# Six Sigma Exam 2

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ndifranco94's
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2016-12-07 06:42

## Section

Question | Answer |
---|---|

Factors | independent variables (continuous or discrete) an investigator manipulates to capture changes in output of process |

Responses | dependent variable measured to describe output of process |

Treatment Combinations (run) | experimental trial where are factors are set at specified level |

DOE | formal 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 work | makes 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 about | the effect various factors have on a response variable |

DOE can help determine | optimal settings for factors affecting response variable |

Basic Steps in DOE | 1. design experiment 2. collect data 3. statistical analysis 4. reach conclusions and offer recommendations |

Replication | repetition 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" |

Randomization | minimize 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 |

Blocking | increase 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 |

Confounding | multiple effects are tied together into one parent effect and cannot be separated |

Example of confounding | two people flipping two coins --> effect of PERSON and effect of COIN are confounded |

One-Way Analysis of Variance | used to test hypothesis that means of several populations are EQUAL |

Factorial Design | x*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) Designs | experiments involving several factors (k = # of factors), where each factor is set to "low" and "high" level |

When are 2^k factorial designs useful | early 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 design | sample size increases exponentially |

Main Effect | effect of a variable on output |

How to evaluate main effect for x | average of high x effects - average of low x effects |

Interaction Effects | differences 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 y | 0.5*[(difference b/n high x effects) - (difference b/n high y effects)] |

Statistical Process Control | monitors production process over time, signal when something goes "wrong" and corrective action should be taken |

Acceptance Sampling | inspect part of production batch; based on outcome either accept/reject entire batch |

Why use SPC | know when to take action to correct process, know when to leave process alone and avoid overadjustment |

Applications of control charts | establish state of statistical control, monitor process, determine process capability |

Control Chart | primary tool of SPC, shows how process is performing OVER TIME, emphasizes variation of process, can be used for various product attributes |

In-Control | process is in-control if there is no reason to doubt it is operating normally (according to capabilities) |

Being in-control is not necessarily | related to product specs; process could be in-control and out of spec (just incapable) |

Out of Control | reason to doubt process is operating normally |

Unfavorable variation | investigate to correct |

Favorable variation | investigate to exploit |

Causes of Variation | random, assignable (machines, workers, matls) |

Dual Purpose of control charts | detect assignable cause and signal alarm; leave process alone under common causes |

Control Limits | typically +- 3 sigma, only 1/1000 chance of false alarm |

Warning limits | sometimes set at +- 2 sigma |

For high-volume processes, control charts are calculated by | taking small samples of data periodically; aggregate sample and put as single point on chart |

Xbar charts | show mean of each sample (Xbar) |

R charts | show the range of each sample (max-min) |

S charts | show the standard deviation of each sample |

Centerline of R chart | average range of all samples (Rbar) |

Centerline of Xbar chart | average mean of all samples (Xbarbar) |

Control Limits for R chart | D3*R and D4*R |

Control Limits for Xbar chart | Xbarbar - A2*Rbar and Xbarbar + A2*Rbar |

n | # of observations WITHIN EACH SAMPLE; NOT THE # OF SAMPLES!!!!! |

Rules of thumb for in-control | no 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 limit | calculation error in sample mean/range, sudden power surge, broken tool, etc |

Cycles in Xbar chart | operator rotations, fatigue, diff gauges, etc |

Cycles in S chart | maintenance 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 VARIABLE | Xbar and R chart |

Sample size = 1 for VARIABLE | Individual (I) chart, Moving Range (MR) chart |

At most 1 defect ATTRIBUTE | P-chart |

Each sample tested may have 0,1,2,etc defects + Units are of same size | C-chart (car crashes on Euclid) |

Each sample tested may have 0,1,2,etc defects + Units are of different size | U-chart (metal pieces w/ diff sizes) |

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