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78 Cards in this Set
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Statistics

The science concerned with “the collection, organization, analysis, interpretation, and presentation of data


experiment

a process that results in some outcome.


outcome

a result that we observe


sample space

The collection of all possible outcomes of an experiment


Probability

the likelihood that an outcome occurs


Probability Properties

Label the n outcomes in a sample space as O1, O2, … On, where Oi represents the ith outcome in the sample space.


event

a collection of one or more outcomes from a sample space


Calculating Probabilities

Rule 1: The probability of any event is the sum of the probabilities of the outcomes that compose that event.
Rule 2: The probability of the complement of any event A is P(Ac) = 1 – P(A). Rule 3: If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B) Rule 4: If two events A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B) 

Conditional probability

the probability of occurrence of one event A, given that another event B is known to be true or have already occurred
P(AB) = P(A and B)/P(B) 

random variable, X

a numerical description of the outcome of an experiment. Formally, a random variable is a function that assigns a numerical value to every possible outcome in a sample space.


probability distribution, f(x),

is a characterization of the possible values that a random variable may assume along with the probability of assuming these values.


cumulative distribution function, F(x),

specifies the probability that the random variable X will assume a value less than or equal to a specified value, x, denoted as P(X ≤ x).


binomial distribution

the probability of obtaining exactly x “successes” in a sequence of n identical experiments, called trials.


Poisson Distribution

Allows the sample size to become very large and the probability of success or failure to become very small while the expected value remains constant


Probability Density Function

A curve that characterizes outcomes of a continuous random variable, and is described by a mathematical function f(x).
Probabilities are only defined over intervals. 

standard normal distribution

If a normal random variable has a mean μ = 0 and a standard deviation σ = 1,
It is represented by z 

Calculating Normal Probabilities

z= (xu)/s


Exponential Distribution

models the time between randomly occurring events, such as the time to or between failures of mechanical or electrical components.


Simple Random Sampling

Every item in the population has an equal probability of being selected.


Stratified Sampling

The population is partitioned into groups, or strata, and a sample is selected from each group


Systematic Sampling

Every nth (4th, 5th, etc.) item is selected.


Cluster Sampling

A population is partitioned into groups (clusters) and a sample of clusters is selected. Either all elements in the chosen clusters are included in the sample or a random sample is taken from each of them.


Judgment Sampling

Expert opinion is used to determine the sample.


Sampling Error

occurs naturally and results from the fact that a sample may not always be representative of the population, no matter how carefully it is selected.
Only way to reduce sampling error is to take a larger sample from the population 

Systematic Error

result from poor sample design and can be reduced or eliminated by careful planning of the sampling study


Population

a complete set of collection of objects of interest


Sample

a subset of objects taken from the population


mode

occurs most frequently


Range

simplest measure of dispersion and is computed as the difference between the ex and min values in the data set


variance

a measure of dispersion that depends on all the data. The larger the variance, the more the data are "spread out" from the mean, and the more variability one can expect in the observations


Skewness

the lack of symmetry of data
If the mean and median are equal, then the distribution is symmetrical. If the mean is greater than the median, then the distribution is skewed to the right. Vice Versa 

Coefficient of skewnesss

If CS is positive, the distribution of values is positively skewed; if negative, it is negatively skewed
The closer CS is to zero, the less the degree of skewness 

kurtosis

refers to peakedness of a histogram


Sampling Distribution

the distribution of a statistic for all possible samples of a fixed size


Confidence Intervals

An interval estimate of a population parameter that also specifies the likelihood that the interval contains the true population parameter


Idea Generation (Product Development Phase 1)

New or redesigned product ideas should incorporate customer needs and expectations


Preliminary Concept Development (Product Development Phase 2)

New ideas are studied for feasibility


Product/Process Development (Product Development Phase 3)

If an idea survives the concept stage, the actual design process begins by evaluating design alternatives and determining engineering specifications for all materials, components, and parts.


