Godwin Thomas

Trial and error is the simplest experimental approach. Currently, across many industries, this approach is often coupled with fail fast, fail often concept to promote aggressive experimentation to learn and explore new ways of designing products/processes. Gordon Moore, founder of Intel, noted: “With engineering, I view this year's failure as next year's opportunity to try it again. Failures are not something to be avoided. You want to have them happen as quickly as you can so you can make progress rapidly.”
In the trial and error method, a 4 step approach is typically followed, wherein the experts start by first observing a problem, then make assumptions on what could or could not possibly work, devise & deploy a solution based on the assumptions, learn valuable lessons from the outcome of the deployed solution. This approach is repeated again and again, each time with adjustments made to the design based on previous learnings, until a convincing solution is arrived at (or a decision is made to simply stop the experiment based on several other factors).
 
Trial and error has many advantages compared with the other experimental setups:
a) it is easy and quick to setup
b) it does not need special expertise and can easily be implemented by the specific subject matter experts
c) it promotes a culture of learning by doing and observing
 
Trial and error should be the last resort if other approaches cannot be used due to the following disadvantages:
a) Not rule based and hence, does not provide a structured thinking on all the factors that could affect the experiment
b) Its best suited only for simple problems, whereas typical real world problems have a wide variety of variables as inputs
c) It cannot be used to predict an outcome as it does not provide enough clues on why a solution works
d) It cannot be used to find the best possible solution or all possible solutions
 
Examples to understand trial and error: Our day Is filled with instances where we continuously experiment with new things. Trial and error seen in nature: A monkey figuring out to open a soda bottle with a bottle opener; Trial and error seen in our everyday life: A person trying to figure out the best transportation to commute to work, a baby trying to stand up and walk; Trial and error seen in industry: Supervised machine learning.
 
One factor at a time: As the name implies, an experimental approach in which the factors are tested one at a time. This approach is also known by various other acronyms such as OVAT, OVaaT (one variable at a time). Suppose we have a process with inputs X1, X2 that are processed to provide an output Y. In OFAT, we keep X2 constant and vary X1 to find the optimum result. Once the optimum output is achieved, X1 is fixed at that point and we then vary X2 to find its optimum value. In this way, one factor or variable (ie)., X1 or X2, is varied at a time till all the input factors are exhausted.  
 
The main advantage of OFAT is that it serves as a good alternative to multi factor analysis when collecting data for multi factor is cumbersome or not economically viable.
 
OFAT has the following disadvantages:
a) Cannot figure out interaction effects between the variables under analysis. This means, OFAT cannot be used if the input variables to a process interact with each other and the interaction also has an impact on the output.
b) In certain cases, depending on the number of variables, can lead to large number of experimental runs with a negative impact on cost and time.
 
If you want to understand adding 2 strawberries or 4 strawberries (factor / variables) to 1 glass of milk, with 2 spoons of sugar, mixed for 3 mins in the same mixer (fixed entities) gives the best strawberry smoothie, we can use OFAT.
 
Multiple Factors at a time: When multiple factors are manipulated to study their effect on the response/output, its called multi factor at a time experimental approach. This solves the major disadvantage with OFAT pertaining to interaction effect as the response pertaining to changes on multiple factors at the same time are observed to find the optimum response. In case of random selection of input variables as followed in trial and error, there is no structure which gives clear understanding if all possible combinations of inputs have been analyzed in an orderly way. Hence, with trial and error, its not possible to quantify if the solution finalized is the best optimum. With multi factor analysis, as the experiment can be designed to include all the interactions that is of interest, probability of achieving the best optimum solution with an orderly experimentation is high. Further, the multi factor analysis also provides key insights on the key factors to be considered, the optimal settings for each input variable to be set that would result in the least variation in the process output.
 
Despite the advantages, the subject matter experts in coordination with the management should determine the right use cases for doing a multi factor analysis by taking the complexity, cost of experimentation, multiple runs, practical feasibility for simulation and time needed.  
 
An OEM that manufactures Turbines for power generation can use a multi factor analysis experimental approach to find which operational conditions such as ambient temperature, fuel used, fuel gas temperature, etc will result in the maximum power efficiency.