Tutorial 10 An engineer is designing a battery for use in a device that will be subjected to some extreme variations in temperature. The only design parameter that he can select is the plate material for the battery, and he has three possible choices. When the device is manufactured and is shipped to the field, the engineer has no control over the temperature extremes that the device will encounter, and he knows from experience that temperature will probably affect the effective battery life. However, temperature can be controlled in the product development laboratory for the purposes of a test. The engineer decides to test all three plate materials at three temperature levels –15,70 and 125F- because these temperature levels are consistent with the product end-use environment. Four batteries are tested at each combination of plate material and temperature, and all 36 tests are run in random order. The experiment and the resulting observed battery life data are given in the file battery (life is given in hours). The engineer wants to answer the following questions: 1. What effects do material type and temperature have on the life of the battery? 2. Is there any choice of material that would give uniformly long life regardless of temperature? Perform the analysis of the data and write a report for the client as if you were the engineer. Analysis 1. Make clear the aim of the study 2. Look at the data (interaction plot): descriptive statistics 3. Write a model 4. Fit the model 5. Diagnostic check 6. Results 7. Write a report (introduction, methods, results, conclusion, appendix) Commands #Factor variables battery$Material <- factor(battery$Material) battery$Temp <- factor(battery$Temp)
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Tutorial 10 An engineer is designing a battery for use in a
device that will be subjected to some extreme variations in
temperature. The only design parameter that he can select is the
plate material for the battery, and he has three possible choices.
When the device is manufactured and is shipped to the field, the
engineer has no control over the temperature extremes that the
device will encounter, and he knows from experience that
temperature will probably affect the effective battery life.
However, temperature can be controlled in the product development
laboratory for the purposes of a test. The engineer decides to test
all three plate materials at three temperature levels 15,70 and
125F- because these temperature levels are consistent with the
product end-use environment. Four batteries are tested at each
combination of plate material and temperature, and all 36 tests are
run in random order. The experiment and the resulting observed
battery life data are given in the file battery (life is given in
hours). The engineer wants to answer the following questions:
1. What effects do material type and temperature have on the
life of the battery?
2. Is there any choice of material that would give uniformly
long life regardless of temperature?
Perform the analysis of the data and write a report for the
client as if you were the engineer. Analysis
1. Make clear the aim of the study 2. Look at the data
(interaction plot): descriptive statistics 3. Write a model 4. Fit
the model 5. Diagnostic check 6. Results 7. Write a report
(introduction, methods, results, conclusion, appendix)
Commands #Factor variables battery$Material
#Ordering variables battery$Material
Where T, B and TB represent temperature, material and
interaction effects, respectively. A diagnostic analysis was
performed and a test of hypothesis for the interaction effect.
Results In the model adequacy checking no deviations from normality
were observed. Some mild suggestions of non equal variances were
observed indicating that outliers could be present, but after
checking with the company it was confirmed that they were right
observations. As the experiment was randomized in all the possible
phases the assumption of independence is assumed to be hold. Anova
table for battery data Analysis of Variance Table Response: Life
Terms added sequentially (first to last) Df Sum of Sq Mean Sq F
Value Pr(F) Temp 2 39118.72 19559.36 28.96769 0.00000019 Material 2
10683.72 5341.86 7.91137 0.00197608 Temp:Material 4 9613.78 2403.44
3.55954 0.01861117 Residuals 27 18230.75 675.21 There was some
evidence of an interaction effect between material type and
temperature level (p=0.019). The next plot gives an idea about how
they interact with each other.
Temp
mea
n of
Life
6080
100
120
140
160
15 70 125
Material
312
In general, longer life is attained at low temperature,
regardless of material type. Changing from low to intermediate
temperature, battery life with material type 3 actually increases,
whereas it decreases for types 1 and 2. From intermediate to high
temperature, battery life decreases for material types 2 and 3 and
is essentially unchanged for type 1. Conclusion and discussion
Material type 3 gives the best results if the interest is to
achieve less loss of effective life as the temperature changes. In
this analysis is possible to make multiple comparison of means
response for different levels of material and temperature, and in
this way check more formally the differences in levels of
combination material-temperature. Appendix Model Call: lm(formula =
Life ~ Temp * Material, data = battery) Residuals: Min 1Q Median 3Q
Max
