Statistical Thinking and Applications Chapter 9 Statistical Thinking and Applications

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

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&M’s® Chocolate Candies, 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 Methods Descriptive statistics Statistical inference Predictive statistics

Review of Key Concepts 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

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

Design of Experiments A test or series of tests to compare two or more methods to determine which is better, or to determine levels of controllable factors to optimize the yield of a process or minimize the variability of a response variable. Factorial experiment Analysis of all combinations of factor levels to understand main effects and interactions

Excel Descriptive Statistics Tool Tools…Data Analysis… Descriptive Statistics

Excel Histogram Tool Tools…Data Analysis…Histogram

Process Capability The range over which the natural variation of a process occurs as determined by the system of common causes Measured by the proportion of output that can be produced within design specifications

Types of Capability Studies Peak performance study - how a process performs under ideal conditions Process characterization study - how a process performs under actual operating conditions Component variability study - relative contribution of different sources of variation (e.g., process factors, measurement system)

Process Capability Study Choose a representative machine or process Define the process conditions Select a representative operator Provide the right materials Specify the gauging or measurement method Record the measurements Construct a histogram and compute descriptive statistics: mean and standard deviation Compare results with specified tolerances

Process Capability specification natural variation (a) (b) (c) (d)

Process Capability Index UTL - LTL 6s Cp = UTL - m 3s Cpu = m - LTL 3s Cpl = Cpk = min{ Cpl, Cpu }

PROCESS_CAPABILITY.XLS