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Logistic Model

General Examples Using the Logistic Model

Discrete (Success/Failure) Data

Reliability Data

Confidence Bounds for the Logistic Model

Least squares is used to estimate the parameters of the following Logistic model.

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Thus the confidence bounds on the parameters are given by:

MATH (11)

where:

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and:

MATH (12)

where:

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Since the reliability is always between 0 and 1, the logit transformation is used to obtain the confidence bounds on reliability.

MATH (13)

Logistic Model Example 4

For the data given for Example 1 in Table 8.1, calculate the 2-sided 90% confidence bounds under the Logistic model for the following:

  1. The parameters b and k.
  2. Reliability at month 5.
Solution to Logistic Model Example 4
  1. The values of $\widehat{b}$ and $\widehat{k}$ estimated from the least squares analysis in Example 1:

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Thus the 2-sided 90% confidence bounds on parameter b using Eqn. (11) are:

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The 2-sided 90% confidence bounds on parameter k using Eqn. (12) are:

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  1. First calculate the reliability estimation at month 5:
 

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Thus the 2-sided 90% confidence bounds on reliability at month 5 using Eqn. (13) are:

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Figure 8.6 shows a graph of the reliability plotted with 2-sided 90% confidence bounds.

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Figure 8.6: Logistic Reliability vs. Time plot with 2-sided 90% confidence bounds