Calculus v. Statistics is it an Ongoing Battle?

Calculus v. Statistics is it an Ongoing Battle?

Which is more useful? Which is more significant to science and business or civilization?

I believe calculus has to come first but I don’t really think either is better.  This is my opinion. Both have their own appropriate applications and end goals.

Just a quick high-level review and opinion refresher here…

Calculus is Deterministic, if you need to plot a course to Mars, you would use calculus.

Statistics is Relativistic. Statistics would be used more to decide where you would want to land on Mars.

Vs. 

According to Wikipedia Calculus is the mathematical study of change as Geometry is the study of shape and algebra is the study of operations and their application to solving equations.

The study of Calculus has two major branches; differential calculus (rates of change and slopes of curves) and integral calculus (accumulation and area under a curve)

Statistics on the other hand is about the collection, all aspects of analysis, interpretation, presentation, and organization of data.

The two main branches of statistics are  1) Descriptive statistics which is about quantitatively describing or summarizing the main features of a collection of information or the quantitative description of the data itself.  Concepts like the mean and the standard deviation are the realm of Descriptive Statistics. and 2) Inferential statistics are used to infer properties about a population of data: this includes testing hypotheses and deriving estimates. The population is assumed to be larger than the observed data set; in other words, the observed data is assumed to be sampled from a larger population which attempts to infer propositions.  Point estimates and interval estimates are the realms of Inferential Statistics, according to Wikipedia, interval (Statistical) estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, in contrast to point estimation, which is a single number.

Calculus is used in every branch of science, computer science, (even) statistics, engineering, economics, business, medicine, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change or vice versa. Often studying a problem where we know one and are trying to find the other related data.

Statistics helps us find truths or trends in the mountains of data we produce, often reducing the need to do Calculus on each and every alternate possibility.

People often lean towards one or the other as a preference but I think there isn’t really a battle of one being better than the other.

Personally, I prefer Calculus for its deterministic nature. Maybe also due to being exposed to more of it in school and work. If I had to choose one it would be Calculus.

As a final comparison on the more practical level in my work, Calculus is used to design the circuit; Statistics are used to determine the most effective testing of the product functionality and reliability before shipment.

Both apply if you are doing product testing.  If you are thermal testing in temperature chambers or on a thermal platform, you might be verifying a design built on Calculus or using Statistics to ask the questions and get answers about the yield on your production.

Rant on Polarized Power Plugs

Rant on Polarized Power Plugs

I like to talk on topics relevant to thermal testing however this post is a little break from normal and an opportunity to whine about a common annoyance.  I welcome anyone else who thinks differently or believes I am off base to chime in.

I know polarized power plugs are that way for our safety and I should be grateful but on the other hand, I find them particularly annoying,  especially when going into the supposedly modern flat face receptacles that don’t have the usual ‘funnel shape’ designed to guide the plugin for easier insertion.  The plug on the coffee grinder I start my day with has a habit of going far enough in backward to get stuck but not far enough to work.

I often think that a three-pronged plug is less annoying because it is pretty clear which way it goes in before you get close, the ground lug is designed to make contact first plus it otherwise genuinely does a better job of increasing safety and ease of mating.

The concept of the polarized plug is pretty simple but far from foolproof. For agreed-upon safety reasons, 120v. wiring in the US and the standard line voltage in many other countries have one leg that is ‘hot’ and the second leg is neutral. The ‘hot’ wire is connected to the very slightly smaller receptacle, (right side). Neutral means that it is connected to the ground at the main circuit panel. You generally can’t get shocked by touching just this wire unless someone has miswired things. Keeping this ‘polarity’ extended internally to the device allows the product to be made somewhat safer.

In this graphic from allaboutcircuits.com, when the switch at the top-right is OFF, the accidental contact would have been safe if the plug polarity had been maintained.

Should the accidental contact happen on the other side of the load (top right) and polarity be correct, there would still be shock hazard but it would be limited to the time that the power switch is ON.  Sometimes manufacturers can look at the product and otherwise predict which wire is more likely to make some accidental contact (motors for example).

Additional safety would be provided if the product case (shown with dashed lines) is connected to the ground with a grounded power cord. The intention of the ground is to cause an external fuse or breaker (not shown) to blow should this ‘accidental contact’ from the circuit to the product case occur. This renders the product unusable until short is cleared.

Safety engineers have agreed that we should have a third wire, not to rely on the proper connection of the other two even though one is connected to the ground already. Under normal conditions, no current would be flowing through a separate ground wire. A nay-sayer like me might argue that there are more opportunities for wiring errors and a grounded product housing might provide another pathway to get shocked if a person touched wiring and the housing at the same time but I am sure that like seatbelts, statistically many more lives and injuries are saved when grounding wiring is used.  Even if not always 100% properly used.  An additional benefit from a third wire is for protection from electrical noise on today’s products that are generally becoming more sensitive to electrical noise.

