or gauges or software that seems fixed and invariable. Many times the variation in the output is a function of the inability of the input controller to hold the input at the same value. Collecting Data (y amp。 storage plan (who, what, when, etc.) 6. Describe the procedure and settings used to run the process 7. Assemble and train the team. Define responsibilities 8. Collect the data 9. Analyze the data 10. Verify the results 11. Draw conclusions. Report results. Make remendations Injection Molding Example 1. Clearly state the objective Determine the process capability of the injection molding process 中國(guó)最大的管 理 資料下載中心 (收集 \整理 . 大量免費(fèi)資源共享 ) 第 18 頁(yè) 共 67 頁(yè) Determine the major sources of noise variation 2. List the X’s and Y’s to be studied Output: Thickness Inputs: Cavity (slot), cycle, sample 3. Ensure measurement system capability An MSA was conducted and the system was found capable 4. Describe the sampling plan One sample from each slot, five consecutive runs, four times a day for five days. 5. Describe the data collection amp。 6 What is the shortterm process capability? What is the longterm process capability? Are these good or bad values? Remember, one goal of Six Sigma is to reduce variation, which will increase capability. It is always important to understand the process capability. Preparing Data for Marginal Plot by “Slot” Marginal plots require both variables to be defined numerically  We need to convert “Slot” to a numeric column first  Step 1: Convert “Slot” 中國(guó)最大的管 理 資料下載中心 (收集 \整理 . 大量免費(fèi)資源共享 ) 第 17 頁(yè) 共 67 頁(yè) ManipCodeText to Numeric Manip Code Text to Numeric MultiVari Analysis – Defined A graphical analysis tool Uses logical subgrouping Analyzes the effects of discrete X’s on continuous Y’s A capability and process analysis tool Data collected for a relatively short time  Data can estimate capability, stability, and y = f(x)’s Major focus: study uncontrolled noise variation first Variation in noise variables produces chronic and acute mean shifts, changes in variability, and instability Noise variation must be reduced or eliminated in order to leverage the important controllable variables systematically Multivari analysis is a very useful tool for graphically identifying sources of variation, especially noise variation. Later this week, we will be studying correlation amp。 Detection FMEA Examples Plating Example An aerospace plating pany was shipping product to its customers with nickel plating that was too thin. Parts were failing corrosion testing at the customer. Shipping Example The shipping department of an electronics pany is unable to ship an assembly without its clam shell protective packaging. This causes occasional late shipments to the customer. In the following examples, a single line from the FMEA is used as an illustration for each of the above examples. 圖形技術(shù)分析 : Graphical Methods Process Variation Noise variation from discrete inputs Different operators, machines, setups Different days, shifts Different batches, mixtures, raw materials Noise variation from continuous inputs Ambient temperature, humidity, pressure Wear, drift, erosion, chemical depletion ) ,..., , ( 2 1 k Process x x x f y =) ,..., , ( 2 1 k Noise n n n f + Intentional Unwanted The equation just means that any output is determined by the intentional process settings and the unwanted noise variation. Common Classification of Noise Variables Positional (within part variation) Variation within a single production unit Thickness variation across a plated part Variation across a unit containing many parts Variation across a semiconductor wafer with many die Variation by position in a batch process Cavitytocavity variations in an injection molding operation Cyclical (parttopart variation) Variation between consecutive production units Batchtobatch average differences – consecutive batches Temporal (timetotime variation) Shifttoshift, DaytoDay, Setuptosetup