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

9

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?