Prior to taking SYSE 515, I used to think that Systems Engineering was limited to the physical, mechanical, and mathematical realms, but now I know that it indeed, encompasses areas such as Operational Strategy, Managerial Economics, Microeconomics, Political Science, Urban Dynamics, and socio-organic, non-linear dynamic systems. In particular, I was captivated by the perspectives/works of Jay Wright Forrester (Father of System Dynamics), Gordon Brown (feedback control mechanisms), and legendary System Scientist Karl Popper, whose keen perspective and paradoxical quotations immediately captivated my interest. However, it was from the work of Forrester during his time at the Massachusetts Institute of Technology (MIT) Sloan School which I truly experienced a new perspective and deeper understanding of what Systems Engineering is. Systems Engineering is not merely an understanding of an electrical or mechanical system, but a deep, multispectral, introspection of any organized ontology of similar pieces, parts, segments, aspects, elements, people, and the list goes on and on. It is a deep study of interfaces, dependencies, and most of all, the essence of cause-and-effect. System Dynamics taught me that causalities and feed-back loops can be seen in everything and are everywhere, much like the systems in which they are attributed to. Consider that the very first Systems Modeling Language (SysML) was Simulation of Industrial Management Problems (SIMPLE), written by Richard Bennett in 1958 and subsequently computer-modeled by Forrester. This work was critical for developing the basic framework for Engineering Control Theory, Feedback-Loop Theory, and counter-intuitive behavior in dynamic, non-linear systems. Furthermore, Forrester’s work in itself birthed completely new perspectives in the field of Management Science such as Industrial Dynamics and Behaviors in Organic Social Systems (Lane, 2008, pg. 6-24). I used to think that analysis was the key to understanding, but now I know that it is in observation that we, as engineers/scientists can most readily gain meaningful insights into the workings of complex systems.

                “The thing in itself is unknowable: we can only know its appearances which are to be understood as resulting in the thing itself, and from our own perceiving apparatus (Popper, 2002, pg. 476).”

-Karl Popper

Above: Forrester examining an electrostatic discharge tube. Courtesy of Systems Dynamics Review (Lange, 2008, pg. 9)

Lange, D. C. (2008). The Power of the Bond Between Cause and Effect: Jay Wright Forrester and the Field of System Dynamics. System Dynamics Review, 23(2-3), 1-34. https://systemdynamics.org/wp-content/uploads/assets/jay-w-forrester/JWForresterBio.pdf

Popper, K. (2002). The logic of scientific discovery (2nd ed.). Routledge.

 

System Dynamics and Complexity

                I truly have enjoyed the learning material and assignments over the past two modules, as they have touched on System Dynamics, Systems Thinking, and the nature of complexity within every system (even those which are seemingly simple). Additionally, I am keenly interested in the doctrines of Engineering Control Theory and the teachings of System Engineering pioneers such as Jay Wright Forrester and Karl Popper. It seems like such a dichotomy to me, that these men lived in periods where technology was still largely un-developed. Yet, it seems they possessed an uncanny (call it brilliance) ability to quantify key assertations and core foundations for understanding System Complexity, which are more relevant today than ever before. Much like Sterman pointed out, I am of the firm belief that Human Beings represent the most dynamic/complex systems (at least that we know of) on earth. As such, we are highly resilient, adaptable, and prone to broad, highly varied behavioral/functional states. This in large part, is due to a critical dependence on initial conditions, coupled with a complex sensitivity to our environment (the world around us) (Sterman, 2002). As Popper pointed out, a major aspect of the Human Machine Interface (HMI) lies within Human Cognitive Induction, and the ability to formulate validities or universal truths based on iterations of mental modeling. Through experience, we as humans formulate hypothesis/assumptions regarding our world (top-level SoS) and the sub-sets of systems within it, which we interface with (Popper, 2002). As a Systems Test Engineer, I often deal with the testing of complex Systems, leveraging equally complex control systems, and I am directly impacted by consequences related to System Dynamics and Chaotic Behavior. For example, a ubiquitous joke among Software Test Engineers is that on many days, they ask, “Why is it not working?” and on a few days they ask, “Why is it working?”  With this in mind, I pulled three major take-aways from Sterman, Popper, and Forrester’s teachings on Systems Thinking:

1.       Sampling size is Paramount. Not just in statistics, but with regards to cognitive mental modeling. The more iterations of an experience someone can model through cognitive visualization/analysis, the greater the fidelity of their mental models. THIS is the key to accurate induction. Reliability increases through expansion of the iterative modeling process (Popper, 2002).