Full Scale Production (Product Development Phase 4)

Once the design is approved and the production process has been set up, the company releases the product to manufacturing or service delivery teams


Market Introduction (Product Development Phase 5)

The product is distributed to customers


Market Evaluation (Product Development Phase 6)

Ongoing product development process that relies on market evaluation and customer feedback


Concurrent Engineering

a process in which all major functions involved with bringing a product to market are continuously involved with product development form conception through sales


Design for Six Sigma (DFSS)

represents a structured approach to product development and a set of tools and methodologies for ensuring that goods and services will meet customer needs and achieve performance objectives, and that the processes used to make and deliver them achieve high levels of quality.


DFSS four principal activities

Concept development
Detailed design Design optimization Design verification 

Concept development

the process of applying scientific, engineering, and business knowledge to produce a basic functional design that meets both customer needs and manufacturing or service delivery requirements.


Innovation

involves the adoption of an idea, process, technology, product, or business model that is either new or new to its proposed application.


Theory of Inventive Problem Solving (TRIZ)

Developed by a Russian patent clerk who studied thousands of submissions, and observed patterns of innovation common to the evolution of scientific and technical advances.
He recognized that these concepts could be taught, and he developed some 200 exercises to foster creative problem solving. 

Axiomatic design

based on the premise that good design is governed by laws similar to those in natural science.


Independence Axiom

good design occurs when the functional requirements of the design are independent of one another.


Information Axiom

good design corresponds to minimum complexity.


Quality Function Deployment (QFD)

is a planning process to guide the design, manufacturing, and marketing of goods by integrating the voice of the customer throughout the organization.


Four Linked Houses of Quality

Customer Requirements
v Technical Requirements v Component Characteristics v Process Operations v Quality Control Plan 

Nominal dimensions

the ideal dimension or target value that manufacturing seeks to meet


tolerance

permissible variation, recognizing the difficulty of meeting a target conistently


tolerance design

involves determining the permissible variation in a dimension


Taguchi Loss Function

Measures quality as the variation from the target value of a design specification, and then translates that variation into an economic "loss function" that expresses the cost of variation in monetary terms


Reliability

the probability that a product, piece of equipment, or system performs its intended function for a stated period of time under specified operating conditions.


Key elements of reliability

Probability
Time Performance Operating conditions 

Functional failure

failure that occurs at the start of product life due to manufacturing or material detects


Reliability failure

failure after some period of use


Inherent reliability

predicted reliability determined by the design of the product or process.


Achieved reliability

actual reliability observed during use.


Failure Rate

Number of failures/Total unit operating hours


mean time to failure (MTTF).

For items that must be replaced when a failure occurs, the reciprocal of the failure rate


mean time between failures (MTBF)

For repairable items


Product Life Characteristics Curve

shows the instantaneous failure rate at any point in time (referred to as a "bathtub" curve)


Infant Mortality Period

early failure period


reliability function, R(T),

characterizes the probability of survival to time T.


Series system

all components must function or the system will fail.


Parallel system

uses redundancy. The system will successfully operate as long as one component functions


Robust design

designing goods and services that are insensitive to variation in manufacturing processes and when consumers use them


Design failure mode and effects analysis (DFMEA)

identification of all the ways in which a failure can occur, to estimate the effect and seriousness of the failure, and to recommend corrective design actions.


Fault Tree Analysis

a method to describe combinations of conditions or events that can lead to a failure.


Design for Manufacturability

the process of designing a product for efficient production at the highest level of quality


Design for Excellence

 an emerging concept that includes many designrelated initiatives such as concurrent engineering, design for manufacturability, design for assembly, design for environment, and other “design for” approaches


Life testing

run devices until failure occurs


Accelerated life testing

overstress devices to reduce time to failure


Highly accelerated life testing

focused on discovering latent defects that would not otherwise be found through conventional methods.
