Applied Survival Data Analysis Assignment
1. Show that for a continuous F(t), h(t) = 1/θ, t > 0 is a constant (i.e., not dependent on t) if and only if T follows an exponential distribution (T ∼ EXP(θ)).
2. Show that if T is LOGNOR(µ, σ), then 1/T is LOGNOR(-µ, σ).
3. Consider the ball bearing fatigue data
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Table 1: Ball Bearing Failure Times in Millions of Revolutions
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17.88
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28.92
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33.00
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41.52
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42.12
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45.60
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48.40
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51.84
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51.96
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54.12
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55.56
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67.80
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68.64
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68.64
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68.88
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84.12
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93.12
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98.64
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105.12
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105.84
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127.92
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128.04
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173.40
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Use JMP to do the followings:
a. Compute a nonparametric estimate of F(t), the proportion of units failing as function of time. Plot your estimates with linear scale.
b. Make a lognormal probability plot of the data.
c. Make a Weibull probability plot of the data.
d. Combine the plots in a., b. and c. with Weibull scale.
e. Comment on the adequacy of the lognormal and Weibull models to describe these data.