2.       There is always context in Systems Thinking; the idea that no one situation is the same as the next. This is often exhibited in Human Behavior, where individuals will address once problem with the same solution they used for a previous, differing problem (Popper, 2002).

3.       With regards to Systems Thinking and understanding complexity in Dynamic Systems: The central idea behind Systems Thinking is to eliminate Uncertainty, Ambiguity, and Chaos through the development (and constant refining) of accurate models of System and Human behavior, over as many iterations and situations (perspectives) as possible. Simply put, increasing experience provides a greater level of understanding (Sterman, 2002).

In retrospect, I have been impacted on a profound level by the understanding attained from my analysis of Engineering Control Theory and System Dynamics. It truly is empowering to develop a greater respect for (in my case) and understanding of the critical importance statistical modeling and mathematics plays in the science of my work/home life. I am eager to see where the next bend in my learning path will lead. It is also worth noting, the The Logic of Scientific Discovery by Karl Popper transcends both time and language translation, to provide sound, dynamic principles for addressing Dynamical System Context. It is a fascinating read. Furthermore, Sterman’s real-world examples of Policy Resistance in dynamic systems are astounding and poignant.

"There is nothing more necessary to the man of science than its history, and the logic of discovery...: the way error is detected, the use of hypothesis, of imagination, the mode of testing (Popper, 2002)."

-Lord Acton

 

Popper, K. (2002). The logic of scientific discovery (2nd ed.). Routledge.

Sterman, J. D. (2002). System Dynamics: Systems Thinking and Modeling for a Complex World (ESD-WP-2003-01.13). MIT/Engineering Systems Division. https://dspace.mit.edu/bitstream/handle/1721.1/102741/esd-wp-2003-01.13.pdf?sequence=1

 

Understanding ANOVA Techniques with Excel and Learning to Decipher Variances

BlogDate_4/14/21

Topic: Analysis of Variance (ANOVA)

                                                            As I progress through the assignments in this class, I have begun to feel a deep sense of satisfaction and empowerment from the knowledge gained and the skillsets obtained. Up until I began taking this class, there were certain aspects of mathematics (statistics in particular) and relative applications in my professional life with which I was quite familiar but had always felt intimidated by because I was not leveraging the statistical concept along with the application to their full potential. Case in point, Microsoft Excel. I have leveraged the application daily to quantify variances and similarities in exceptionally large data sets for many years, but while I am sufficiently comfortable reading, analyzing, and interpreting, I have always felt frustrated by an inability to manipulate data sets within Excel myself., particularly with regards to Analysis of Variance (ANOVA). This is a tool I could often leverage in my professional life but lack the know-how. Additionally, while I was aware of the immense capabilities the application possessed, I did not have sufficient training and practice to leverage these capabilities in my work/home life. However, that completely changed for me after completing the Excel Data Analysis Tool Pak assignment. Looking over the assignment at first, I was apprehensive, but after installing the Tool Pak and running through the Laundry list of analysis tasks, I was elated; not only with being able to perform all the ANOVA functions within the data tool set, but with the understanding of how each functioned operated and WHY it was important to the data in question. For example, I never really understood the difference between a t-test, which observes the sample mean and ANOVA, which examines the variance (FordHamStats, 2010). Additionally, I could not explain the significance of each ANOVA function and its interpretation of the data at hand. I think the most valuable capability Excel retains is the ability to produce both Descriptive and Inferential statistical data. Armed with my newly acquired knowledge and confidence, I considered satellites (a subject of keen interest to me) and the host of data accompanying them. After some research, I was able to download a data sheet of all satellites by country via the Union of Concerned Scientists (UCS) webpage. The file was quite large, as there was a host of data available, from owner/operator, to apogee, longitude, perigee, inclination, class of orbit, orbit type, etc. I must confess, I have never been so excited about observing and manipulating data, but it was meaningful. Consider that there are well over 3,000 satellites in 4 different orbital classes spotted about the globe right now (UCS, 2021). What are they doing? What is the function of each? Which countries have the most? Is the number of satellites per country skewed, or proportional? The questions were endless for me. The real difference-maker was the knowledge and ability to perform the functions which could answer these questions. So, with that, I began experimenting with different functions, taking my time to understand what the variability between the different factors indicated. The spreadsheet proved to be an enjoyable wormhole of data, and I have included it with this post. In retrospect, the concepts, and skills I have acquired in the past couple weeks relate to the job duties I perform daily, and that is exciting for me. With regards to the text material, I think 9.6.1, Simple Linear Regression Analysis tied in with the ANOVA concepts I learned rather nicely because the scatter plots offer such a quick visual medium for assessing variability within large data sets like the UCS Satellite data (Khisty et al., 2012). As I continue forward in this class, I am just trying to focus on one module at a time, absorbing quality data and pondering its significance in my life.

