THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 1 Chapter 9 Statistical Thinking and Applications

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 2 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

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 3 Sources of Variation in Production Processes Materials Tools OperatorsMethods Measurement Instruments Human Inspection Performance EnvironmentMachines INPUTSPROCESSOUTPUTS

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 4 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

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 5 Importance of Understanding Variation time PREDICTABLE ? UNPREDECTIBLE

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 6 Management Mistakes in Attempting Process Improvement 1.Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to common causes 2.Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to a special cause

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 7 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

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 8 Production Setup 1.Take the bag in your left hand. 2.Tear a 3/4” opening in the right corner. (only large enough for one piece at a time)

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 9 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.

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 10 Do it right the first time! Be a Quality Worker! Take Pride in Your Work!

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 11 Lessons Learned Quality is made at the top, i.e., management is responsible for the system 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. Variations exists in systems and, if stable, can be predicted

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 12 Statistical Methods Descriptive statistics Statistical inference Predictive statistics

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 13 Review of Key Concepts Random variables Probability distributions Populations and samples Point estimates Sampling distributions Standard error of the mean

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 14 Important Probability Distributions Discrete –Binomial –Poisson Continuous –Normal –Exponential

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 15 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. The mean of the distribution of sample means approaches the mean of the population distribution The standard deviation of the distribution approaches the standard deviation of the population distribution divided by the square root of the sample size

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 16 Factors to Consider When Designing a Study 1.What is the objective of the study? 2.What type of sample should be used? 3.What possible error might result from sampling? 4.What will the study cost?

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 17 Sampling Methods Simple random sampling Stratified sampling Systematic sampling Cluster sampling Judgment sampling

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 18 Sampling Error Sampling error (statistical error) Nonsampling error (systematic error) Factors to consider: –Sample size –Appropriate sample design

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 19 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

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 20 Excel Descriptive Statistics Tool Tools…Data Analysis… Descriptive Statistics

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 21

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 22 Excel Histogram Tool Tools…Data Analysis…Histogram

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 23

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 24 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

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 25 The Process (1 of 2) Over time, the output of any process will have a certain amount of natural or inherent variability This is also referred to as random or common variability This variability is due to countless minor factors and is assumed to be out of management’s control in the short run, i.e., it is something you have to live with

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 26 Process distribution Mean The Process (2 of 2) The distribution of the output of a process has a mean, , and a standard deviation,  ; it can have a wide variety of shapes

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 27 Process Capability (1 of 3) When selecting a process to perform an operation on a particular item, the inherent variability of process should be compared to the tolerance (range of output) allowed by the designer’s specifications for that operation

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 28 Process Capability (2 of 3) Lower Specification Upper Specification process distribution Almost all of the process output fits within the specification width Much of the process output fits within specification width A significant portion of the process output falls outside of the specification width

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 29 Process Capability (3 of 3) Lower Specification Upper Specification process distribution Much of the process output fits within specification width A significant portion of the process output falls outside of the specification width Almost all of the process output fits within the specification width

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 30 Process Capability Study Where is the process centered? How much variability exists in the process? Is the performance acceptable? Is the process stable? What factors contribute to variability?

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 31 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)

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 32 Process Capability Study 1.Choose a representative machine or process 2.Define the process conditions 3.Select a representative operator 4.Provide the right materials 5.Specify the gauging or measurement method 6.Record the measurements 7.Construct a histogram and compute descriptive statistics: mean and standard deviation 8.Compare results with specified tolerances

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 33 Process Capability (3 of 3) The process capability index (c p ) compares the width of the design specifications with a measure of process variability

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 34 Process Capability Indices C p = UTL - LTL 6  C pl, C pu } UTL -  3  C pl =  - LTL 3  C pk = min{ C pu = A process capability index compares the width of the design specifications with a measure of process variability

THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM 35 PROCESS_CAPABILITY.XLS