My position is that manufacturers should do one little inexpensive change to make the product a bit safer before relying on the polarized plug. A double pole power switch would isolate both sides of the circuit should ‘accidental contact’ occur anywhere downstream from the switches (when OFF). When the switch is ON, some equally reduced risk of shock still exists in either case.  The level of safety is the same with a double pole switch as provided by the properly connected polarized plug when the switch is ON.

I am also in favor of additional use of technology that is pretty much commonplace and better refined today. This is the Ground fault interrupter or GFI receptacle/circuit. These circuits are now more reliable and fit into the electrical box inside the power receptacle. The theory is that if the sensors in the GFI since even a very small difference in current measured on one leg to that of the other, they will immediately interrupt the circuit. If the currents are not the exactly same, the presumption is the current is somehow going through a ground fault which may be through a human body. GFI circuits provide safety regardless is the switch is on or off and generally are the only disruption to life when there is definitely a problem. Nothing could go wrong, right?

Well generally that is the expected result without too much deviation and I would say that for the cost, higher risk areas, receptacles should be protected with GFI devices, especially in labs, kitchens, garages and where things get worked on and other risks such as water or pipes (grounding) exist. I say instead of polarized plugs, all devices should employ switches on both the hot and the neutral in the event that a plug or wiring is somehow backward, or something else unexpected goes wrong. Get rid of the polarized plug. What say ye?

That’s just the way it is done…

That’s just the way it is done…

Yes, we all have heard that or some similar version at least a few times over history.

…And understandably for many things. Clearly, when there is work to be done, there are benefits to following tried and tested methods that are known to produce expected good results.

It may be a cop-out for not taking time to explain or re-think the latest methods or it may be that there truly has been a lot of thought put in and a certain existing methodology really has merit above others.

Temperature testing in a chamber is “Just the way it is done”   That may be a good heuristic to follow, or not.

Methodologies change, occasionally rules of thumb do, but the laws of thermodynamics, not so.  Some technologies evolve pretty quickly when a new and better way is obvious.  CRT monitors, for example, made the exit quickly,  GPIB not so. That’s a whole separate story but there are valid arguments why some say ‘Viva GPIB‘.

So, to the point, we don’t foresee standard or custom temperature chambers ever exiting the scene. New methods do evolve. When you look at a large temperature chamber in the lab, you don’t have to think about an old tube monitor. Think instead of a more optimal solution. The Hybrid Benchtop Chamber can be thought of as an extension of the capabilities of either a temperature chamber or a thermal platform. Small chambers are more efficient, take up little space, and have the versatility to perform most thermal testing tasks right on the benchtop.

Thermal platforms (hot & cold plates) as an alternative to chambers can handily improve the speed of many thermal testing tasks, especially for testing devices that are more massive, with higher power dissipation and devices that have at least one flat conductive surface.

Especially when temperatures are not so extreme, some people will use thermal platforms with no cover at all.  A variety of Polycarbonate covers (shown below) are available that reduce condensation, corrosion plus keep temperature-shifting air currents away from devices under test.  A dry Nitrogen purge added to covers further reduces the effects of water condensation on the device while only minimally affecting the thermal performance.  One further step in thermal performance enhancement is to add the conditioning option to the purge system.  The purge gas is run through an extra heat exchanger in the platform as indicated here using arrows.

This simple solution gets the air temperature inside a cover close to the platform temperature which is very beneficial for reducing thermal gradients. Unfortunately, there will always be some gradient between the platform temperature and air temperature.  The Hybrid Benchtop Chamber optimizes the performance boost with greater airflow and the air temperature is actually controlled to the same or independent temperature from the platform.  Temperatures can be adjusted manually or with advanced temperature control algorithms to help get the whole device to the required temperature as quickly as practical or desired.

Combining convection and conduction to enhance thermal test performance is a big advantage when it comes to getting thermal testing done in a minimal amount of time. Below right HBC144N and below right is the HBC49N

Often cutting test times in half! At the same time, the Hybrid Benchtop chamber with Synergy Nano controller provides verification that one or several measurement points on the device actually achieved the required temperature profile.  PDF reports of results can be automatically printed directly to a network printer or FTP file destination.

The Hybrid Benchtop Chamber is a performance advancement of thermal platforms as well as an advancement in small benchtop chambers, combining the benefits of both.  It can even be retrofitted to existing Thermal Platforms.

And remember, If it turns out that the “Traditional way it is done” is the way it should be done, the chamber or platform can be used by itself as a small benchtop chamber or thermal platform.

Talk to us about your RF / Electronics / Power thermal testing requirements. We have qualified people here to answer your thermal testing questions.