Transcript ISO/TC69 Meeting in Beijing and Has the rate of

ASQ 1401 Section
El Paso, TEXAS
2009 January 14
Rudy Kittlitz
ISO/TC 69
Application of Statistical Methods
 This Technical Committee [TC] has several
subcommittees [SC] and working groups [WG]
 Terminology and symbols
 Statistical interpretation of data
 Applications of statistical methods in process
management
 Acceptance sampling
 Measurement methods and results
 Six Sigma applications
th
30
Plenary Meeting
 Beijing 2008 October 11-17
 Approximately 75 delegates
 From India, Germany, France, Denmark, United
Kingdom, etc.
US Technical Advisory Group [TAG]
 One-day meetings in the spring and the fall
 Rudy became involved in ISO/TC 69 with the 1995 March
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

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meeting of the US TAG
His first international meeting was in 1996 June in
Stockholm and has attended each year
In 2001 Rudy was elected as Chair of the US TAG and has
continued
ANSI [American National Standards Institute] is the
official contact with ISO
All USA Delegates represent the USA and ANSI, not their
company, university, etc.
Meetings in Beijing
 Arrived Friday night, 10/10
 First meeting on Saturday
 A special committee meeting on Sunday
 Monday through Friday meetings
 Took a tour on Tuesday and on Thursday
 Left on Saturday, 10/18
Using Statistics To Answer The Question:
“Has The Rate of Category 3+ Atlantic Hurricanes Changed
Since 1940?”
 This is not a talk on Global Warming
 But a statistical assessment on whether or not the rate
(i.e., number of hurricanes per year) of category 3+
Atlantic hurricanes has changed since 1940
 Cat 3+ are also known as “Major Hurricanes”
 Over the past few years all sorts of statements about
“cycles of Atlantic hurricanes”, “increased intensity”, and
others
 A simple statistical assessment should be able to answer
Figure 1. Atlantic Category 3+ Hurricanes By Year
Ref. http://weather.unisys.com/hurricane/atlantic
9
8
Category 3+
7
6
5
4
3
2
1
0
1940
1950
1960
1970
1980
Year
1990
2000
2010
Initial Comments About The Data
 Some possible “up and down” for these 68 data points,
but has the rate changed?
 Proper application of statistical analysis and Statistical
Process Control (SPC) should be able to answer this
question
 Mean of the data is 2.588
 Standard deviation is 1.863
Figure 2. Frequency Of Category 3+ Atlantic Hurricanes
Ref. Figure 1
20
Frequency
15
10
5
0
0
2
4
Category 3+
6
8
The Poisson Distribution
 The Poisson is a candidate to describe this data
 It is a count distribution
 Only need to know the mean or the average
 For small averages, the positive skew is evident
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This is seen in Figure 2
 The theoretical standard deviation is
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Avg
Observed std dev = 1.893 vs theoretical std dev = 1.609
F-test indicates no significant difference [p = 0.234]
 A SPC chart of Poisson data is the c-chart
Usual Calculations For The c-Chart
 Upper Control Limit [UCL]
 UCL = Avg + 3
 UCL = 2.588 + 3
Avg
2.588
= 7.414
 Lower Control Limit [LCL]
 LCL = Avg – 3
 LCL = 2.588 – 3

Avg
2.588
= - 2.238
No LCL since calculated LCL is below zero
 These simple calculations ignore the skewness of the
Poisson
Improved Limits For Poisson Data
 Article in Quality Engineering
 Kittlitz, R. G. Jr. (2006). Calculating the (Almost) Exact Control
Limits for a C-Chart. Quality Engineering, 18:359-366.
 The improved limits are based on a simple transformation of
the original data
2
 It is  c  0.25 3
 Kittlitz, R. G. Jr. (2003). Transforming The Poisson Distribution
To Symmetry For SPC Applications and Other Statistical
Analysis. MS Capstone Project for University of Alabama at
Huntsville
 For the hurricane data this transformation produces a
skewness of 0.47 vs original of 0.98
Improved Limits For Poisson Data Cont’d
 UCL =

1
 Avg  
12 

23

1
 Avg  
12 

23
 LCL =

2
16
 3  Avg  
3


2
16
 3  Avg  
3

32
32
3

4
1

4
 Don’t let these equations scare you!
 Programmable calculator performs the calculations
 Improved UCL = 8.07
 Improved LCL = No Lower Limit
 Calculations produces a negative number inside bracket
Figure 3. Atlantic Category 3+ Hurricanes By Year
Ref. Figure 1
9
UB=8.07
8
Individual Value
7
6
5
4
_
X=2.588
3
2
1
0
No LB
1940
1950
1960
1970
1980
Year
1990
2000
2010
Initial Conclusions From Analysis
 The typical “run-rules” for an SPC chart did not trigger
any signals
 The 1950 data point of 8 “Cat 3+” hurricanes is close to
the limit, but the cumulative probability of 8 for an
average of 2.588 is 0.99856 which is less than the limit
of 0.99865
 Unless the rate changes, we can expect 0 to 8 “Cat 3+”
hurricanes per year
Some Additional Analysis
 Advances have been made to detect a shift in the mean of data
more efficiently/quicker and is an improvement over the
typical “counting rules”
 Exponentially Weighted Moving Average [EWMA]
 Cumulative Summation or CUSUM
 An EWMA chart will be used to analyze the transformed data
 The 2003 reference details how the transformed mean and
the transformed standard deviation can be calculated from
the original mean
 Transformed mean = 1.92443
 Transformed standard deviation = 0.777823
 The EWMA chart is shown in Figure 4
Figure 4. EWMA Chart of Transformed Atlantic Category 3+ Hurricanes by Year
Ref. Figure 1
2.8
UCL=2.702
2.6
2.4
EWMA
2.2
_
_
X=1.924
2.0
1.8
1.6
1.4
1.2
LCL=1.147
1.0
1940
1950
1960
1970
1980
Year
1990
2000
Comments About Figure 4
 Remember for an EWMA chart that “counting rules”
cannot be used since the points are not independent
 Likewise the “wandering” of the points are typical of an
EWMA chart and no conclusions can be drawn from any
apparent “cycles”
 The only valid signal is if a point exceeds the limits
 No points exceed either the upper or lower limits
 Thus, no significant change in the mean
Questions?