In our last blog we discussed the use of diffusion models for forecasting new product introductions. In 1969, Frank Bass developed a diffusion model for forecasting consumer durable products. The model predicts a product life cycle (PLC) sales curve (source: : “Forecasting the Sales of New Products and the Bass Model”, The model is designed for two primary purposes: 1) Determine how many customers will adopt a product, and 2) determine when customers will adopt the product.

The Model

One of the main assumptions of the model is that the diffusion process decision is binary (either customers adopt or they decide to wait). Other assumptions of the model include:
• Constant maximum potential number of buyers (m)
• Eventually, customers will buy the product to fulfill the maximum number of buyers.
• No repeat purchase, or replacement purchase
• The impact of the word-of-mouth is independent of adoption time
• Innovation is considered independent of substitutes
• The marketing strategies supporting the innovation are not explicitly included

Fortunately, the model only has a few parameters:
m, is the number of products ultimately to be sold (i.e. max. market value)
p, is the coefficient of innovation (adoption based on external factors and mass media)
q, is the coefficient of imitation (adoption based on word-of-mouth)

The mathematics behind the model can be left to those better suited to solve the differential equation (see source document for detailed equation). In the rest of this paper, I will discuss application of the model, particularly how it pertains to LED Lighting.

Application to LED Lighting

With the advent of LED lighting, we have a new product technology that is displacing existing technology in the market place. Eventually, LED lighting will replace all incandescent and fluorescent sources of lighting in the market. Cost savings and longer life will drive this transformation. The question many in the industry are asking is “When will we hit peak demand for LED lighting”.

The Bass Diffusion model can help to estimate this effect. The model only needs 3 parameters. Fortunately for us, m, the number of products ultimately to be sold, can be estimated from government data. For instance in the US, there are approximately 1 billion linear fluorescent lamps (Source: “Adoption of Light Emitting Diodes in Common Applications”, Prepared for the US Department of Energy Solid-State Lighting Program by Navigant, July 2015, page V (executive summary).

Estimating p and q needs to come from empirical evidence of other launches in the market place. A value of p=0.005 and q=0.5 creates an estimate of 12-13 million units sold after 2 years. The DOE data suggest that 12 million LED fixtures have been sold in 2014 (approximately 2 years after the first linear LED entered the market).

How do we know that the value of p and q are correct? For the introduction of the Color TV, the Bass Diffusion model utilized p=0.005 and q=0.84. One can argue that LED’s coefficient of imitation should be higher than average but less than that of a TV, which had mass appeal as time passed. Therefore q=0.5 is a realistic approach for now.

Results from the Model

Now that the model parameters are established (m=1 billion units, p=0.005, and q=0.5), we can provide some predictions.

• We are still in the early phase of growth of linear LED replacement lamps/fixtures.
• At 12 million lamps cumulatively sold through 2104, we still have a long way to go to peak demand.
• Utilizing the model, the estimated peak demand will be around 2022 with around 125 million units sold annually.
• After 2022, the model predicts an annual decline in sales.

Should we accept all of these conclusions from the Bass Model? No. LED’s have the ability to re-define the lighting category, even for LED linear lighting. New LED products will not be limited to the existing shapes and spaces of existing linear fluorescent lighting. LED’s will take lighting in new directions and create new categories that will eclipse the parameters defined from the model. OLED’s (organic LED’s) have the ability to re-shape lighting so that it can come directly from the walls, ceiling, or floor.

Why Use the Model

The Bass Diffusion model allows marketers and manufacturers to estimate and predict product growth curves for new products. Using industry specific empirical evidence, one can predict p and q. The maximum number of units, m, may be derived from existing data sources or predicted by marketing. Matching manufacturing capacity to market demand is essential for companies wanting to maximize products. While not perfect, the Bass Diffusion model can provide that prediction. Some amount of skepticism must always enter into any decision. However, having a prediction is better than having no prediction.

About the Author: Garrett Grega is a Certified Business Coach with FocalPoint Business Coaching in Branchburg, New Jersey, where he specializes in reconnecting executives, business owners, and managers with their business passions! He has 20+ years helping international companies launch new products and processes. He previously spent 8 years launching LED lighting products for various lighting companies. His professional experience includes: strategic planning, business development, marketing, and product development. See more at


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