Potential Sources of Error
In computing reliability parameters such as MTBF, two conditions have to be fulfilled. The first is that the items must be identical in design and operating context. The second is that the performance of any item in a set should not influence that of another item in the set. These are the so called 'identical and independent' conditions.
When we do statistical analysis, we need large data sets. If items are pooled together to obtain larger data sets, all items in the set must have the same operating context and be of the same make, model, and size. Further, no item should influence the performance of another item in the set. In many cases, it is not practical to find many of the same make, model, size, and operating in identical conditions. So we make approximations of the type described in the case of PRVs above.
Let us look at a simple situation in a company operating a fleet of automobiles. Let us say we want to compute the MTBF of tires. If there are 100 cars, our data set may appear at first sight to be 400 tires. Is this true? Does the wear of the right side tires influence that of the left side tires? Does the wear on the front tires affect the rear tires? Clearly tires have an influence on each other, so they cannot be considered independent. Next, are the front tires performing the same function as the rear tires? They are used for steering, and they experience higher wheel loads than the rear tires for most of their life. Depending on whether the car has front-wheel, rear-wheel, or four-wheel drive, the traction effort and, hence, tire wear will also differ.
From this discussion, it will be clear that the operating context for each tire position is different. Though the physical construction and design of all the tires is identical, their operating contexts are different, so the second condition is also not fulfilled.
A new complication arises from the maintenance policy applied during servicing. If during pit-stops, the tires are rotated, i.e., installed in different positions, then each tire sees different operating conditions over its life. In practice, we often ignore these effects, thereby introducing errors. This discussion should make us aware that the magical MTBF figures produced by the analysts may not be as accurate as they seem.