Statistical Quality Control, 7th Edition by Douglas C. Montgomery.

Slides:



Advertisements
Similar presentations
BPT2423 – STATISTICAL PROCESS CONTROL
Advertisements

Goal Sharing Team Training Statistical Resource Leaders (2) Peter Ping Liu, Ph D, PE, CQE, OCP and CSIT Professor and Coordinator of Graduate Programs.
Chapter 5. Methods and Philosophy of Statistical Process Control
 Variable - a single quality characteristic that can be measured on a numerical scale.  When working with variables, we should monitor both the mean.
Chapter 18 Introduction to Quality
Chapter 4 Control Charts for Measurements with Subgrouping (for One Variable)
Copyright (c) 2009 John Wiley & Sons, Inc.
Software Quality Control Methods. Introduction Quality control methods have received a world wide surge of interest within the past couple of decades.
8 Statistical Intervals for a Single Sample CHAPTER OUTLINE
Control Charts for Variables
Control Charts for Attributes
15 Statistical Quality Control CHAPTER OUTLINE
Methods and Philosophy of Statistical Process Control
Chapter 51Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. Copyright (c) 2005 John Wiley & Sons, Inc.
Design and Robustness of Some Statistical Quality Control Tools Dr. Maria Calzada Loyola University New Orleans.
Chapter 9 Title and Outline 1 9 Tests of Hypotheses for a Single Sample 9-1 Hypothesis Testing Statistical Hypotheses Tests of Statistical.
Steps in Using the and R Chart
 Review homework Problems: Chapter 5 - 2, 8, 18, 19 and control chart handout  Process capability  Other variable control charts  Week 11 Assignment.
Introduction to Statistical Quality Control, 4th Edition
 Review homework Problems: Chapter 5 - 2, 8, 18, 19 and control chart handout  Process capability  Other variable control charts  Week 11 Assignment.
Chapter 6. Control Charts for Variables. Subgroup Data with Unknown  and 
Chapter 4 Control Charts for Measurements with Subgrouping (for One Variable)
6. Control chart for variable It is important to control over both the process mean and the process variability. –Control the process by using the x chart.
Chapter 91Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc.
C HAPTER 6 Control Charts for Variables I NTRODUCTION Variable - a single quality characteristic that can be measured on a numerical scale. We monitor.
Chapter 7. Control Charts for Attributes
1 Six Sigma Green Belt Introduction to Control Charts Sigma Quality Management.
Chapter 61Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8. Process and Measurement System Capability Analysis
Dr. Dipayan Das Assistant Professor Dept. of Textile Technology Indian Institute of Technology Delhi Phone:
1 CHAPTER (7) Attributes Control Charts. 2 Introduction Data that can be classified into one of several categories or classifications is known as attribute.
Chapter 31Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
10 March 2016Materi ke-3 Lecture 3 Statistical Process Control Using Control Charts.
Les Jones IET 603. Shewhart Control Charts for: characteristics such as: length, width, temperature and volume. 1.Understand the statistical basis of.
1 Statistical Analysis - Graphical Techniques Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering EMIS 7370/5370 STAT 5340 : PROBABILITY AND.
Chapter 81Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Chapter 51Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Chapter 61Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.
Chapter 15Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. 1.
Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Statistical Intervals Based on a Single Sample
Copyright (c) 2005 John Wiley & Sons, Inc.
Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Sample Size Determination
Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 7 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.
10 Quality Control.
Agenda Review homework Lecture/discussion Week 10 assignment
Chapter 9 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.
QUALITY CONTROL AND QUALITY ASSURANCE (Contd.)
Chapter 7 Estimation: Single Population
Process Capability Process capability For Variables
Basic Training for Statistical Process Control
IENG 486: Statistical Quality & Process Control
Basic Training for Statistical Process Control
Process and Performance Capability Assessment
Process Capability.
Process and Performance Capability Assessment
Control chart (Ex 3-2) Subgroup No. Measurement Average Range Date
Individual values VS Averages
SIMPLE LINEAR REGRESSION
Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Steps in Using the and R Chart
Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Chapter 8 Alternatives to Shewhart Charts
Presumptions Subgroups (samples) of data are formed.
Statistical Quality Control
Presentation transcript:

