Wednesday, February 2, 2011

Isochrones Representation

If one takes the cumulative failure proportions (ppm) of products of the same age (time between manufacturing and registration is constant) from a step table, then it is possible to derive the so-called isochrones representation (the isochrones diagram). Isochrones are curves referring to the same product age.

Failures in this case are not plotted versus the registration quarter, but are rather plotted against the quarter of manufacture.
In the above representation, the isochrones are drawn for the product-age quarters 0, 1, 2, 3, 4 and 5.
The 0-quarter isochrone includes failures of products, whose age is less than one quarter.
In this case the manufacturing quarter and registration quarter are therefore identical, in correspondence with the entries at the stepped lower edge of the step table.
If one follows an isochrone towards the right, then temporal changes of product quality can directly be identified. It is especially convenient to mark measures towards quality improvement.
For instance, marking improvements in the form of design modifications or changes of the production
and assembly processes on the time axis. Their effectiveness is then recognisable on further development of the isochrones with a corresponding time delay. Similarly, through the behaviour of the lowest isochrone, one can early enough discern a critical tendency regarding the product quality of a manufacturing quarter.
Since the failed products of a manufacturing quarter are summed up until the end of a recording period, the isochrones cannot intersect themselves. At most it is possible that all products of a manufacturing quarter, which could fail, actually failed after a certain amount of time. In this case the failure portion of this manufacturing quarter does not further increase and the following isochrones touch themselves at the corresponding point.
The values of the isochrones for a certain manufacturing quarter (from the bottom upwards) correspond to the values to be read in the step table from the right to the left in the row corresponding to the considered
manufacturing quarter.

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