Statistical Thinking and Applications Chapter 11 The Management & Control of Quality, 7e 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.

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

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

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

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.

Importance of Understanding Variation time PREDICTABLE ? UNPREDECTIBLE

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

Note to Instructors The following slides can be used to guide a class demonstration and discussion of the Deming Red Bead experiment using small bags of M&Ms, from a suggestion I found on a TQ newsgroup several years ago. The good output (“red beads”) are the blue M&Ms, with the instructor playing the role of Dr. Deming.

We’re Going into Business!!! We have a new global customer and have to start up several factories. So I need teams of 5 to do the work: 1 production worker 2 inspectors 1 Chief Inspector 1 Recorder

Production Setup Take the bag in your left hand. Tear a 3/4” opening in the right corner. (only large enough for one piece at a time)

Production Process 1. Production worker produces 10 pieces and places them on the napkin. 2. Each inspector, independently, counts the blue ones, and passes to the Chief Inspector to verify. 3. If Chief Inspector agrees, s/he tells the recorder, who reports it to me.

Be a Quality Worker! Take Pride in Your Work! Do it right the first time! Take Pride in Your Work! Be a Quality Worker!

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

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.

Sampling Methods Simple random sampling Stratified sampling Systematic sampling Cluster sampling Judgment sampling

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.

Sampling Error Sampling error (statistical error) Nonsampling error (systematic error) Factors to consider: Sample size Appropriate sample design

Statistical Methods Descriptive statistics Statistical inference Predictive statistics

Statistical Tools

Excel Tools for Statistics Tools…Data Analysis… Descriptive Statistics Tools…Data Analysis…Histogram

Key Idea One of the biggest mistakes that people make in using statistical methods is confusing data that are sampled from a static population (cross-sectional data) with data sampled from a dynamic process (time series data).

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.