The design of a solar thermal installation is based on the lowest irradiance levels that occur during winter. However, there are consecutive days with irradiance levels well below those used for the design, which are called in this work “critical irradiance levels”. To solve this challenge, a statistical analysis is carried out to find a representative percentile of 22 years of consecutive days with “critical irradiance levels”. A case study of a cotton-dyeing industrial process requires 18.5 m3 of hot water and operates for 2.75 h at temperatures between 40 and 90 °C. Environmental variables for 22 years were analyzed and validated to design a solar thermal installation (solar collector network and storage system) and a coupled heat pump. The fifth percentile, with three consecutive days and low irradiance levels, was the most repetitive. For this case, a storage system of 46.5 m3 guaranteed heat load at target temperature. The simple payback was 14.1 years, and the energy cost was 0.094 USD/kWh, which was competitive against the energy cost from using fossil fuels, 0.064 USD/kWh. The design based on critical environmental conditions guarantees a continuous supply of energy to the industrial process and defines the minimum availability of solar energy to supply a process.