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 6 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Subgroup Data with Unknown  and  Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Phase I Application of and R Charts Eqns 6.4 and 6.5 are trial control limits Determined from m initial samples Typically 20-25 subgroups of size n between 3 and 5 Any out-of-control points should be examined for assignable causes If assignable causes are found, discard points from calculations and revise the trial control limits Continue examination until all points plot in control Adopt resulting trial control limits for use If no assignable cause is found, there are two options Eliminate point as if an assignable cause were found and revise limits Retain point and consider limits appropriate for control If there are many out-of-control points they should be examined for patterns that may identify underlying process problems Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Example 6.1 The Hard Bake Process Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Revision of Control Limits and Center Lines Effective use of control charts requires periodic review and revision of control limits and center lines Sometimes users replace the center line on the chart with a target value When R chart is out of control, out-of-control points are often eliminated to recompute a revised value of which is used to determine new limits and center line on R chart and new limits on chart Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Phase II Operation of Charts Use of control chart for monitoring future production, once a set of reliable limits are established, is called phase II of control chart usage (Figure 6.4) A run chart showing individuals observations in each sample, called a tolerance chart or tier diagram (Figure 6.5), may reveal patterns or unusual observations in the data Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Control vs. Specification Limits Control limits are derived from natural process variability, or the natural tolerance limits of a process Specification limits are determined externally, for example by customers or designers There is no mathematical or statistical relationship between the control limits and the specification limits Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Rational Subgroups charts monitor between-sample variability R charts measure within-sample variability Standard deviation estimate of  used to construct control limits is calculated from within-sample variability It is not correct to estimate  using Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Guidelines for Control Chart Design Control chart design requires specification of sample size, control limit width, and sampling frequency Exact solution requires detailed information on statistical characteristics as well as economic factors The problem of choosing sample size and sampling frequency is one of allocating sampling effort For chart, choose as small a sample size is consistent with magnitude of process shift one is trying to detect. For moderate to large shifts, relatively small samples are effective. For small shifts, larger samples are needed. For small samples, R chart is relatively insensitive to changes in process standard deviation. For larger samples (n > 10 or 12), s or s2 charts are better choices. Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

6.2.4 Interpretation of Control Charts Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

6.2.5 The Effect of Non-normality An assumption in performance properties is that the underlying distribution of quality characteristic is normal If underlying distribution is not normal, sampling distributions can be derived and exact probability limits obtained Burr (1967) notes the usual normal theory control limits are very robust to normality assumption Schilling and Nelson (1976) indicate that in most cases, samples of size 4 or 5 are sufficient to ensure reasonable robustness to normality assumption for chart Sampling distribution of R is not symmetric, thus symmetric 3-sigma limits are an approximation and -risk is not 0.0027. R chart is more sensitive to departures from normality than chart. Assumptions of normality and independence are not a primary concern in phase I Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

6.2.6 The Operating Characteristic Function Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

If the shift is 1.0σ and the sample size is n = 5, then β = 0.75. Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Development of the control limits: Thius produces the control limits in equation (6.27) Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

This produces the control limits in equation (6.28) Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Average Run Lengths Crowder (1987b) showed that ARL0 of combined individuals and moving-range chart with conventional 3-sigma limits is generally much less than ARL0 (= 370) of standard Shewhart control chart Ability of individuals chart to detect small shifts is very poor Rather than narrowing the 3-sigma limits, correct approach to detecting small shifts is a cumulative-sum or exponentially weighted moving-average control chart (Chapter 9) Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Normality Borror, Montgomery, and Runger (1999) report that the in-control ARL is dramatically affected by nonnormal data One approach for nonnormal data is to determine control limits for individuals control chart based on percentiles of correct underlying distribution Requires at least 100 and preferably 200 observations Transformations can also be useful Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.

Learning Objectives Chapter 6 Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012  John Wiley & Sons, Inc.