introduction to statistical quality control, 5th edition · title: introduction to statistical...
Post on 20-Mar-2020
140 Views
Preview:
TRANSCRIPT
Chapter 5 1 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 2 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 3 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 4 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Subgroup Data with Unknown and
Chapter 5 5 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 6 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 7 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 8 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 9 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Phase I Application of and R Charts
• Eqns 5-4 and 5-5 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
1. Eliminate point as if an assignable cause were found and revise limits
2. 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
x
Chapter 5 10 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 11 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 12 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 13 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 14 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 15 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 16 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 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
x
x
R
Chapter 5 17 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 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 5-4)
• A run chart showing individuals observations
in each sample, called a tolerance chart or
tier diagram (Figure 5-5), may reveal patterns
or unusual observations in the data
Chapter 5 18 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 19 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 20 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 21 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Control vs. Specification Limits
• Control limits – Derived from natural process
variability, or the natural tolerance limits of a process
• Specification limits – Determined externally
– i.e. by customers or designers
• No mathematical or statistical relationship b/w the control limits and the specification limits
Chapter 5 22 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 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
• DO NOT use to calculate !!!
x
Chapter 5 23 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 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 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 (efficiency drops dramatically in efficiency as n increases)
• For larger samples (n > 10 or 12), s or s2 charts are better choices.
x
Chapter 5 24 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Changing Sample Size
• Due to:
– Cost effectiveness
– Process has exhibited good stability
– Fewer resources are being allocated for process monitoring
• To calculate the new control limit:
oldoldd
newd
oldoldd
newd
RAxLCL
RAxUCL
Chartx
)(
)(
2
)(
)(
2
2
2
2
2
oldoldd
newd
oldoldd
newd
new
oldoldd
newd
RDLCL
RRCL
RDUCL
ChartR
)(
)(
3
)(
)(
)(
)(
4
2
2
2
2
2
2
,0max
Chapter 5 25 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 26 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Read page 229 – 232!
Chapter 5 27 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 28 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 29 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 30 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
For the out-of-control ARL
Chapter 5 31 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
• ATS: average time to signal = # of time
periods that occur until a signal is generated on
the control chart.
– Given that samples are taken at equally spaced
intervals of time h
• Useful to express the ARL in terms of the
number of individual units sampled (I)
Chapter 5 32 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Read page 237!
Chapter 5 33 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 34 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 35 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 36 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 37 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 38 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 39 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 40 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 41 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 42 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 43 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 44 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 45 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 46 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 47 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
2
2
3
3
d
RMxLCL
xLineCenter
d
RMxUCL
Chapter 5 48 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 5 49 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.
Copyright (c) 2005 John Wiley & Sons, Inc.
top related