The Toyo Engineering Company (TEC) identified in its position paper two life-histories:
The life history of the product is what the customer sees - from the initial idea of the product, the decision to commision a plant which can produce the product, through to the manufacturing, distribution and use of that product.
The life history of the plant is what the engineering company sees - from the development of technologies that make it possible for the engineering company to tender for designing and building a plant, the tendering, preliminary design, pilot, design, detailed design and building / construction of the plant, contract maintenance, and eventual plant renewal or decomissioning.
This view was illustrated by the Toyo Engineering Company in the "railway-crossing diagram" (Fig.1) below. Fig.1 shows that the "build/construct" phase of the plant's life-history produces the facility that manufactures the product. I.e. this is where the two life-histories meet .
Figure 1. The plant produces the product
The Purdue Enterprise Reference Architecture (PERA) describes the types and logical relationships of activities that happen to any entity during its life. These types of activities are arranged in "layers" as in Fig.2.
This diagram is referred to as a life-cycle diagram, or architecture for the given entity. It is called the "architecture" for the entity, as it logically arranges all those activities that are needed to create that entity. For example, both the plant and the product have their own architectures (life-cycles) which can be described using the Purdue Enterprise Reference Architecture (PERA).
Figure 2. The PERA Life-cycle layers
Often we shall symbolically represent the PERA life-cycle diagram by a simpler symbol ("chocolate bar") as in Fig.3 and label it with the names of the PERA life-cycle layers.
Note that we added the "decomissioning layer" to the life-cycle diagram (this layer was not originally represented on the PERA diagram).

Figure 3. Shorthand representation of a life-cycle
Occasionally we shall turn this symbol on its side with the "operation" layer highlighted as in Fig.4
Figure 4. Shorthand representation of a plant life-cycle showing the Management / Control vs Service components of the entity