© Mark Biegert and Math Encounters, 2021. Publication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Mark Biegert and Math Encounters with appropriate and specific direction to the original content.
DisclaimerAll content provided on the mathscinotes.com blog is for informational purposes only. The owner of this blog makes no representations as to the accuracy or completeness of any information on this site or found by following any link on this site. The owner of mathscinotes.com will not be liable for any errors or omissions in this information nor for the availability of this information. The owner will not be liable for any losses, injuries, or damages from the display or use of this information.
Category Archives: Statistics
Until the arrival of the coronavirus, I looked forward every week to volunteering at a local library as a tutor for university students. Now that COVID is raging around me, I have moved the tutoring online. Most of the students are training for some form of a medical career. This week a student presented me with bacterial growth data and was wondering how to estimate the growth rate and doubling time for the bacteria using Excel. This exercise nicely illustrates the entire data analysis process (Figure 1) in a single example and I decided to post my solution here. Continue reading
erforming an MTBF prediction is to designing HW as putting a license plate on your car is to driving the car. You need the license to legally drive the car, but it adds no value to your driving experience. Similarly, every company I have worked for demands a predicted MTBF for every HW product, but it adds no value to the design process. In fact, I would argue that generating the MTBF predictions actually adds negative value to the product deployment because it generates a number that is often misused by customers to estimate spare requirements and field support costs. Since no one has told customers otherwise, they think the MTBF value accurately reflects the real failure rate of a product. In fact, MTBF predictions provide a gross estimate of the rate of random parts failure at product maturity. Continue reading
I spend a lot of time in northern Minnesota now that I have a home there. I have been surprised as to how popular curling is in the area (Figure 1). The US curling team at the 2018 Olympics is dominated by people from northern Minnesota. I also notice that there are quite a few Minnesotans participating in the games other sports – the numbers are large enough that the New York Times has even written an article called "Team USA? More Like Team Minnesota" on the topic (PDF of the article). Our state does not have a huge population, ~5 million, and most of that population is concentrated around Minneapolis and St. Paul. The northern part of the state is only sparsely populated as it is covered with national forests and wilderness areas. Continue reading
I was reading a post on Statista showing the NFL teams with the most Super Bowl wins. Since my staff includes a number of football fans — mainly Viking and Packer supporters — I decided it would be a good training exercise to show them how to gather the football statistics and present them in the same manner as shown on Statista. I should mention that I do not follow football at all; this is purely a data analysis exercise for me. Continue reading
The only television news program that I watch is the PBS Newshour. I particularly like the discussions between Mark Shields, a reasonable liberal, and David Brooks, a reasonable conservative. On inauguration day (20-Jan-2017), they had an interesting discussion about the challenges the US faces and what can be done about them. Continue reading
I do not watch much reality television, but one show I do watch is Naked and Afraid (N&A). I have always been interested in primitive survival skills (e.g. I have blogged about knot tying and rigging), and this show really puts those skills to the test. I like the fact that the participants are presented with survival challenges from around the world (Figure 1). They have been on all the continents but Antarctica – I could not imagine someone surviving naked in Antarctica for any length of time. Continue reading
One of the more distasteful tasks I need to do is make estimates of annual product failure rates using MTBF predictions based on part count methods. I find this task distasteful because I have never seen any indication that MTBF predictions are correlated in any way with field failure rates. This is not solely my observation – the US Army has cancelled its use of part count method MTBF predictions (i.e. based on MIL-HDBK-217). However, the telecommunications industry has continued to use these predictions through their use of SR-332. If you want to see a simple example of an SR-332-based reliability prediction, see this very clear example from Avago. Continue reading
I had never seen coal until my first trip to China when I saw people on bicycles transporting coal to their homes for heat. I started to wonder just how much coal a home would need for heating. I have seen numerous values for the heat content of the various types of coal. I recalled from primary school that there were three types of coal: anthracite, bituminous, and lignite. So I would have expected three values for the heat output of coal. When I actually looked, I found dozens of grades of three primary types of coal. Each of the different grades would generate different amounts of heat per kilogram. I thought I would take a closer look at how the heat output from coal could be modeled using regression and a simplified model based on chemical heats of formation. Continue reading
I recently finished a course on Bayesian analysis from Statistics.com and I have been looking for application examples that will provide me with some experience using these methods. I like to compare the Bayesian solutions with the standard solutions (usually called Frequentist). Continue reading