Introductions
Syllabus
Course overview
Purpose - To provide a foundation for applying statistical procedures for
decision making
related to continuous improvement.
Focus - Selecting appropriate statistical "tool" and practical applications.
Logical progression:
Descriptive Statistics
Exploratory Data Analys (EDA)
Inferential Statistics - Population - Sample - Analysis of Variation (B/W)
- Inference - Probability
T-tests
Descriptive Statistics
Variation
Mean - arithmetic average
Median - mid point (middle)
Mode- Most frequently occuring
Variance
Magniture of measure (Sum of Squares): S(X-m)2
Standard Deviation: s = sqrt ((S(X-m)2/N) (population formula)
Z scores - meaning
(Note more coverage next week)
Characteristics
of Normal Distribution
+/- One Standard deviation 68% of area under normal curve
+/- Two Standard Deviations 95% of area under normal curve
+/- Three Standard Deeviations 99.7% of area under normal curve
EXCEL
Uses: Calculations, Graphs,
Functions (IF...Min, Max, ..Sum, Average..etc)
Basic Statistics Functions (e.g. SDDEV, AVERAGE, NORMDIST ...etc)
Analysis Tool Pak
Review of Statistics and Quality Control
Quality may be defined by different people using various descriptors; however, it ultimately means how satisfied the customer is or to what degree is a product or service "fit for use". Quality is achieved through either quality of design or quality of conformance. Quality design means the different levels of performance, reliability, function or serviceability that result from decisions made by engineering and management. On the other hand, conformance means the systematic reduction of variability and elimination of defects. Further, standards have been adopted to assure not only how, but the manner in which quality is carried out. Suppliers may be required to become certified in order to maintain the business of being a vendor to a manufacturer in other words "Vendor Certification" and ISO Certification may be required. While, these topics are beyond the intention of this module, the are mentioned to emphasize a point: THERE ARE NO ABSOLUTES, EVERYTHING VARIES IN INDUSTRY OR EVERYDAY LIFE. There are differences in twins, or ball bearings or basketballs, cookies, or sparkplugs....everything varies. The goal, is to identify and measure, and control the sources of variation. Sounds too simple....it is. We will look at a few common tools used in trying to seek improvement in quality. Quality is NOT something that can be added on in the end it must be integrated throughout and become a holistic approach for continuous improvement throughout the organization.
INSPECTION
By the strick definition, quality control implies meausrement and inspection (usually after the fact) and thus is a method of detection. On the other hand, quality assurance is a prevention system that seeks to correct problems BEFORE bad parts are produced. In either case, inspection is necessary to determine if a product is within the required specifications. Inspections are conducted is to check how well a product conforms to specifications. Quality is not cheep! Usually it isn't possible to check 100% of all product; thus, sampling methods are used in making decisions about whether to reject or accept a lot or production run. This inspection must be on-going and continuous because of variation. There are two basic ways in which inspections can be carried out. These involve checking attributes or variables. Attributes are measured using pass/fail, or GO/NOGO gauging. While checks can be carried out simply, analysis of "why" or trending, cannot be conducted without variable measurement. Variable measurement is a quantitative measurement of specific characteristics of interest such as dimensions, mechanical properties, and surface finish roughness. An example of attribute versus variable inspection is shown below.
STATISTICAL METHODS FOR QUALITY CONTROL
Statistical methods are used to evaluate
not only if a product is conforming to specifications, but also how well
it conforms. In other words, the goal is to seek and detect variation
in the process. There are too major types of variation that occur.
Common cause variation and special cause variation. Other terms commonly
used are natural chance causes or assignable causes. An assignable
causes can be traced to a specific and controllable cause.
While the source of variation is is virtually infinite, there are typically
five categories of variation of concern.
These include variation in or by humans, materials, machines, measurement,
and the environment. Similarly, there are quality tools that
are available to assist in the detection of variation including both graphical
and statistical.
The major graphical tools of statistical methods include:
1. Histograms
Descriptive Statistical Measures
Consider a process that involves an assembly of a gear
on a shaft. One of the variables of interest would be the outside
diameter of the shaft and the the other the inside diameter of the gear.
The attribute approach would simply check to see if the tolerance range
is met by each.
However if quantitative measurements are taken, the degree of variation can be determined through statistical tools, and a systematic analysis of determining causal relationships can begin.
The range is the difference between the maximum and minimum
values recorded.
Range only describes the overall "spread" but does not tell how much the data values vary from the mean. A more useful measure of variability is the standard deviation. Remember that sampling is usually conducted and the "statistics" of the sample are used to estimate the "parameters" of the population.
The standard deviation is very useful when the distribution of the
process variable under consideration is NORMAL. The sample
standard deviation is the square root of the variance and is found using
the following formula:
Problems Set 1 - Inclass overview and preliminary work (if needed)
