The Ford Explorer/Firestone tyre story is old news, but Ford have just gone public with how they figured out what went wrong and why the company is sure that its SUV wasn’t to blame. During a recent conference in London, Richard Parry-Jones, Ford Global Product Engineering boss explained how the company borrowed a statistical analysis technique from the medical world called Hazard Analysis. Gary Beecroft reports.
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The conference was held at the Institution of Mechanical Engineers (I.Mech.E.) in central London at the same time as, in a special session of Parliament, just round the corner, prime minister Tony Blair was explaining his policy on Iraq, and underground the Tube workers were on strike to explain their need for more cash. At the two-day conference statisticians discussed what they were doing with Bayesian statistics, radial basis functions and multivariate correlation techniques.
Fortunately, Parry-Jones’ paper was delivered in a fashion that meant those without an engineering, science or statistics degree had a chance of understanding.
When it was noticed that a worrying number of Ford Explorer SUVs were throwing the treads of their Firestone tyres into the scenery, it wasn’t long before Ford and Firestone were blaming each other for the problem. One of Firestone’s arguments was that the same tyres were used on other vehicles and there didn’t seem to be a problem. Ford now counters with its explanation that the problem is pretty rare, even on a model that is produced at rates of between 300,000 and 500,000 units per year. If you produce a lower volume model, the problem will not be picked up, or simply not exist.
Ford needed to be able to reproduce the tyre failure in its labs in order to get some data. The problem that was occurring is called TBS (tread and belt separation). The tyre involved used a common construction, whereby, it was reinforced by two steel belts, one on top of the other, which went all the way round the tyre.What was happening was that the tread plus the top belt was coming off the remainder of the tyre.
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By GlobalDataWhen this happens for real it can lead to a loss of control of the vehicle or the tyre can blow out. Picking up tyres from the roadside after real incidents involving TBS is only slightly helpful. The tyre is usually so badly damaged that it is difficult to tell what went wrong.
To reproduce TBS, Ford tested tyres in its labs. It ran the tyres under heavy loads and at high speed until TBS occurred, or the tyre failed in some other way. However, it was then faced with the same problem encountered when picking up tyres from real on-the-road incidents. The tyres were wrecked by the test. One of the key measurements Ford needed to make was the “peel force”: the force necessary to tear the outer steel belt from the inner one. To measure this, at least some of the tread needs to remain attached to the tyre.
Then Ford’s own R&D team came to the rescue. They noticed that during the 30 seconds or so before the tyre fell apart, there was a measurable change in the vibrations and noise being recorded on the test rig. As soon as these were detected it would be possible to stop the test and inspect the tyre, just before it came apart, or at least, still had some of the tread attached. Ford is now patenting this detection system.
This was vital as it meant that the tyre could be examined to see what was happening and the peel force measured by pulling off the remaining tread on the tyre. Comparisons could then be made between Firestone tyres on the Explorer and those supplied by other brands (which was less than 10% of production). Comparisons could also be made with other similar tyres.
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It soon became apparent that the tyres were cracking close to the wedge. This is a wedge of material going all the way round the tyre, between the two steel belts, close to each tyre sidewall. There are two per tyre. The wedges exist to help the tyre withstand the very high stresses and temperatures generated in this part of the tyre.
Ageing
We know what happens when steel oxidises – it turns into rust. However tyres also deteriorate in an oxygen environment. This means that as a tyre gets older, the materials it is made from loose the beneficial properties they had when new. Ford data suggested that old tyres were more likely to suffer from TBS than new ones. Was this the case ?
Hazard
We must now introduce the medical concept of hazard. If you think about the whole population of an entire country, then the chance of any one of them dropping dead at any one time is pretty small. This brings us neatly to the statistical concept of Hazard.
This can be expressed as:
If we take the population of interest to be all those born in the last twenty years, then the number at risk will be high and the number of deaths low. Therefore the Hazard number will be low. If you look at this same group of people fifty years later then the number of deaths will be high and the number at risk (those surviving) will be low. Therefore the Hazard number will be high.
So what has this got to do with tyres? Well, how about taking the group we examine to be three years of Ford Explorer production. Depending on which years you were to take, this could involve 1.0 to 1.5 million vehicles. Over time one could observe the number of tyre failures and compare this with the number still in use to calculate the Hazard number. Exhibit 1 shows a typical form that a failure rate curve might take.
Exhibit 1: Example TBS failure rate for a tyre versus time (years)
However, it isn’t that straightforward. Ford was only interested in TBS failures, so all other failures had to be eliminated. Also, tyres wear out and are replaced, which is not a failure. These would also have to be allowed for. So it’s back to the test rig.
Ford then tested Firestone and other brands of tyre that were fitted to the Explorer until TBS occurred. The tyres were then cut up and measurements made. Statistical analysis showed that the significant measurements were:
- Wedge gauge (thickness of the tyre wedge)
- Peel force (force required to separate the two steel belts and cause TBS)
- Inter-belt gauge (distance between the two steel belts inside the tyre)
Now this was progress! Knowing the statistically significant variables meant that it was possible to build a model that would predict when a tyre would fail. However, at this stage it predicts what will happen on the test rig – not on the road. Nevertheless, it is often reasonable to presume that the tyres will react in a similar way in both circumstances.
Exhibit 2: Hazard number for TBS tyre failure against time (years)
Using the computer model it is possible to construct a cumulative hazard plot for various tyres. What this shows is that tyres with certain values of wedge gauge, peel force and inter-belt gauge are likely to suffer TBS long before other tyres. In other words, what Ford is saying, is that the Firestone tyres had poor performance on the three criteria compared to tyres of other brands.
Ford’s computer model allowed it to calculate the Hazard. Exhibit 2 shows the Hazard number (defined above) for tyre failure. Bear in mind these are pure estimates calculated by the author – not Ford data. Ford’s analysis showed that the relationship with time is almost linear.
Exhibit 3 shows a cumulative Hazard plot for tyre failure. Unlike the previous exhibit it rises exponentially. The plot for a poor tyre rises much more quickly than that of a good tyre. This was the crucial fact that Ford was able to establish: with Firestone tyres, the Cumulative Hazard number shoots up much more quickly than that of comparable brands.
Exhibit 3: Cumulative Hazard number for TBS tyre failure versus time (years)
Ford is also able to show that the Firestone tyres fitted to the Explorer had different hazard numbers depending on which Firestone plant they came from, because the wedge and inter-belt gauge, and the peel force, was different in the three plants.
Well that about raps it up for the statistics lesson. It looks as if Ford is having the last word on this controversy, but remember … statistics are often used as a drunken man uses lamp posts… for support rather than illumination.
Gary Beecroft is an independent consultant serving the automotive industry.
Tel: +44 20 8892 8379
E-mail: gbeecroft@onetel.net.uk
Web: http://web.onetel.net.uk/~gbeecroft
