Statistical Thinking and Applications Chapter 10 Statistical Thinking and Applications

Key Idea Raw data collected from the field do not provide the information necessary for quality control or improvement. Data must be organized, analyzed, and interpreted. Statistics provide an efficient and effective way of obtaining meaningful information from data, allowing managers and workers to control and improve processes.

Principles of Statistical Thinking All work occurs in a system of interconnected processes Variation exists in all processes Understanding and reducing variation are the keys to success

Variation Many sources of uncontrollable variation exist (common causes) Special (assignable) causes of variation can be recognized and controlled Failure to understand these differences can increase variation in a system

Sources of Variation in Production Processes Measurement Instruments Operators Methods Materials INPUTS PROCESS OUTPUTS Tools Human Inspection Performance Machines Environment

Key Idea A system governed only by common causes is called a stable system. Understanding a stable system and the differences between special and common causes of variation is essential for managing any system.

Problems Created by Variation Variation increases unpredictability. Variation reduces capacity utilization. Variation contributes to a “bullwhip” effect. Variation makes it difficult to find root causes. Variation makes it difficult to detect potential problems early.

Two Fundamental Management Mistakes Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to common causes Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to a special cause

Deming’s Red Bead Experiment – Round 1

Control Chart of Results

Lessons Learned Quality is made at the top. Rigid procedures are not enough. People are not always the main source of variability. Numerical goals are often meaningless. Inspection is expensive and does not improve quality.

Statistical Foundations Random variables Probability distributions Populations and samples Point estimates Sampling distributions Standard error of the mean

Important Probability Distributions Discrete Binomial Poisson Continuous Normal Exponential

Key Idea A good sampling plan should select a sample at the lowest cost that will provide the best possible representation of the population, consistent with the objectives of precision and reliability that have been determined for the study.

Histogram

Central Limit Theorem If simple random samples of size n are taken from any population, the probability distribution of sample means will be approximately normal as n becomes large.

Example

Confidence Intervals

Hypothesis Testing Formulate the hypotheses to test. Select a level of significance that defines the risk of drawing an incorrect conclusion about the assumed hypothesis that is actually true. Determine a decision rule on which to base a conclusion. Collect data and calculate a test statistic. Apply the decision rule to the test statistic and draw a conclusion.

Enumerative and Analytic Studies Enumerative study – analysis of a static population Analytic study – analysis of a dynamic time series

Design of Experiments A designed experiment is a test or series of tests that enables the experimenter to compare two or more methods to determine which is better, or determine levels of controllable factors to optimize the yield of a process or minimize the variability of a response variable. DOE is an increasingly important tool for Six Sigma.

Main Effects Measures the difference that a change in a factor level has on the response. E.g., what is the effect of increasing the launch angle? Main effect = average response at high level – average response at low level

Interactions An interaction is when the effect of changing one factor depends on the levels of the other factors. Response Factor 2 at level 1 Factor 2 at level 2 Factor 1

Analysis of Variance ANOVA is a methodology for drawing conclusions about equality of means of multiple populations. ANOVA tests the hypothesis that the means of all populations are equal against the alternative hypothesis that at least one mean differs from the others.

Regression and Correlation Regression analysis is a tool for building statistical models that characterize relationships between a dependent variable and one or more independent variables, all of which are numerical. Correlation is a measure of a linear relationship between two variables, X and Y, and is measured by the (population) correlation coefficient.

Example: Voltmeter Calibration

Regression Line and Equation