 

 

 

 

Perigee (km)	3372	24543339	7278.570285	178534742.6
Apogee (km)	3372	27894247	8272.315243	304840208.3
Variance of Satellite by Type of Orbit, Longitude, Apogee, Perigee,
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	1.42838E+12	3371	423725880.4	7.103645997	0	1.058305
Columns	1664973966	1	1664973966	27.91282334	1.3496E-07	3.844219
Error	2.01077E+11	3371	59649070.44
Total	1.63112E+12	6743

(UCS, 2021)

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
# Launched	34	3372	99.17647059	47164.27094
USA	34	1903	55.97058824	27950.57487
China	20	405	20.25	541.7763158
Russia	34	174	5.117647059	43.98573975
United Kingdom	20	166	8.3	530.6421053
France	34	13	0.382352941	0.667557932
Spain	14	21	1.5	1.653846154
Germany	34	40	1.176470588	4.331550802
Japan	34	89	2.617647059	14.84937611
Italy	34	13	0.382352941	0.546345811
Argentina	34	28	0.823529412	6.08912656
Israel	34	16	0.470588235	0.983957219
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	343596.6676	11	31236.0607	4.34537363	4.19E-06	1.816209
Within Groups	2501545.332	348	7188.348656
Total	2845142	359
(UCS, 2021)

 

Anova: Two-Factor With Replication
SUMMARY	179	215	1634	Total
2
Count	11	11	11	33
Sum	491	393	3028	3912
Average	44.6364	35.72727	275.2727	118.5455
Variance	9693.65	8061.618	472623.8	165922.6
Total
Count	11	11	11
Sum	491	393	3028
Average	44.6364	35.72727	275.2727
Variance	9693.65	8061.618	472623.8
(UCS, 2021)
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0	0	65535	65535	#NUM!	#NUM!
Columns	405733	2	202866.6	1.24108	0.303491	3.31583
Interaction	0	0	65535	65535	#NUM!	#NUM!
Within	4903791	30	163459.7
Total	5309524	32
(UCS, 2021)

 

 

 

 

 

 

 

 

 

 

 

Anova: Two-Factor Without Replication
		Descriptive Data
SUMMARY	Count	Sum	Average	Variance
USA	4	2058	514.5	563427
China	4	405	101.25	19525.58
Russia	4	174	43.5	1619.667
UK	4	293	73.25	3852.25
France	4	20	5	22
Spain	4	21	5.25	36.91667
Germany	4	40	10	349.3333
Italy	4	13	3.25	27.58333
Japan	4	82	20.5	620.3333
Argentina	4	28	7	161.3333
Israel	4	16	4	38
Total	4	3150	787.5	1063326
Elliptical	12	360	30	3528.909
GEO	12	670	55.83333	10316.88
MEO	12	608	50.66667	10006.97
LEO	12	4662	388.5	583503
(UCS, 2021)
ANOVA			Inferential Data
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	2785222	11	253202	2.144848	0.04469	2.093254
Columns	1063326	3	354441.9	3.002441	0.04437	2.891564
Error	3895691	33	118051.3
Total	7744239	47
(UCS, 2021)

 

 

 

 

 

FordhamStats. (2010, May 7). Excel Techniques - 11 - ANOVA - Two Factor without Replication [Video]. YouTube. https://www.youtube.com/watch?v=STqxo4ToN18

Khisty, C. J., Mohammadi, J., & Amedkudzi, A. A. (2012). Systems engineering with economics, probability, and statistics (2nd ed.). J. Ross Publishing.

Association, 5(10). https://doi.org/10.1161/jaha.116.004142

Union of Concerned Scientists (UCS). (2021, January 1). UCS Satellite Database. UCSUSA.org. https://www.ucsusa.org/resources/satellite-database