Engineering 9516 Similitude, Modelling and Data Analysis Memorial University of Newfoundland January April 2009 Term Paper Use of DOE Methodology for Investigating Factors that Influence the Operating Time of the Eton Grundig FR-200 Emergency Radio R. Harvey 1 1 Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John s, NL, Canada, A1B 3X5. Abstract: The Eton Grundig FR-200 Emergency Radio has the ability to be powered solely by a built in Ni-MH battery that takes its charge from a dynamo-crank. This paper uses the statistical design of experiments methodology to identify the influence of four factors on the overall operating time of the radio. A 2 x 2 4 factorial design was used to first explore the effect of cranking time, use of the emergency light, operating volume and listening band (AM or FM). In this first experiment a square root transformed model for operating time was developed with all four main effects found to be significant. A follow-up experiment was conducted using response surface methodology... insert the remainder... 1. Introduction The Eton Grundig FR200 Emergency Radio (as shown in Figure 1) is a lightweight and portable shortwave radio that has the ability to be powered solely by a built-in Ni-MH battery that takes its charge from a dynamo-crank. The self-power capability of the FR200 makes it an excellent radio for both emergency situations and recreational pursuits. According to the product manual for the FR200, 60 to 90 seconds of vigorous dynamo-cranking will result in an operating time of 40 to 60 minutes when the operating volume is set to low (Eton Corporation, 2007). The product manual also states that the user has the option to run an emergency light at the same time as the radio, but doing so will dramatically reduce the playback time. From my own personal experience, I have found that perhaps it is not just the cranking time and use of the emergency light that will determine the resulting operating time of the radio. Figure 1. Eton Grundig FR200 Emergency Radio 1
In this paper, I have used the statistical design of experiments (DOE) methodology to examine four factors that I thought were influencing the operating time of the radio. A two-level full factorial design with 2 replicates, 2 x 2 4, was used to first explore the effect of cranking time, use of the emergency light, operating volume and listening band (AM or FM) on the operating time. 2. Design of Experiments Methodology Experiments are an important part of the scientific decision-making process in that they provide insight into how a system or a process works. The validity of any conclusion drawn from an experiment will be highly dependant on how the experiment itself was conducted. It is for this reason that the design of an experiment will play a major role in determining the eventual solution of the problem that motivated the experiment (Montgomery and Runger, 2007). There are currently a number of experimental design methods that can be used for determining the effect of changing the level of some factors of interest on a particular response. One traditional approach involves changing one factor at a time while keeping all others constant (known as the one factor at a time or OFAT approach). This OFAT approach lacks the ability to identify factor interaction (when the effect of some factor depends on the level of another factor) and overall it is considered to be highly inefficient. All in all, it is unfortunate that this approach is still being used quite frequently in today s scientific community (Montgomery and Runger, 2007). An alternative and more efficient approach to experimentation would be to use the design of experiments (DOE) methodology developed in the 1920 s by Ronald A. Fisher. The DOE approach systematically applies statistics to experimentation and gives us the ability to learn about the processes we are investigating, screen for important factors and determine if there are any interactions between factors. The DOE approach also lets us build mathematical models and optimize the response being measured (Hawkins and Lye, 2006). One of the more general DOE techniques for experimentation involving two or more factors is known as the general factorial design and involves performing the experimental trials, or runs, at all combinations of factor levels. For factorial experiments with more than three factors this general approach will require many runs - particularly if the factors have more than two levels. A special case of the general factorial design is that of k factors each at only two levels known as the 2 k factorial design. This design works quite well for preliminary testing purposes and tends to be the most commonly used in industrial experiments. For my initial explorations with the radio I chose to use a two-level factorial design with two replicates, known as a 2 x 2 4 design. A technique known as blocking was used for dividing the required 32 runs in 4 separate groups of 8 runs. 2
3. The First Exploratory Experiment The following factors were chosen for my first exploratory experiment with the radio: A. Cranking time (30 seconds 60 seconds) B. Volume level (0 low 1 high) C. Use of the emergency light (off on for 10 seconds) D. Operating band (AM FM) 3.1 Determining the Factor Levels The high and low levels that were selected for this first experiment were based on previous experience I had with the radio and are shown in Table 1. Table 1: Design Summary for First Exploratory Experiment Factor Name Low Actual High Actual Low Coded High Coded A Cranking time 30 seconds 60 seconds -1.00 +1.00 B Volume Level Low High -1.00 +1.00 C Emergency Light Off 10 seconds -1.00 +1.00 D Operating Band AM FM -1.00 +1.00 For Factor A, cranking time, the product manual specifies that 60 to 90 seconds of vigorous cranking will result in an operating time of 40-60 minutes if the radio is kept at low volume (Eton Corporation, 2007). However, cranking for longer than 60 seconds can be quite tiring and tends to overstress the cranking handle (a previous radio had its handle cranked when an overeager operator tried cranking as fast as they could for 90 seconds). For the low level I know that cranking the radio for around 30 seconds will usually keep it powered for about 3 minutes or the average length of a radio song. The low level for Factor B, volume level, was selected as the minimum level that would allow the radio to be audible from 10 feet away (a position on the volume dial slightly above the volume off point). The high level was selected as the highest level that would not stress the speakers too much (slightly below the volume maximum level). I did not use the loudest volume setting on the radio as the high level as at this uppermost limit the radio tends to provide a lot of feedback and is not pleasant to listen to. These positions were marked on the volume control dial for easy selection during the experimental runs. The high and low levels for Factor C, use of the emergency light, were selected to represent actual use of the radio s emergency light in the field. The product specifications for the radio state that use of the emergency light will drastically reduce the operating time and from previous experience I ve found that it is best to use the light for only short periods of time. An upper level of 10 seconds of light use at the start of the operating time was selected to represent those times in the field when light was needed for only a short moment. Any longer than 10 seconds and operating time of the radio will certainly be quite limited. 3
