customers with nickel plating that was too thin. Parts were failing corrosion testing at the customer. Shipping Example
The shipping department of an electronics company 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.
图形技术分析:
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
Cavity-to-cavity variations in an injection molding operation Cyclical (part-to-part variation)
Variation between consecutive production units
Batch-to-batch average differences – consecutive batches Temporal (time-to-time variation)
Shift-to-shift, Day-to-Day, Setup-to-setup
Variation not accounted for by Positional or Cyclical
2 2 2 2
Temporal Cyclical Positional Noise σ σ σ ++=
Graphical Analysis – Example
Injection molding is used to make a type of socket, four pieces at a time, one
piece per slot. Measurements of the sockets consist of thickness values in
excess of 5.00 millimeters. The gauges measure in hundredths of a millimeter. The specification is 11 ± 6.
Four times a day the supervisor would go to the press and gather up the
parts produced by five consecutive cycles of the press. Since each cycle
produced four parts, he would have 20 parts to measure every two hours.
The supervisor kept track of the cycle and the cavity from which each part
came and wrote his twenty measurements in an array like this:
The supervisor collected samples four times a day for five days (20 samples
total, 20 parts per sample). Calculate the process capability and use a Multi-Vari
chart to help determine sources of variation. A BCDE
S1 18 19 20 19 21 S2 13 16 14 13 13 S3 10 11 13 10 13 S4 11 12 13 13 13
Exercise: Determine Capability
Using Minitab, analyze the Thick data in SocketData.mtw for process capability Remember, the specifications are: 11 ± 6 What is the short-term process capability? What is the long-term 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”
Manip>Code>Text to Numeric Manip > Code > Text to Numeric
Multi-Vari Analysis – Defined A graphical analysis tool Uses logical sub-grouping
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 Multi-vari analysis is a very useful tool for graphically identifying sources of
variation, especially noise variation. Later this week, we will be studying correlation & regression (an analysis of the effect of
continuous X’s on continuous Y’s), analysis of variance (ANOVA) and the General Linear Model (GLM), both numerical analyses of variance data.
Multi-vari analyses will help identify the
variation sources with the purpose of reducing or eliminating them.
A Multi-Vari Plan
1. Clearly state the objective
2. List the X’s and Y’s to be studied
3. Ensure measurement system capability
4. Describe the sampling plan
5. Describe the data collection & 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 recommendations Injection Molding Example 1. Clearly state the objective
Determine the process capability of the injection molding process 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 & storage plan (who, what, when, where, etc.)
The supervisor collected the data and entered it in a worksheet 6. Describe the procedure and settings used to run the process Standard, constant process settings.
7. Assemble and train the team. Define responsibilities. For a small project, the supervisor did all the work 8. Collect the data.
The data are in Minitab worksheet SocketData.mtw 9. Analyze the data
Analysis is on the following slides
中心限理论:
Central Limit Theorem
Q: Why Are So Many Distributions Normal? Why is something this complicated so common?
Science has shown us that variables that vary randomly are distributed normally. So a normal distribution is actually a random distribution.
Another reason why some distributions are normally distributed is because measurements are actually averages over time of many sub-measurements. The single measurement that we think we are making is actually the average (or sum) of many measurements. The Central Limit Theorem, discussed in the following slides, provides an explanation of why averages of non-normal data appear normal.
Dice Demonstration (Integer Distribution) What does a probability distribution from a single die look like? What is the mean?
What is the standard deviation? Construct a dataset in Minitab
Select Calc > Random Data > Integer… from the main menu
Generate 1,000 rows of data in C1: Min = 1, Max = 6 Use Minitab’s Graphical Summary routine for analysis Stat > Basic Statistics > Display Descriptive Statistics… Minitab Output (Typical)
The probability distribution of the
possible outcomes of the roll of a single die is obviously non-normal.
A perfect distribution would have had all six bars exactly equal, but even with 10,000 data points, there is still some
6Sigma项目运作实例
