# Six Sigma Exam 2

version from 2016-12-07 06:42

## Section

Factorsindependent variables (continuous or discrete) an investigator manipulates to capture changes in output of process
Responsesdependent variable measured to describe output of process
Treatment Combinations (run)experimental trial where are factors are set at specified level
DOEformal mathematical method for systematically planning and conducting scientific studies that change experimental variables together in order to determine their effect of a given response
How does DOE workmakes controlled changes to input variables in order to gain maximum amts of information on cause-and-effect relationships w/in minimum sample size
DOE generates information aboutthe effect various factors have on a response variable
DOE can help determineoptimal settings for factors affecting response variable
Basic Steps in DOE1. design experiment 2. collect data 3. statistical analysis 4. reach conclusions and offer recommendations
Replicationrepetition of a basic experiment w/out changing any factor settings
Why use replication?Allows experimenter to estimate experimental error (noise) in the system; helps determine what differences are "real" or "just noise"
Randomizationminimize potential uncontrollable biases in experiment by randomly assigning matl, people. order that trials are conducted, or any other factor not under control of experimenter
Why use randomization?"average out" the risks of extraneous factors that may be present in order to minimize the risk of these factors affecting experimental results
Blockingincrease precision of experiment by breaking experiment into homogeneous segments (blocks) in order to control any potential block to block variability (multiple lots of matl, several shifts, several machines, several inspectors)
Why use blocking?Minimize chance that variability between blocks will affect experimental results
Confoundingmultiple effects are tied together into one parent effect and cannot be separated
Example of confoundingtwo people flipping two coins --> effect of PERSON and effect of COIN are confounded
One-Way Analysis of Varianceused to test hypothesis that means of several populations are EQUAL
Factorial Designx*y*z means experimental design with 3 FACTORS; factor 1 = x treament levels, factor 2 = y treamtent levels, factor 3 = z treatment levels
Factorial (2^k) Designsexperiments involving several factors (k = # of factors), where each factor is set to "low" and "high" level
When are 2^k factorial designs usefulearly stages of experimental work when you are likely to have many factors to investigate and many to minimize # of treatment combos while testing all k factors in complete factorial arrangement
What is k in 2^k factorial designs?# of treatments
As k increases in 2^k factorial designsample size increases exponentially
Main Effecteffect of a variable on output
How to evaluate main effect for xaverage of high x effects - average of low x effects
Interaction Effectsdifferences on one factor depend on the level of another factor; there is an interaction between factors (not levels); can't talk about effect on one factor without mentioning other factor
Interaction Effect Equation for x and y0.5*[(difference b/n high x effects) - (difference b/n high y effects)]
Statistical Process Controlmonitors production process over time, signal when something goes "wrong" and corrective action should be taken
Acceptance Samplinginspect part of production batch; based on outcome either accept/reject entire batch
Why use SPCknow when to take action to correct process, know when to leave process alone and avoid overadjustment
Applications of control chartsestablish state of statistical control, monitor process, determine process capability
Control Chartprimary tool of SPC, shows how process is performing OVER TIME, emphasizes variation of process, can be used for various product attributes
In-Controlprocess is in-control if there is no reason to doubt it is operating normally (according to capabilities)
Being in-control is not necessarilyrelated to product specs; process could be in-control and out of spec (just incapable)
Out of Controlreason to doubt process is operating normally
Unfavorable variationinvestigate to correct
Favorable variationinvestigate to exploit
Causes of Variationrandom, assignable (machines, workers, matls)
Dual Purpose of control chartsdetect assignable cause and signal alarm; leave process alone under common causes
Control Limitstypically +- 3 sigma, only 1/1000 chance of false alarm
Warning limitssometimes set at +- 2 sigma
For high-volume processes, control charts are calculated bytaking small samples of data periodically; aggregate sample and put as single point on chart
Xbar chartsshow mean of each sample (Xbar)
R chartsshow the range of each sample (max-min)
S chartsshow the standard deviation of each sample
Centerline of R chartaverage range of all samples (Rbar)
Centerline of Xbar chartaverage mean of all samples (Xbarbar)
Control Limits for R chartD3*R and D4*R
Control Limits for Xbar chartXbarbar - A2*Rbar and Xbarbar + A2*Rbar
n# of observations WITHIN EACH SAMPLE; NOT THE # OF SAMPLES!!!!!
Rules of thumb for in-controlno points outside control limits, about half of points are above and below line, points seem to fall randomly above and below (no trends), most points are near center line and few are close to limits
Point outside control limitcalculation error in sample mean/range, sudden power surge, broken tool, etc
Cycles in Xbar chartoperator rotations, fatigue, diff gauges, etc
Cycles in S chartmaintenance schedules, rotation of fixtures, diffs in shifts, etc
For a capable process, control limits must be sufficiently far inside of ____tolerance range
How to measure VARIABLE (quantitative feature)Xbar and R charts
How to measure ATTRIBUTE (qualitative feature)P-chart, C-chart, U-chart
Sample size >=2 for VARIABLEXbar and R chart
Sample size = 1 for VARIABLEIndividual (I) chart, Moving Range (MR) chart
At most 1 defect ATTRIBUTEP-chart
Each sample tested may have 0,1,2,etc defects + Units are of same sizeC-chart (car crashes on Euclid)
Each sample tested may have 0,1,2,etc defects + Units are of different sizeU-chart (metal pieces w/ diff sizes)