Reid & Sanders, Operations Management © Wiley 2002 Statistical Quality Control 6 C H A P T E R

Reid & Sanders, Operations Management © Wiley 2002 Page 2 Learning Objectives Describe quality control methods Understand the use of statistical process control Describe & apply control charts Distinguish x-bar, R, p and c-charts Define process capability Describe & apply capability indexes Define six-sigma capability

Reid & Sanders, Operations Management © Wiley 2002 Page 3 Quality Control Methods Descriptive statistics: –Used to describe distributions of data Statistical process control (SPC): –Used to determine whether a process is performing as expected Acceptance sampling: –Used to accept or reject entire batches by only inspecting a few items

Reid & Sanders, Operations Management © Wiley 2002 Page 4 Descriptive Statistics Mean (x-bar): –The average or central tendency of a data set Standard deviation (sigma): –Describes the amount of spread or observed variation in the data set Range: –Another measure of spread –The range measures the difference between the largest & smallest observed values in the data set

Reid & Sanders, Operations Management © Wiley 2002 Page 5 The Normal Distribution

Reid & Sanders, Operations Management © Wiley 2002 Page 6 Equations Mean: Standard deviation:

Reid & Sanders, Operations Management © Wiley 2002 Page 7 Impact of Standard Deviation

Reid & Sanders, Operations Management © Wiley 2002 Page 8 Skewed Distributions (One Form of Non-Normal Distribution)

Reid & Sanders, Operations Management © Wiley 2002 Page 9 SPC Methods Control charts –Use statistical limits to identify when a sample of data falls within a normal range of variation

Reid & Sanders, Operations Management © Wiley 2002 Page 10 Setting Limits Requires Balancing Risks Control limits are based on a willingness to think something’s wrong, when it’s actually not (Type I or alpha error), balanced against the sensitivity of the tool - the ability to quickly reveal a problem (failure is Type II or beta error)

Reid & Sanders, Operations Management © Wiley 2002 Page 11 Types of Data Variable level data: –Can be measured using a continuous scale –Examples: length, weight, time, & temperature Attribute level data: –Can only be described by discrete characteristics –Example: defective & not defective

Reid & Sanders, Operations Management © Wiley 2002 Page 12 Control Charts for Variable Data Mean (x-bar) charts –Tracks the central tendency (the average value observed) over time Range (R) charts: –Tracks the spread of the distribution over time (estimates the observed variation)

Reid & Sanders, Operations Management © Wiley 2002 Page 13 x-Bar Computations

Reid & Sanders, Operations Management © Wiley 2002 Page 14 Example Assume the standard deviation of the process is given as 1.13 ounces Management wants a 3-sigma chart (only 0.26% chance of alpha error) Observed values shown in the table are in ounces Time 1Time 2Time 3 Observation Observation Observation Observation Sample means

Reid & Sanders, Operations Management © Wiley 2002 Page 15 Computations Center line (x-double bar): Control limits:

Reid & Sanders, Operations Management © Wiley 2002 Page 16 2 nd Method Using R-bar

Reid & Sanders, Operations Management © Wiley 2002 Page 17 Control Chart Factors

Reid & Sanders, Operations Management © Wiley 2002 Page 18 Example Time 1Time 2Time 3 Observation Observation Observation Observation Sample means Sample ranges

Reid & Sanders, Operations Management © Wiley 2002 Page 19 Computations

Reid & Sanders, Operations Management © Wiley 2002 Page 20 Example x-bar Chart

Reid & Sanders, Operations Management © Wiley 2002 Page 21 R-chart Computations (Use D3 & D4 Factors: Table 6-1)

Reid & Sanders, Operations Management © Wiley 2002 Page 22 Example R-chart

Reid & Sanders, Operations Management © Wiley 2002 Page 23 Using x-bar & R-charts Use together Reveal different problems

Reid & Sanders, Operations Management © Wiley 2002 Page 24 Control Charts for Attribute Data p-Charts: –Track the proportion defective in a sample c-Charts: –Track the average number of defects per unit of output

Reid & Sanders, Operations Management © Wiley 2002 Page 25 Process Capability A measure of the ability of a process to meet preset design specifications: –Determines whether the process can do what we are asking it to do Design specifications (a/k/a tolerance limits): –Preset by design engineers to define the acceptable range of individual product characteristics (e.g.: physical dimensions, elapsed time, etc.) –Based upon customer expectations & how the product works (not statistics!)

Reid & Sanders, Operations Management © Wiley 2002 Page 26 Measuring Process Capability Compare the width of design specifications & observed process output

Reid & Sanders, Operations Management © Wiley 2002 Page 27 Capability Indexes Centered Process (C p ): Any Process (C pk ):

Reid & Sanders, Operations Management © Wiley 2002 Page 28 Example Design specifications call for a target value of /-0.2 microns (USL = 16.2 & LSL = 15.8) Observed process output has a mean of 15.9 and a standard deviation of 0.1 microns

Reid & Sanders, Operations Management © Wiley 2002 Page 29 Computations C p : C pk :

Reid & Sanders, Operations Management © Wiley 2002 Page 30 Three Sigma Capability Until now, we assumed process output should be modeled as +/- 3 standard deviations By doing so, we ignore the 0.26% of output that falls outside +/- 3 sigma range The result: a 3-sigma capable process produces 2600 defects for every million units produced

Reid & Sanders, Operations Management © Wiley 2002 Page 31 Six Sigma Capability Six sigma capability assumes the process is capable of producing output where +/- 6 standard deviations fall within the design specifications (even when the mean output drifts up to 1.5 standard deviations off target) The result: only 3.4 defects for every million produced

Reid & Sanders, Operations Management © Wiley 2002 Page 32 3-Sigma versus 6-Sigma

Reid & Sanders, Operations Management © Wiley 2002 Page 33 The End Copyright © 2002 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United State Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.