A Reliability Growth Model Can be Developed from Historic Data Using the Crow-AMSAA System Reliability Analysis Method
Unlike Weibull Reliability Analysis, where you model a failure mode’s history, a Crow-AMSAA Reliability Growth Model represents the complete system behaviour
In the example below, a safety system is modeled using the three Moura Underground Coal Mine disasters that happened in Queensland, Australia, between 1975 and 1994
A Crow-AMSAA Reliability Growth Model plots points on log10-log10 axes. The angle of the line between two neighbouring points reflects the reliability growth of the system
August 2014 was the twentieth anniversary of the Moura No. 2 underground mine explosion, the third underground coal mine disaster in the Moura region of central Queensland, Australia. Mining started in the area around 1960. In 1962 the Thiess Peabody Mitsui Coal Pty Ltd joint venture company was formed to operate the Queensland Kianga and Moura mines and export coking coal to Japan. BHP acquired Peabody Coal’s Australian assets in 1976-77, and gained a 60 percent stake in the Moura and Kianga coal mines. In 1985 BHP increased its holding to more than 80 percent in the operator of the Moura and Kianga mines, Thiess Dampier Mitsui.
On 20 September 1975 at Kianga Mine, 13 miners died from a spontaneous combustion methane explosion. On 16 July 1986 12 miners died at Moura No. 4 Mine from a suspected methane explosion. Just before midnight on Sunday, 7 August 1994 there was the first of two explosions in Moura No. 2 underground mine which killed 11 men. Within less than 20 years 36 men had died from underground explosions. Underground mining ceased after 1994 and only open-cut mining has continued ever since.
We decided to plot those ‘failure’ events on a Crow-AMSAA reliability growth model to see what could be gleaned from the chart. You can see the data and plot in the log10-log10 graph below.
A reliability growth model is traditionally used to predict when failure events will occur to a system based on the historic events that have already occurred. Typically the system was a machine or an equipment item. But it does not need to be a physical asset. A system can also be a business or an organisation. It can be a production line, or a railway line.
What matters is that the behaviour of the system follows a log10-log10 power law. Normally, you confirm if historic data is a log10-log10 power law by plotting each individual event point on log10-log10 axes and seeing if the set of historic points form a straight line. The proximity of the points to a straight line indicates goodness of fit for the data points.
When a reliability growth model has many data points, the goodness-of-fit to a straight line gives confidence that the system behaviour can be represented in a log10-log10 graph. It is reasonable to deduce that because the past events fall in a straight line, then by extending the line into the future you can estimate the future events. It is possible that curvature and discontinuities are observed, but these are all part of the behavior of the system and its processes being monitored. As the modeled system’s reliability changes, one expects a bend or corner to appear on the graph at the point in time a change is made to the system. From this date onward, a new straight line representing the future progress of the changed system is fitted to the system reliability model. There have been times when a Crow-AMSAA model forecast future events so accurately, it was a prediction. When that happens it gives you the shivers, and the hairs on the back of your neck stand out straight.
That is not so in this Crow-AMSAA plot. Each point plotted in the chart above is one of the three mining disasters (the fourth point is not a disaster; it is simply today’s date used as a reference date). If they did form a straight line the conclusion is the ‘system’ behaviour was unchanged during the two decade time period covering the three mining disasters. But we are looking to see if the system behaviour did change between one point and the next. We want to measure the slope of the line between each point to check if there was system reliability improvement, or the system performance was stable, or it was worsening. In developing a Crow-AMSAA plot using few points, you make the assumption that a log10-log10 power law applies to the small amount of available data. If it is a wrong assumption you will get meaningless forecasts, and not know that they are not believable.
When log10-log10 power law behaviour occurs it implies particular conditions. It reflects the presence of risks occurring within the system. The frequency of the failure events are not purely random but are being produced by the system itself. The slope of the line, known as its Beta value, is indicative of the effort being made to make changes to the system’s reliability. It can be said the Moura region underground mining ‘system’ disasters were outcomes of the sum of the effects of all the various processes used in the mines.
The Beta values in the plot also have significance. A Beta of one means the frequency of events is constant. Beta less than one means reliability is improving, and more than one it is worsening. In the Moura area plot, the Beta values during the two decades when the disasters occurred are more than one. One can begin to draw the conclusion that many risks existed and on three occasions their combination unfortunately ended in disaster. Since 1994 the underground mining stopped and only open cut mining continued. The bend in the plot and the low Beta slope value tell us that the accumulated effects of the changes made in 1994 have made the Moura area mines much safer places.
If you continue the line with a beta of 1.32 to the line representing the next incident date, you get about 5,000 days to the third explosion, which would be roughly 13 years later, in 1999. The third explosion was in 1994.
Had the mines remained underground operations, the extended line with a beta of 1.53 crosses the ‘next’ disaster incident, a fourth explosion, at about 4,000 days after the 1994 explosion, or some 11 years later, in 2005.
You can model your own failure and safety data using a Crow-AMSAA reliability growth model to give you fresh and profound insights into what is happening to the failure and safety processes in your operation.
The table and plot in the above example were developed using the Crow-AMSAA reliability growth model Excel spread sheet we sell at our online store. The Excel spread sheet you get comes with a thorough explanation of how to use it. You also get articles and white papers specifically describing the Crow-AMSAA methodology written by a Crow-AMSAA analysis specialist. In the white papers are more Crow-AMSAA reliability growth model examples. Follow this webpage link Crow-AMSAA Reliability Growth Model using MS Excel to get more information on the Crow-AMSAA modeling spread sheet.
All the best to you,
Mike Sondalini
Director
Lifetime Reliability Solutions HQ