Where M is the total equipment count, T is the reporting time, and R is the number of failures during the reporting time. For example, let’s say we have 200 pumps in the population, and there are 20 failures in a 3-month reporting period. This would mean that the mean time between failures is 200 x 3/20 or 30 months between failures.
A higher MTBF is preferred. If one pump population (A) has a higher after MTBF value than another pump population (B), we can conclude, on average, the pumps in the A population will last longer in service than the pumps in the B population and are therefore more reliable than the pumps in the B population. Since the MTBF metric provides an idea as to how long the equipment will work without failure, it is a useful tool for forecasting repairs and replacement costs.
Note that sometimes MTBF and MTBR (Mean Time Between Repairs) metrics are used interchangeably. While they appear to be identical, they are not. The reason is that we may not know the exact time of failure, but we do usually know when a repair was done. Consider an example where one of a pair of spared pumps fails and is shut down and the spare pump is immediately started to keep the process running. It’s possible that the failed pump may not be repaired for weeks, depending on the condition of its twin and the shop’s workload. Therefore, we may not document the actual time of the failure, but we will know the time of repair. Make sure you know if the metric is based on failure data or repair data before using it to make decisions.
Additional Reliability Assessment Tools for Spared Machines
Useful reliability analysis tools take the available historical failure data and transforms them into either visual or concise tabular results. These visual displays can identify reliability problems that require our attention. Here are some of the types of reliability analysis tools we will cover and/or review:
Pareto failure plots (for more information, see Pareto Charts & 80-20 Rule insert below).
Bad actor forced rankings
Reliability growth plots
MTBF trends
Let’s start by reviewing a simple tool that looks at failures on a sitewide basis. Table 2.1 contains a forced ranking of pump failures for various processing units across a site. By listing the mean time between repairs (MTBF) over the last 12 months, we can quickly identify the potential areas that may need addressing. In the case shown here, the Cat Cracking area seems to be the most problematic of all.
The pump failure data from Table 2.1 can also be converted into a Pareto chart to provide a summary of pump reliability at a glance (Figure 2.4). (A Pareto chart, seen in Figure 2.4, is a bar graph display of the frequency that events or measurements appear in a data group of interest.) In our Pareto chart example, pump failure frequencies over the last 12 months for various processing areas are plotted in order of decreasing failure frequency from left to right. Pareto charts are extremely useful for identifying issues that should be addressed first. The reader can quickly see that the Catalytic Cracking area had the most pump repairs over the last 12 months, and that the South Terminal area had the fewest repairs over the same time period. The visual results from this Pareto chart suggest that more study of the catalytic cracker pump failures is warranted.
Table 2.1 A hypothetical table of pump failures across a processing facility.
| Number of pump trains | Number of repairs last year | Total repair cost, $ | MTBF (Months) | |
| Catalytic Cracker | 50 | 34 | 272000 | 17.65 |
| Coker Unit | 42 | 21 | 168000 | 24 |
| Crude Unit | 40 | 15 | 120000 | 32 |
| Alky Unit | 35 | 15 | 120000 | 28 |
| Fractionation Unit | 40 | 15 | 120000 | 32 |
| Sulfur Unit | 25 | 15 | 120000 | 20 |
| Utilities | 42 | 12 | 96000 | 42 |
| Hydrotreating | 32 | 12 | 96000 | 32 |
| North Terminal | 30 | 8 | 64000 | 45 |
| South Terminal | 32 | 8 | 64000 | 48 |
Figure 2.4 Pareto chart of total pump failures over the last 12 months for various processing units. The “cumulative percentage” line helps in determining how various groups add to the total failure population. For example, the Cat Cracker and Coker Unit failures represent about 35% of total plantwide pump failures.
Table 2.2 A forced ranking of pump failures in a hypothetical cat cracking unit.
| Pump | Failures in last 12 months | Total repair costs for the last 12 months |
| 31-P-09 A&B | 5 | $ 50,000 |
| 31-P-05 A&B | 4 | $ 40,000 |
| 31-P-04 A&B | 3 | $ 30,000 |
| 31-P-08 A&B |
3
|