EMIS 7300 SYSTEMS ANALYSIS METHODS FALL 2005 Dr. John Lipp Copyright © 2005 Dr. John Lipp

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-2 Course Outline Part 1: Rank (Order) and Non-Parametric Statistics. Part 2: Statistical Process Control. Part 3: Reliability. Mid-term Exam.

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-3 Today’s Topics Statistical Process Control –In Control? –Rational Groups –X-chart –R-chart –Western Electric Rules –Samples with n = 1 –Other Control Charts

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-4 In Control? Defects come from –Chance causes –Assignable causes Identify and eliminate assignable causes reduces variability and thereby creating quality. –Product variability is a loss to society (Taguchi) You cannot “inspect” quality into a product. –Quality comes from building it right the first time.

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-5 Rational Groups A rational group is a small sample from a process –Usually 4-6 points in the sample –Selected to minimize assignable variability Several approaches to defining the group sample points –Consecutively produced units  interested in shifts in the process –Randomly selected units since last sample  determine if all the units since the last sample meet requirements Statistics are computed on the sample:

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-6 X-bar Control Chart Center Line Lower Control Limit Upper Control Limit d 2 from Table X

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-7 The R-chart d 3, D 3, D 4 from Table X

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-8 Rules of thumb for the Center Line and Control Limits Minimum of preliminary samples. If the preliminary samples fall outside the control limits, they probably have assignable causes that should be investigated! Need to stabilize range (or standard deviation) of the process first using R-chart or S-chart before interpreting X-bar chart.

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-9 Out-of-Control: Western Electric Rules First published in The Western Electric Handbook of 1956 –Rules of Thumb for recognizing non-random patterns 1.One point outside 3-sigma control limits 2.Two out of three consecutive points outside the same 2- sigma control limit. 3.Four out of five consecutive points outside either 1-sigma control limit. 4.Eight consecutive points plot on the same side of the control line.

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-10 Rational Subgroups of Individuals (n = 1) Cannot compute range and standard deviation when n = 1 – Use the moving range to estimate variability –X-bar-chart  Individual Chart –R-chart  Moving Range Chart

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-11 SPC Experiment: Hot Wheels ® Launcher Before putting together your launcher setup, I need a handwriting sample for each team member: I wonder what the doc will read in my writing? Argh! The result will determine my (mis)fortune.

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-12 Other Control Charts Shewhart Control Charts (named after inventor) –S-chart (uses standard deviation instead of range) –X-bar-chart created with s (instead of r) –Tolerance chart (AKA Tier chart) –P-chart (p for proportion nonconforming) –U-chart (defects per unit) CUMSUM-chart (sensitive to small mean shifts) –V-mask control scheme –Tabular control scheme

EMIS7300 Fall 2005 Copyright  2005 Dr. John Lipp S3P2-13 Homework Use Excel to solve the following problems (the data sets are on the textbook’s CD-ROM)