Crow (1984), Jewell (1984), or Ushakov (1994) for a more detailed description of the models and methods mentioned in this chapter, as well as for discussion of related topics that we chose not to feature here.

While there were both formal and informal developments in the area of reliability growth prior to 1964, the field as we know it today had its beginning that year with a highly influential paper by J. T. Duane. The subject of the paper was the observed growth in reliability of specific manufactured items related to the aerospace industry. A simple regression analysis appeared to suggest that the logarithm of the cumulative failure rate of an item at time t was linearly related to the logarithm of t, a relationship that might be expressed as

ln(λt) = a – b ln(t).

The coefficient b of ln(t) appeared to vary from one application to the next, depending, for example, on whether the item in question was mechanical or electronic, but the fit of the Duane model in a large collection of quite different applications appeared truly uncanny. Duane’s application called for a coefficient of b = 0.5, but as applications proliferated, it was observed that b would generally fall in the interval [0, 0.6]. One famous military application of the Duane curve was to the failure rate of the F15-A fighter when its performance was tracked for 4 years in the mid-1970s.

The Duane model gained substantial popularity through the 1960s and 1970s. It appeared to fit reliability growth processes well enough that attempts were initiated to predict the future reliability of an item based on its fitted Duane curve. Such a practice was a bold move indeed, given that the fitted curve offered no explanation of the concomitants of growth, providing no understanding of the growth process itself. Surely the various interventions that occurred as a prototype was developed and improved were somehow linked to the reliability improvement one would experience, but such interventions played no formal role in the Duane model. The model appeared to be saying that it matters little what one does (as long as one does something); the improvement seen will follow a Duane curve.

In the early 1980s, Larry Crow, working at the Army Materiel System Analysis Activity (AMSAA), developed a modification of the Duane model that proved to be substantially more flexible. The essence of the AMSAA model was that it was in reality a collection of successive models. It was



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