An organization owns a fleet of 10 vessels. Each vessel contains a non-repairable item, which is vital for its operations.

**Objective of the analysis: **

What is the projected number of failures over the next 2 years in order to avoid operation downtime due to lack of spare, assuming each vessel is expected to operate 100 hours per year?

Following is the repair information of the fleet.

Take vessel 1 for example, the Time-To-Failure (TTF) of the first 2 items were 631 and 336 (967- 361) hours respectively. In addition, one item is still operating after 445 hours of operation (Suspension time of 445 hours).

Similarly, the Time-To-Events (TTF and Suspensions) are derived. The following table shows the complete failure dataset of the items.

The dataset is fitted to a Weibull Distribution.

The analysis shows that the Weibull Distribution with beta = 3.461 and Eta = 908.8 hours best describes the failure rate behavior of the item. Following images are Probability-Weibull, Reliability vs Time, Probability Density Function and Failure Rate vs Time plots of this dataset.

Given that the failure distribution of the item, and the current age of each of the 10 items are known, what is the total number of failures can we expect if each vessel operates 200 hours.

The item on vessel 1, for example, has accumulated a current age of 796 hours. We can query the model for Conditional Probability of Failure for an additional mission time of 200, F(200/796).

Therefore, for vessel 1 to operate for 200 hours, there is a 52.34% chance to observe a failure.

Similarly, the Conditional Probability of Failure for an additional mission time of 200, of the item for all the other vessels is determined.

The expected total number of failures if each vessel operates 200 hours is 3.9875.

In this analysis, the mission time is only 200 hours. One would not expect more than 1 failure per vessel. If the mission time is 1000 hours for example, more than 1 failure is expected. In this case, this procedure is not correct, and simulation approach is preferred.

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