asq 1401 section el paso, texas 2009 january 14 rudy kittlitz
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ASQ 1401 SectionEl Paso, TEXAS
2009 January 14Rudy Kittlitz
ISO/TC 69Application of Statistical MethodsThis Technical Committee [TC] has several
subcommittees [SC] and working groups [WG]Terminology and symbolsStatistical interpretation of dataApplications of statistical methods in process
managementAcceptance samplingMeasurement methods and resultsSix Sigma applications
30th Plenary MeetingBeijing 2008 October 11-17Approximately 75 delegatesFrom India, Germany, France, Denmark,
United Kingdom, etc.
US Technical Advisory Group [TAG]One-day meetings in the spring and the fallRudy became involved in ISO/TC 69 with the
1995 March meeting of the US TAGHis first international meeting was in 1996 June
in Stockholm and has attended each yearIn 2001 Rudy was elected as Chair of the US TAG
and has continuedANSI [American National Standards Institute] is
the official contact with ISOAll USA Delegates represent the USA and ANSI, not their company, university, etc.
Meetings in BeijingArrived Friday night, 10/10First meeting on SaturdayA special committee meeting on SundayMonday through Friday meetingsTook a tour on Tuesday and on ThursdayLeft 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 1940Cat 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
20102000199019801970196019501940
9
8
7
6
5
4
3
2
1
0
Year
Cate
gory
3+
Figure 1. Atlantic Category 3+ Hurricanes By YearRef. http://weather.unisys.com/hurricane/atlantic
Initial Comments About The DataSome 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
86420
20
15
10
5
0
Category 3+
Frequency
Figure 2. Frequency Of Category 3+ Atlantic HurricanesRef. Figure 1
The Poisson DistributionThe Poisson is a candidate to describe this
dataIt is a count distributionOnly need to know the mean or the averageFor small averages, the positive skew is evident
This is seen in Figure 2The theoretical standard deviation is
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
Avg
Usual Calculations For The c-ChartUpper Control Limit [UCL]
UCL = Avg + 3UCL = 2.588 + 3 = 7.414
Lower Control Limit [LCL]LCL = Avg – 3LCL = 2.588 – 3 = - 2.238
No LCL since calculated LCL is below zero
These simple calculations ignore the skewness of the Poisson
Avg
588.2
Avg
588.2
Improved Limits For Poisson DataArticle 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 dataIt is 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
32
25.0c
Improved Limits For Poisson Data Cont’d
UCL =
LCL =
Don’t let these equations scare you!Programmable calculator performs the calculations
Improved UCL = 8.07Improved LCL = No Lower Limit
Calculations produces a negative number inside bracket
4
3Avg
3
23
12
1Avg
23
6132
4
1Avg
3
23
12
1Avg
23
6132
20102000199019801970196019501940
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8
7
6
5
4
3
2
1
0
Year
Indiv
idual V
alu
e
_X=2.588
UB=8.07
No LB
Figure 3. Atlantic Category 3+ Hurricanes By YearRef. Figure 1
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 AnalysisAdvances 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 dataThe 2003 reference details how the transformed
mean and the transformed standard deviation can be calculated from the original mean
Transformed mean = 1.92443Transformed standard deviation = 0.777823
The EWMA chart is shown in Figure 4
2000199019801970196019501940
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
Year
EWM
A __X=1.924
UCL=2.702
LCL=1.147
Figure 4. EWMA Chart of Transformed Atlantic Category 3+ Hurricanes by YearRef. Figure 1
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 limitsNo points exceed either the upper or lower limitsThus, no significant change in the mean
Questions?