Statistics for Engineer

Statistics  Deals with  Collection  Presentation  Analysis and use of data to make decision  Solve problems and design products and processes  Can be powerful tool for  Designing new products and systems  Improving existing design  Designing, developing and improving production processes

Variability

Collecting Engineering Data  Retrospective Study  Would be either all or a sample of the historical process data.  Observational Study  Would be either observations of process or population.  Are usually conducted for short time period.  Designed Experiments  Collect the observations of the resulting system output data.

Random Samples  Statistical methods work correctly and produce valid results. Random samples must be used.  Each possible sample of size n has an equally likely chance of being selected.

Population and Sample Population ◦ An entire group of objects that have been made or will be made, described by a characteristic of interest ◦ Population parameters are unknown and usually unknowable Sample ◦ The group of objects actually measured in a statistical study ◦ A sample is usually a subset of the population of interest ◦ Sample statistics estimate population parameters “ Population Parameters ” “ Sample Statistics ”  = Population mean s = Sample standard deviation Sample Population  = Population standard deviation X = Sample mean 6

Population and Sample Probability (sampling) Inference (predict) Population Parameters: , , , etc. Sample Statistics: x, s, p, r, etc. 7

Data type u Attribute data –Discrete, proportion and count of defects are the most common –We can count u Variable data –Continuous data –We can measure variables Variable data ให้ข้อมูลที่ ดีกว่า และต้องการจำนวน ข้อมูลน้อยกว่า 8

Parameters PopulationSample Mean µ Variance S 2 or SD 2 Standard Deviation S or SD Standard scoreZ 9