10-1Quality Control William J. Stevenson Operations Management 8 th edition

10-2Quality Control CHAPTER 10 Quality Control McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.

10-3Quality Control Phases of Quality Assurance Acceptance sampling Process control Continuous improvement Inspection before/after production Inspection and corrective action during production Quality built into the process The least progressive The most progressive Figure 10.1

10-4Quality Control Inspection  How Much/How Often  Where/When  Centralized vs. On-site InputsTransformationOutputs Acceptance sampling Process control Acceptance sampling Figure 10.2

10-5Quality Control Cost Optimal Amount of Inspection Inspection Costs Cost of inspection Cost of passing defectives Total Cost Figure 10.3

10-6Quality Control Where to Inspect in the Process  Raw materials and purchased parts  Finished products  Before a costly operation  Before an irreversible process  Before a covering process

10-7Quality Control Examples of Inspection Points Table 10.1

10-8Quality Control  Statistical Process Control: Statistical evaluation of the output of a process during production  Quality of Conformance: A product or service conforms to specifications

10-9Quality Control Control Chart  Control Chart  Purpose: to monitor process output to see if it is random  A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means)  Upper and lower control limits define the range of acceptable variation

10-10Quality Control Control Chart UCL LCL Sample number Mean Out of control Normal variation due to chance Abnormal variation due to assignable sources Figure 10.4

10-11Quality Control Statistical Process Control  The essence of statistical process control is to assure that the output of a process is random so that future output will be random.

10-12Quality Control Statistical Process Control  The Control Process  Define  Measure  Compare  Evaluate  Correct  Monitor results

10-13Quality Control Statistical Process Control  Variations and Control  Random variation: Natural variations in the output of a process, created by countless minor factors  Assignable variation: A variation whose source can be identified

10-14Quality Control Sampling Distribution Sampling distribution Process distribution Mean Figure 10.5

10-15Quality Control Normal Distribution Mean  95.44% 99.74%  Standard deviation Figure 10.6

10-16Quality Control Control Limits Sampling distribution Process distribution Mean Lower control limit Upper control limit Figure 10.7

10-17Quality Control SPC Errors  Type I error  Concluding a process is not in control when it actually is.  Type II error  Concluding a process is in control when it is not.

10-18Quality Control Type I Error Mean LCLUCL  /2  Probability of Type I error Figure 10.8

10-19Quality Control Observations from Sample Distribution Sample number UCL LCL 1234 Figure 10.9

10-20Quality Control Control Charts for Variables  Mean control charts  Used to monitor the central tendency of a process.  X bar charts  Range control charts  Used to monitor the process dispersion  R charts Variables generate data that are measured.

10-21Quality Control Mean and Range Charts UCL LCL UCL LCL R-chart x-Chart Detects shift Does not detect shift Figure 10.10A (process mean is shifting upward) Sampling Distribution

10-22Quality Control x-Chart UCL Does not reveal increase Mean and Range Charts UCL LCL R-chart Reveals increase Figure 10.10B (process variability is increasing) Sampling Distribution

10-23Quality Control Control Chart for Attributes  p-Chart - Control chart used to monitor the proportion of defectives in a process  c-Chart - Control chart used to monitor the number of defects per unit Attributes generate data that are counted.

10-24Quality Control Use of p-Charts  When observations can be placed into two categories.  Good or bad  Pass or fail  Operate or don’t operate  When the data consists of multiple samples of several observations each Table 10.3

10-25Quality Control Use of c-Charts  Use only when the number of occurrences per unit of measure can be counted; non- occurrences cannot be counted.  Scratches, chips, dents, or errors per item  Cracks or faults per unit of distance  Breaks or Tears per unit of area  Bacteria or pollutants per unit of volume  Calls, complaints, failures per unit of time Table 10.3

10-26Quality Control Use of Control Charts  At what point in the process to use control charts  What size samples to take  What type of control chart to use  Variables  Attributes

10-27Quality Control Run Tests  Run test – a test for randomness  Any sort of pattern in the data would suggest a non-random process  All points are within the control limits - the process may not be random

10-28Quality Control Nonrandom Patterns in Control charts  Trend  Cycles  Bias  Mean shift  Too much dispersion Figure 10.11

10-29Quality Control Counting Above/Below Median Runs(7 runs) Counting Up/Down Runs(8 runs) U U D U D U D U U D B A A B A B B B A A B Figure Figure Counting Runs

10-30Quality Control  Tolerances or specifications  Range of acceptable values established by engineering design or customer requirements  Process variability  Natural variability in a process  Process capability  Process variability relative to specification Process Capability

10-31Quality Control Process Capability Lower Specification Upper Specification A. Process variability matches specifications Lower Specification Upper Specification B. Process variability well within specifications Lower Specification Upper Specification C. Process variability exceeds specifications Figure 10.15

10-32Quality Control Process Capability Ratio Process capability ratio, Cp = specification width process width Upper specification – lower specification 6  Cp =

10-33Quality Control Process mean Lower specification Upper specification 1350 ppm 1.7 ppm +/- 3 Sigma +/- 6 Sigma 3 Sigma and 6 Sigma Quality

10-34Quality Control Improving Process Capability  Simplify  Standardize  Mistake-proof  Upgrade equipment  Automate

10-35Quality Control Taguchi Loss Function Cost Target Lower spec Upper spec Traditional cost function Taguchi cost function Figure 10.17

10-36Quality Control Limitations of Capability Indexes 1. Process may not be stable 2. Process output may not be normally distributed 3. Process not centered but C p is used

10-37Quality Control Additional PowerPoint slides contributed by Geoff Willis, University of Central Oklahoma. CHAPTER 10

10-38Quality Control Statistical Process Control (SPC)  Invented by Walter Shewhart at Western Electric  Distinguishes between  common cause variability (random)  special cause variability (assignable)  Based on repeated samples from a process

10-39Quality Control Empirical Rule -3  -1  -2  +1  +2  +3  68% 95% 99.7%

10-40Quality Control Control Charts in General  Are named according to the statistics being plotted, i.e., X bar, R, p, and c  Have a center line that is the overall average  Have limits above and below the center line at ± 3 standard deviations (usually) Center line Lower Control Limit (LCL) Upper Control Limit (UCL)

10-41Quality Control Variables Data Charts  Process Centering  X bar chart  X bar is a sample mean  Process Dispersion (consistency)  R chart  R is a sample range

10-42Quality Control X bar charts  Center line is the grand mean (X double bar)  Points are X bars -OR-

10-43Quality Control R Charts  Center line is the grand mean (R bar)  Points are R  D 3 and D 4 values are tabled according to n (sample size)

10-44Quality Control Use of X bar & R charts  Charts are always used in tandem  Data are collected (20-25 samples)  Sample statistics are computed  All data are plotted on the 2 charts  Charts are examined for randomness  If random, then limits are used “forever”

10-45Quality Control Attribute Charts  c charts – used to count defects in a constant sample size

10-46Quality Control Attribute Charts  p charts – used to track a proportion (fraction) defective

10-47Quality Control Process Capability The ratio of process variability to design specifications Upper Spec Lower Spec Natural data spread The natural spread of the data is 6σ -1σ +2σ -2σ +1σ+3σ -3σ µ

10-48Quality Control Training MQ4 Job rotation/quality fatigue at Honda

10-49Quality Control Quality Measurement STA10 Monitoring

10-50Quality Control Services/Measurement STAO3 Survey/Efficiency, Admission/Discharge