Confidence Bounds for the Logistic Model

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

Thus the confidence bounds on the parameters are given by:

(11)

where:

 

and:

(12)

where:

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

(13)
 

Logistic Model Example 4

For the data given 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 and estimated from the least squares analysis in Example 1:

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

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

  1. First calculate the reliability estimation at month 5:

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

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

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

 

See Also:
Logistic

 Go to weibull.com
 Go to ReliaSoft.com

©1992-2005. ReliaSoft Corporation. ALL RIGHTS RESERVED.