The FR200 has the capability to receive radio signals on both the AM and FM frequencies. Factor D, operating band, had its low level set to station CJYQ (930 khz AM) and its high level set to station CKIX (99.1 MHz FM). 3.2 Measurement of the Response The response chosen for measurement was the operating time of the radio in minutes. For each run of the experiment the radio was cranked and the timer started when the radio was switched on. Each run was completed when the radio station was no longer audible. 3.3 Experimental Procedure During testing a conscious effort was made to ensure that some potentially influencing factors were kept constant throughout the testing: - Temperature: set at 22 C (the operating temperature of the radio is 0 to 50 C). - Reception: all testing performed in an open area in my house with the antennae of the radio fully extended. - Cranking speed: during the experiment I tried to keep a constant turning speed of the dynamocrank. This roughly worked out to 50 cranks in 30 seconds and 100 cranks in 60 seconds. - Residual power: after the completion of each test run the radio was left on for a period of 5 minutes to ensure that the battery would be completely drained before cranking the dynamo for the next run. 3.4 Factorial Design for the First Experiment The 2 x 2 4 factorial experiment required 32 runs to determine the influence of the four factors on the operating time of the radio. At the time of experimentation, I had enough time to complete about 8 of these runs a day. Design-Expert software (version 7.1.3) by Stat-Ease was used to develop the 4 smaller blocks of 8 runs I would need to complete the experiment. Design-Expert selected the four factor interaction term ABCD to be the confounded term that would provide the basis for the blocking design. The first two blocks of the blocking design are shown in Table 2. These were determined by examining all the possible treatment combinations for the experiment (1, a, b, ab, c, ac, bc, abc, d, ad, bd, abd, cd, acd, bcd, abcd). The treatment combinations that had an even number of letters in common with ABCD went into the first block (the principal block). The treatment combinations for the reamining block was determined using a technqiue known as MOD-2 multiplication [4]. 4
3.5 Experimental Results After completion of these 32 runs, I found Design-Expert to be an effective tool for quickly determining the significant effects and interactions in an experiment. An effects list for this first experiment is given in Figure 2. Figure 2 Effects List for the First Exploratory Experiment 5
3.6 Interpretation and Discussion of the First Experiment Our ANOVA analysis has shown that only effects A, B and C are significant. An equation for the response (operating time) can be developed as shown in Equation 1. [1] Sqrt (Operating time) 3.74 0.50A 0.28B 0.18C 0. 58D 6
4. The Follow-up Experiment With a model developed for the four factors I was interested in carrying out a follow-up experiment that would further investigate the influence of Factors A, B and C when D was set at FM. Response surface methodology was used to develop the overall design of this experiment. 4.1 Response Surface Methodology With a Response surface methodology (or RSM) is a collection of mathematical and statistical techniques that are useful for modeling and analysis in applications where a response of interest is influence by several variables and the objective is to optimize the response [4]. For this follow-up experiment I used a standard RSM design called a centered central composite design (CCD) for optimization (more information on CCD can be found in [2]). For this follow-up experiment I chose to use the following face centered central composite design (CCF): - 3 factors at 3 levels each: A (cranking time), B (volume level), C (use of the emergency light) - 2 replicates of the factorial points and 4 center points in each factorial block - 2 replicates of the axial (star) points and 2 center points in each axial block - Face centered (alpha = 1.0) This design required 34 runs in total. I had two full days to devote to experimentation, so Design-Expert was used to develop 2 blocks of randomized runs. The complete design along with the measured operating time is shown in Table 5. 7
5. Conclusions The design of experiments methodology was used to develop a two-level full factorial design with 2 replicates, 2 x 2 4, to first explore the effect of cranking time, use of the emergency light, operating volume and listening band (AM or FM) on the operating time of the Grundig FR200 Emergency Radio. A squareroot transformed model consisting of all four main effects was developed. The operating times predicted by the model were found to be in close agreement with the actual operating times found in experimentation. A follow-up experiment was conducted to further investigate the influence of cranking time, operating volume, and use of the emergency light on operating time of the radio when the radio was set to the FM listening band. Response surface methodology was used to develop a face centered central composite design consisting of 32 runs in two blocks. A significant model was developed consisting of all 3 main effects and two factor interactions between cranking time-operating volume and cranking time-use of the emergency light. Graphical plots were found to be quite helpful in understanding both the main and the interaction effects of these factors. The model was checked with follow-up runs and overall the predicted and actual values of operating time were in close agreement. 8
6. What I Would Do Differently If I had the opportunity to re-do the experiment I would change certain aspects of my design. I think that if instead of taking... 9
7. References Eton Corporation. 2007. FR200 Emergency Radio Operation Manual. Eton Corporation, Palo Alto, California, United States of America. Hawkins, D., & Lye, L.M. 2006. Use of DOE methodology for Investigating Conditions that Influence the Tension in Marine Risers for FPSO Ships. 1 st International Structural Speciality Conference, Calgary, Alberta, Canada, May 23-26, 2006. Lye, L. 2007. ENGI 9516: Similitude, Modeling and Data Analysis - Course Notes. Memorial University of Newfoundland and Labrador, Canada. Montgomery, D.C. 1991. Design and Analysis of Experiments 3 rd Edition. John Wiley and Sons, New York, United States of America. Montgomery, D.C. & Runger, G.C. 2007. Applied Statistics and Probability for Engineers 4 th Edition, John Wiley & Sons Incorporated, United States of America. 10