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| The following picture shows the parameters of the lognormal distribution and the converted failure/suspension data. The results are the same as the results shown in the book. | | The following picture shows the parameters of the lognormal distribution and its associated failure/suspension data. The results are the same as the results shown in the book. |
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| [[Image: warranty_results.png|center]] | | [[Image: warranty_results.png|center]] |
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| | The following picture shows the probability plot of the lognormal distribution. |
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| | [[Image: warranty_plot.png|center|550 px]] |
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Warranty Data Analysis Example
|
This example compares the warranty data analysis results.
Reference Case
The data set is from Example 11.2 on page 453 in the book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.
Data
A Nevada chart for the warranty data is provided in Table 11.3. The last two rows were combined, as specified in the example.
|
|
TTF
|
| TIS
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
Total
|
Sales Volume
|
|
|
| 12
|
3 |
0 |
3 |
3 |
4 |
2 |
1 |
5 |
4 |
2 |
3 |
3 |
45 |
2123
|
| 11
|
0 |
1 |
2 |
0 |
4 |
2 |
1 |
2 |
0 |
4 |
3 |
|
30 |
1853
|
| 10
|
1 |
3 |
2 |
2 |
3 |
4 |
3 |
5 |
4 |
8 |
|
|
45 |
2238
|
| 9
|
1 |
2 |
0 |
3 |
4 |
2 |
2 |
3 |
6 |
|
|
|
32 |
3052
|
| 8
|
2 |
3 |
2 |
6 |
2 |
1 |
6 |
4 |
|
|
|
|
34 |
2953
|
| 7
|
1 |
1 |
3 |
2 |
1 |
4 |
8 |
|
|
|
|
|
27 |
2788
|
| 6
|
1 |
0 |
1 |
0 |
1 |
2 |
|
|
|
|
|
|
11 |
2037
|
| 5
|
0 |
0 |
1 |
1 |
0 |
|
|
|
|
|
|
|
7 |
1863
|
| 4
|
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
|
6 |
1231
|
| 3
|
0 |
1 |
1 |
|
|
|
|
|
|
|
|
|
5 |
823
|
| 2
|
0 |
1 |
|
|
|
|
|
|
|
|
|
|
3 |
638
|
| 1
|
0 |
|
|
|
|
|
|
|
|
|
|
|
1 |
568
|
|
|
| Total
|
9 |
12 |
16 |
18 |
19 |
17 |
21 |
19 |
14 |
14 |
6 |
3 |
|
Result
The book first converted the data in the table above into the following format, as given in Table 11.4 in the book.
| TTF (Months)
|
Number of Failures
|
Number of Censored Units
|
| 1 |
9 |
568
|
| 2 |
12 |
637
|
| 3 |
16 |
821
|
| 4 |
18 |
1229
|
| 5 |
19 |
1861
|
| 6 |
17 |
2032
|
| 7 |
21 |
2768
|
| 8 |
19 |
2927
|
| 9 |
14 |
3029
|
| 10 |
14 |
2203
|
| 11 |
6 |
1834
|
| 12 |
3 |
2090
|
A lognormal distribution is used and the fitted model parameters are: Ln-Mean = 6.03 and Ln-Std = 1.63.
Results in Weibull++
In Weibull++, the data set is entered into a warranty folio, using the Nevada chart format. The following pictures show the sales and returns data.
The following picture shows the parameters of the lognormal distribution and its associated failure/suspension data. The results are the same as the results shown in the book.
The following picture shows the probability plot of the lognormal distribution.
