【正文】 ta
What is the mean of the sample averages? Mean ≈
What is the standard deviation of the sample averages? Sigma ≈
Is the distribution normal? What is the pvalue?
What is the relationship between the average of thesample means and the population average?
What is the relationship between the sigma of theaverages and the sigma of the individuals?The Central Limit Theorem
Formal Definition:
If random samples of n measurements are repeatedlydrawn from a population with a finite mean μμμμand a standarddeviation σ σσ σ , then, when n is large, the relative frequencyhistogram for the sample means (calculated from therepeated samples) will be approximately normal with amean μμμμand a standard deviation equal to the populationstandard deviation, σ σσ σ , divided by the square root of n.(Note: The approximation bees more precise as nincreases.)Central Limit Theorem – Exercise
From a Minitab analysis of the uniformly distributeddata:
For an exercise, verify that the Central Limit Theorem isvalid for this uniform dataVariable N Mean StDevn=1 (Individuals) 10000 n=2 (Means) 10000 n=5 (Means) 10000 n=30 (Means) 10000 相關(guān)性及簡單線性回歸:Regression amp。 storage plan (who, what, when, etc.)6. Describe the procedure and settings used to run the process7. Assemble and train the team. Define responsibilities8. Collect the data9. Analyze the data10. Verify the results11. Draw conclusions. Report results. Make remendationsInjection Molding Example1. Clearly state the objective Determine the process capability of the injection molding process Determine the major sources of noise variation2. List the X’s and Y’s to be studied Output: Thickness Inputs: Cavity (slot), cycle, sample3. Ensure measurement system capability An MSA was conducted and the system was found capable4. Describe the sampling plan One sample from each slot, five consecutive runs, four times aday 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 toreduce variation, which will increasecapability. It is always important tounderstand 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”
ManipCodeText to NumericManip Code Text to NumericMultiVari 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 acutemean shifts, changes in variability, and instability
Noise variation must be reduced or eliminated in order toleverage the important controllable variables systematicallyMultivari analysis is a very useful toolfor graphically identifying sources ofvariation, especially noise variation. Laterthis week, we will be studying correlation amp。 DetectionFMEA Examples
Plating ExampleAn aerospace plating pany was shipping product to itscustomers with nickel plating that was too thin. Parts were failingcorrosion testing at the customer.
Shipping ExampleThe shipping department of an electronics pany is unable toship an assembly without its clam shell protective packaging. Thiscauses occasional late shipments to the customer.
In the following examples, a single line from the FMEA is used as anillustration for each of the above examples. 圖形技術(shù)分析:Graphical MethodsProcess 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 isdetermined by the intentional process settingsand 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 Variation not accounted for by Positional or Cyclical2 2 2 2Temporal Cyclical Positional Noise σ σ σ ++=Graphical Analysis – Example
Injection molding is used to make a type of socket, four pieces at a time, onepiece per slot. Measurements of the sockets consist of thickness values inexcess of millimeters. The gauges measure in hundredths of amillimeter. The specification is 11 177。E matrix
Before or after the control plan, depending on the maturityof the processWhy?Warm up exercise:
You have 60 seconds to document: What would you want to know about a “defect”?
For the process:
FMEA improves the reliability of the process
An FMEA identifies problems before they occur
FMEA serves as a record of improvement amp。E matrix team.
May need to add a rep from quality, a supplier, reliability
When should the FMEA be constructed?
After the process map amp。 《6 Sigma項目運作實例》《分析階段》失效模式及后果分析