Tinkering with Gompertz' curves for IoT predictions

October 20, 2016 // By Julien Happich
Visiting customers in Paris last week, Mentor Graphics' Chairman and CEO Wally Rhines gave a talk on the inaccuracies of semiconductor revenue forecasts and why that may be, suggesting that we ought to revive a nineteenth century mathematician's curve, that of Benjamin Gompertz, for better predictions.

"Why is it so difficult to forecast semiconductor revenue?" he asked, acknowledging the volatility of semiconductor revenue in an industry that not only experiences ups and downs but is also subject to design cycles. While, forecasting revenue requires the prediction of both unit volume and average price, volumes alone are more predictable, but with new applications emerging, how could these volumes be forecasted reliably, he asked the audience.

Rhines then turned our attention to nineteenth century mathematician Benjamin Gompertz, after whom a double exponential S-shaped curve is named. The sigmoid function has been successfully used to model the growth of tumors, populations, or market impact in finance, showing total cumulative units on its Y axis as times unfolds on the X axis. It gradually starts with a fast growth rate until unit volume shipments remain stable to reach a growth inflection point, when volume shipment start to decline over the years, with cumulative units growing slower as a market reaches its maturity.

Digging into historical market data, Rhines gave us an insight on where we stand in terms of market maturity for a number of applications.

"You could think that camera sensors are a pretty mature market", he said, before demonstrating that although camera sensors have been commoditized and can be found in every smartphone, the growth of camera sensors has yet to peak, with these devices increasingly found in cars, in the industrial and medical markets, on drones and many novel consumer applications.

Looking at more traditional semiconductor markets, such as desktop PCs, or notebooks, the CEO was remarkably able to snugly fit the right Gomperz curves, confirming already mature markets in decline (mostly driven by a slow-paced replacement).

Now "how about predicting emerging IoT opportunities", Rhines continued, trying to fit Gompertz' curves around fewer data points of cumulative shipped units. Following the same principle and curve analysis, smart meters had still plenty of growth ahead. On the curve, IoT wearables were only at the very start of their journey, expected to peak around 2020 and mature around 2025, but here the data was so scarce and admittedly, because it regrouped many different wearable devices, it broke the rule of only looking at similar units under the same curve.