IE 3302: Engineering Statistics

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IE 3302: Engineering Statistics.

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Introduction to Statistics. Statistics – deals with collection and analysis of data to solve problems having randomness (variability) Example : Assembly operation for a car. Variability comes from: Operator differences Machine differences Supplied materials & parts differences Variation in operating conditions (temperatures, humidity, vibrations, …) Variation in the measurement process itself.

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Statistics in engineering. Modeling Using assumptions made from historical data, can we predict future behavior? Evaluating outcomes Is a new process or product better than the previous? Quality control % defects, detecting quality problems and trends Reliability Expected time or number of failures, risk Analytics & Machine Learning (Data Science).

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Variability. Variability is encountered when a process is too complex to model and control completely, due to: Cost, time, & resource constraints Could we build a desk with +/- 1 nanometer accuracy? Probably. How much would it cost? Would anyone buy it? Incomplete knowledge of process Atomic level interactions in electrical design Inter and intra level molecular interactions in people - pharmaceuticals.

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Definitions. Descriptive Statistics Methods for organizing, summarizing, and presenting data Examples: Mean, standard deviation, histogram, pie chart, bar chart Inferential Statistics Methods for drawing conclusions about the characteristics of a population from a sample of that population.

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Definitions. Data Raw measurements and facts used in analysis Discrete vs. Continuous Discrete: finite or countable possible values Continuous: continuous (real-valued), possibly on a range Quantitative vs. Qualitative data Quantitative data – numeric values defined on a range; order of values is meaningful Physical measurement data : height, age, weight, surface finish Interval data : measurements with arbitrary scales : Likert scale data from surveys Ordinal data : rankings Qualitative data – order of values not meaningful Symbolic data : category data such as gender, degree program Nominal numeric data : numeric data where numbers really correspond to categories (for instance, 1 = engineering and 2= business).

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Definitions. Population Collection of all measurements of interest to the statistical analysis. May be of infinite size. Sample Subset of data extracted from population (usually randomly) Parameter Characteristic of population Statistic Characteristic of sample.

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Definitions. Variation: changes, differences, or uncertainty in a population Probability: two (equivalent) perspectives: Percentage of a population meeting some criteria Chance of any one observation from the population meeting some criteria.

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Example. Question: What is the current average age of a student at LSU? Population: All students currently at LSU (~30K) Sample: All students in a single classroom, or better, a random selection of 100 current LSU students Type of data: Quantitative physical measurement, discrete.

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Typical Statistical Experiment Process. [image] Experiment process starts with design of experiment then data collection then descriptive statistics then identification of probability distributions and parameters testing and validation of hypothesis and finally applying model to solve real world problems.

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Experiments. Elements: Hypothesis Factors & their levels Sample size Statistics.

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Measurement. Carefully defined measurement systems are important Example: Count of number of raisins in a box Need to define a raisin. Is a stem a raisin? Is a raisin fragment a raisin? Is raisin sludge a raisin? Example: Measure pulse rate Issues?.

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Concept Quiz. 1 - 13.