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

30

th

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 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

company, university, etc.

their

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

7 6 9 8 1 0 5 4 3 2 1940

Figure 1. Atlantic Category 3+ Hurricanes By Year

Ref. http://weather.unisys.com/hurricane/atlantic 1950 1960 1970

Year

1980 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

20

Figure 2. Frequency Of Category 3+ Atlantic Hurricanes

Ref. Figure 1 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  This is seen in Figure 2  The theoretical standard deviation is   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 Avg  UCL = 2.588 + 3 2 .

588  Lower Control Limit [LCL] = 7.414

 LCL = Avg – 3 Avg  LCL = 2.588 – 3  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  It is 

c

 0 .

25  2 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 =    Avg  1 12 2 3   3  2 3  Avg  1 6   3 2  3 4  LCL =    Avg  1 12  2 3   3  2 3   1 6   3 2  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

1 0 4 3 2 9 8 7 6 5 1940

Figure 3. Atlantic Category 3+ Hurricanes By Year

Ref. Figure 1 1950 1960 1970

Year

1980 1990 2000 UB=8.07

_ X=2.588

2010 No LB

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

2.2

2.0

1.8

1.6

__ X=1.924

1.4

1.2

1.0

1940 1950 1960 1970

Year

1980 1990 2000 LCL=1.147

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?