Confidence Bounds Examples for the Crow Extended Model

Crow Extended Example 3

Calculate the 2-sided 90% confidence bounds on the demonstrated, projected and growth potential failure intensity for the data in Table 9.1.

Solution to Crow Extended Example 3

The estimated demonstrated failure intensity is . Based on this value, the Fisher Matrix confidence bounds for the demonstrated failure intensity at the 90% confidence level are:

The Crow confidence bounds for the demonstrated failure intensity at the 90% confidence level are:

The projected failure intensity is. Based on this value, the Fisher Matrix confidence bounds at the 90% confidence level for the projected failure intensity are:

The Crow confidence bounds for the projected failure intensity are:

The growth potential failure intensity is. Based on this value, the Fisher Matrix and Crow confidence bounds at the 90% confidence level for the growth potential failure intensity are:

Figure 9.8 shows the Fisher Matrix confidence bounds at the 90% confidence level for the demonstrated, projected and growth potential failure intensity. Figure 9.9 shows these bounds based on the Crow method.

Figure 9.8: Fisher Matrix confidence bounds for the failure intensity

Figure 9.9: Crow confidence bounds for the failure intensity

Crow Extended Example 4

Calculate the two-sided confidence bounds at the 90% confidence level on the demonstrated, projected and growth potential MTBF for the data in Table 9.3.

Crow Extended Example 4 Solution

For this example, there are A, BC and BD failure modes, so the estimated demonstrated failure intensity, , is the simply Crow-AMSAA model applied to all A, BC, and BD data.

Therefore, the demonstrated MTBF is:

Based on this value, the Fisher Matrix confidence bounds for the demonstrated failure intensity at the 90% confidence level are:

The Fisher Matrix confidence bounds for the demonstrated MTBF at the 90% confidence level are:

The Crow confidence bounds for the demonstrated MTBF at the 90% confidence level are:

The projected failure intensity is. Based on this value, the Fisher Matrix confidence bounds at the 90% confidence level for the projected failure intensity are:

The Fisher Matrix confidence bounds for the Projected MTBF at the 90% confidence level are:

The Crow confidence bounds for the projected failure intensity are:

The Crow confidence bounds for the projected MTBF at the 90% confidence level are:

The growth potential failure intensity is. Based on this value, the Fisher Matrix and Crow confidence bounds at the 90% confidence level for the growth potential failure intensity are:

The Fisher Matrix and Crow confidence bounds for the growth potential MTBF at the 90% confidence level are:

Figure 9.10 shows the Fisher Matrix confidence bounds at the 90% confidence level for the the demonstrated, projected and growth potential MTBF. Figure 9.11 shows these bounds based on the Crow method.

Figure 9.10: Fisher Matrix confidence bounds on MTBF

Figure 9.11: Crow confidence bounds on MTBF