Now that we know most of the pump failures occurred in the Cat Cracking unit, we can narrow our focus to those pumps. Table 2.2 shows a forced ranking of the pumps with the most failures. In our hypothetical case, Pumps 31-P-09 A&B failed five times in the last 12 months. Assuming that each repair costs about $10,000, we now see that the worst actor cost us about $50,000 in the last 12 months.
You may choose to label the least reliable pumps at your site as “bad actors.” Bad actors typically make up 7% to 10% of the pumps at your site that cost the most to maintain and cause you the most headaches. It makes sense to aggressively address bad actors first.
Pareto Charts & 80-20 Rule
The Pareto Chart is a very powerful data analysis tool that can be used to show the relative importance of problem areas and their root causes. They are composed of both bars and lines, where individual values are represented in descending order by bars, and the cumulative total of the sample is represented by the curved line. The 80/20 rule (also known as the Pareto principle or the law of the vital few and trivial many) states that, for many events, roughly 80% of the effects come from 20% of the causes. Joseph Juran, a well-regarded Quality Management consultant, suggested the principle and named it after the Italian economist, Vilfredo Pareto, who noted the 80/20 connection in 1896. Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. Pareto also observed that 20% of the peapods in his garden contained 80% of the peas. According to the Pareto Principle, in any group of things that contribute to a common effect, a relatively few contributors account for the majority of the effect.
Cumulative Failure Trends
Management is usually interested in knowing if their pump reliability is getting better or worse. A simple means of visualizing historical failure data is by contructing, then analyzing, a special trend called a reliability growth plot, which is a plot of cumulative failures versus time (see Figure 2.5). This type of graph is constructed by first creating a table of cumulative (total) failures in a population for consecuative time intervals, then plotting cumulative failures over the time period of interest. For example, let us say that in the first month 20 failures occur in a population, in the second month 25 failures occur, and in the third month 30 failures occur. This would mean the first three points in your reliability growth plot would be: Month 1, 20 failures; Month 2, 20+25=45 failures; Month 3, 20 + 25 + 30 = 75 failures, or (1,20), (2,45), and (3,75).
Reliability growth plots allow you to easily see tendencies in the failure data. Figure 2.5 shows three idealized reliability growth plots:
Figure 2.5 Reliability growth plot of pump failures in an operating area.
1 A trend where the slope of the cumulative failures is essentially straight, indicating a constant rate of failure (shown as “Constant” in Figure 2.5).
2 A trend where the slope of the cumulative failures versus time sharply increases in July of 2016, indicating a decreasing failure rate (shown as “Decreasing” in Figure 2.5).
3 A trend where the slope of the cumulative failures versus time decreases in July 2016, indicating an increasing failure rate (shown as “Improving” in Figure 2.5).
When readers study a reliability growth plot, they are able to discern if pump reliability is constant, deteriorating or improving. Other insights that a reliability growth plot provide are when a change in reliability occurred, and if the change in reliability was sudden or gradual. In this case, seen in Figure 2.5, we note the deteriorating case indicating that something changed after July 2016. We should look for changes in operating procedures, repair methods, processing rates, etc., to explain changes in pump reliability. Persistent changes in pump reliability may represent some sort of major change affecting your pump or pumps, while a data blip could simply be measurement error, or some sporadic factor, such as a plant upset.
The next reliability plot we will cover is the mean time between repairs (MTBF) trend plot (