Concurrent or simultaneous failures can happen with redundant or spared systems. This means that both spared equipment can fail at the same time leaving the operator with no production output. For example, we have two alternating pumps operating in a parallel configuration. Each one acts as a spare and at any one time can take over if the other one fails. This article is based on a question I was asked during a recent industry presentation. I thought the example was interesting and informative enough to share with the Maintenance and Reliability community.
The Question and Problem Statement
The conference attendee’s question was as follows:
I have two pumps working in parallel. They are set up as standby pumps. This means that I need only one pump to run at any one time for my process to work. The standby pump automatically takes over if the running pump fails. If both pumps are down at the same time, my process is down, and I lose money.
How should I organize pump running time so that they don’t fail at the same time? I fear that if I run them both for equal periods of time they will fail concurrently. What time intervals should I run each one? Should those be different?
Using a RAM Model to gauge the Probability of Concurrent Failures
Diagram 1 below illustrates the Reliability, Availability and Maintainability (RAM) model for the standby pump system. It is performed in the Reliability Block Diagram software Raptor 7.0™. In order to be functioning, the system requires at least one pump to be operational at any one time. This is also known as the “k out of n” configuration where k=1 and n=2.
The life characteristics of each pump are setup as follows:
- Failure distribution that will govern unplanned failures of each pump: 2 parameter Weibull with Beta (Shape Parameter) = 1.2 and Eta (Scale Parameter) = 35,000 hours
- Repair distribution that will govern the restoration tasks once the pump is failed: Triangular distribution with the following repair time – Minimum = 4 hours, Mean = 8 hours, and Maximum = 24 hours
- The pump is a repairable system. It is NOT “as good as new” when repaired. It is 50% rejuvenated or renewed after each repair. So, it will degrade increasingly over time.
- Neither production output nor cost are used in this example as it is not required.
- This is essentially a “run to failure model”. There is no preventive maintenance task included.
When we run the model for 1,000 lifecycles for a mission time of 175,200 hours or 20 years, we get the following results below.
- Mean System Reliability is 99.70%. This means that the probability of concurrent pumps failures over 20 years is 0.30%.
- Mean Number of system failures is 0.003. That is when 2 pumps are down at the same time (concurrent failures).
In essence even without maintenance there is a “very low” chance of concurrent failures.
Sensitivity Test based on Pump Characteristic Life Value (Eta)
If we reduce the characteristic life of the pump, we essentially increase the failure frequency. In other words, we are trying to see how standby pump arrangements with higher failure rates decrease the reliability of the system. Successive models are run, and the results illustrated in Graph 1 below.
Those results show that system failures over twenty years stay low even if the individual pump reliability decreases. Therefore, the conference attendee can be reassured that concurrent failures in their system are very unlikely to happen. Thought the risk is never zero.
Improving Reliability
Sometimes a reliability value might not be enough for an operator. Let’s say the conference attendee was operating an expensive satellite in space where 99.70% system reliability over 20 years was inadequate. In this case, especially when it comes to scenarios like satellite or airline operations, redundancy is a reliability improvement option. In the above case, we use the first example (i.e. Beta = 1.2 and Eta = 35,000 hours). And add a 3rd pump as illustrated in Diagram 2 below. The system needs only one pump to run at any one time.
With this configuration, System Reliability is 100% and we have zero system failures over the 20 years of operation.
In a normal industrial setting, adding redundancy can be very expensive. And not economically viable. In this case, we turn to maintenance strategies to better predict and avoid pump failures. Those include advanced CBM strategies and thorough analysis of the potential failure modes and their life characteristics. However, every action taken needs to be justified financially as there is a cost attached to maintenance. As well as the risk of “maintenance induced failures”.
In summary, a RAM model is an excellent tool to answer the conference attendee’s question. And the correct answer will largely depend on the context and environment they are operating in.
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