Understanding Availability
The model below can be used to demonstrate the importance of understanding reliability and availability of systems. After the following description, you will be able to change the parameters of the model in order to see the impact of the individual components, the series systems and the overall parallel pumping system used in the model. It has also been left flexible enough that you can apply it to similar systems in your own facility. The algorithms used are the standard industrial engineering availability formulas covered in several of our white papers. Following the model are several exercises that you can apply to the model in order to see how the concept works.
The concept of Availability relates to the chance that a system will operate as designed, or required, with the inverse being the risk that the system will not operate. This means that if a system has an availability of 75%, that it has a 75% chance of operating as designed and a 25% risk that it will not operate as designed.
In order to use the standard Availability formula, or its inverse, the Risk of Failure, with limited data, you need to know the Mean Time Before Failure (MTBF), which is the average time between equipment failures. This can be figured from historical data, industry averages or manufacturers' data and is determined as the total number of hours reviewed divided by the number of failures over that period. So, for instance, if you have three samples and one survives 800 hours, one 1,000 hours and one 1,200 hours, then the MTBF is equal to 3,000 hours divided by 3, or 1,000 hours. The next bit of information required is the amount of time being observed.
The standard availability formula uses this data and applies it to e-t(1/MTBF) where e is the natural log and t is the time of interest, which assumes a natural failure curve. In a series system, such as System 1 or 2 below (power supply, control, motor, coupling, pump and process), the availability of each component can be determined and then the availability of the whole series system can be determined. If considering the parallel system, below, each series system is determined (not including the power supply and process) and then the parallel system availability is calculated and then made part of the series system (ie: calculate all parallel systems first). This provides the Availability of the system.
In the model below, the MTBF for each component can be added (the model allows these to change as variables, you can always reset the system by pushing the reset button) in the space provided for each component. The amount of time that the system has been operating is important as it is assumed that each component in an operating system has aged differently over time due to previous failures, replacements or repairs. The model then allows you to project the age of each individual component, and/or the complete system. Such a model allows the reliability professional to determine which operating strategy is best, should a system be operated with a redundancy or even if a strategy that improves the MTBF of an individual component will have a significant enough impact on the rest of the system.
A few exercises can be found after the model.
Exercises
A description of the model is necessary first:
Each component, Power Supply, Control 1, Control 2, etc., has its own set of data entry points for MTBF and present age. With the TOA and TOI set at '0', the individual component availabilities (Ra), System 1, System 2 and Whole System Availabilities are based on the present age (present time). By increasing the TOA, you change the age of the individual component and by changing the TOI you change the age of the complete redundant system. The System 1 Availability represents the series system of the components labeled as '1' along with the Power Supply and Process. The same condition is for System 2. These are both the 'Series Systems' which allows the user to view a single system versus the parallel system here. The Whole System represents the Availability of the complete redundant or parallel system. (Reset after each exercise).
Exercise 1: By changing the TOI, the user can look at the impact of the age of the whole system, assuming that the hours are balanced between the two, and the resulting Availability of the individual components, series systems and the whole system. For this exercise, replace the '0' in TOI first with 2,000 hours (tab or click outside the entry point after in order to update), then 4,000, 6,000 then 8,760 (which represents 24/7/365). What is the impact on the whole system?
Exercise 2: What if we are only running System 1 and System 2 is on standby? Try replacing the TOA for just the components in System 1 (including the Power Supply and Process) with the same numbers as in Exercise 1. What is the impact on the Availability of the whole system? How about the availability of the redundant system (System 2)?
Exercise 3: Try the same as Exercise 2, except that you will run the redundant system about 25% of the time. So, if you add 1,000 hours to the Power Supply and Process, you will add 750 hours to each of the System 1 components and 250 hours to each of the System 2 components. Try this for the same hours as in Exercise 1. What is the impact? Try different strategies to see what the impact is on the system availability.
Exercise 4: What happens to the Availability if we improve or use substandard components? First, let's say that Motor 2 has just returned from the repair shop, was commissioned and found to be in poor condition reducing the MTBF to about 10,000 (low insulation resistance). Change the 50,000 in MTBF for Motor 2 to 10,000 hours and the operating time to 1. Now age the whole system by increasing the TOI to 6,000 hours. What happens to the Availability of the system? Now, reset and what happens if we improve the couplings and increase the reliability (MTBF = 30,000) for each one. When entering in the new MTBF, reduce the TIS to 1. Now what happens at 6,000 hours to the system reliability?
There are a great many other exercises that you can try on this model. The first four are to get you started.
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