Q 694. In DOE, generally the response variable is continuous data. Can DOE be executed when we have discrete data? Highlight the limitations or risks in working with Discrete data DOE. Provide some examples where it can be used.

 

Note for website visitors -

• This platform hosts two weekly questions, one on Tuesday and the other on Friday. 
• All previous questions can be found here: https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/. 
• To participate in the current question, please visit the forum homepage at https://www.benchmarksixsigma.com/forum/.
• The question will be open until Tuesday or Friday at 5 PM Indian Standard Time, depending on the launch day. 
• Responses will not be visible until they are reviewed, and only non-plagiarised answers with less than 5-10% plagiarism will be approved. 
• If you are unsure about plagiarism, please check your answer using a plagiarism checker tool such as https://smallseotools.com/plagiarism-checker/ before submitting. 
• All correct answers shall be published, and the top-rated answer will be displayed first. The author will receive an honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term.

• Some people seem to be using AI platforms to find forum answers. This is a risky approach as AI responses are error prone as our questions are application-oriented (they are never straightforward). Have a look at this funny example - https://www.benchmarksixsigma.com/forum/topic/39458-using-ai-to-respond-to-forum-questions/

• We also use an AI content detector at https://crossplag.com/ai-content-detector/. Only answers with less than 15-20% AI-generated content will be approved.

Can DOE be executed when we have discrete data?

Ans: DOE can be done on discrete data such as Pass/Fail, Good/Bad, OK/Not Ok.

However in this case the sample size would be larger to detect a significant effect due to nature of discrete data.

 

Highlight the limitations or risks in working with Discrete data DOE.

Experiment will have lack of nuances as we don’t have the continuous data.

Different statistical tools will be used such as logistic regression for binary data or Poisson's regression for count data.

 

Examples:

1)Outcome of the process is Pass/fail, improving customer service experience by reducing the number of complaints-counting data. For different preferences (Categorical data)

 

2) Another Example- If a patient is suffering from cancer and he is advised by doctor to take chemotherapy as early as possible. And Patient did not take any authorization from Insurance company. Later on he came to know that the expenses are not refunded due to non-authorization received from Insurance company.  If we consider that Patient took the prior authorization from the insurance company then the outcome is going to be 'Claim Reimbursed'.

So the discrete outcomes would be ' Claim Denied and Claim Reimbursed'.

 

 

 

 

 

Usually when the response variable in DOE is continuous it helps with most significant source of data 
which would be useful to analyze statistical method that in turn gives detailed data of the relationships between factors and its outcomes. However DOE can be executed with discrete data  with some amount of risks involved in it.
Here are some risks involved stated below-
1. Specific outcomes - Discrete data has limited levels which doesn't go down the level(nitty gritty) of the data,
due to this it becomes difficult to find the most impacting effects
2. Analysis is not smooth - if there multiple factors with multiple levels the data cannot be interpreted easily
3. Lack of correct predictability - Since the data do not include or capture the full range of possible variations
the chances of giving correct prediction is less
In line with the above explanation it can be used for market survey, quality testing of data in a process etc.
To conclude the DOE with discrete data does faces some significant challenges however with the proper planning and correct usage of statistical techniques are very much important to implement DOE with discrete data.

DOE is generally meant for continuous response data. Continuous data can be interpreted very easily as it can be, in most cases, fit into a particular probability distribution and insights can be drawn very easily. Also, the measurement of interactions of the different levels of inputs on the response can be very easily assessed.

However, discrete DOE would be a difficult to handle as the response to the inputs needs to be fit into binary, ordinal or nominal categories. While the output can be fit into distributions like Poisson or Binomial, there is a chance that the result might be misinterpreted on account of limited number of trials. The resolution is not well captured in discrete output as good as it is can be done with continuous data.

 

Despite these challenges, discrete data DOE can be a powerful tool in certain situations. For example, in quality control, we may want to investigate the factors that influence the probability of a product being defective. Or, in marketing, we might be interested in modeling the likelihood of a customer responding to a particular promotion.

 

Design of experiment ( DOE ) responses are generally continuous because these experiments are aim to produce wide range of results using various discreate and continuous variable. 

Still yes there is a possibility that DOE responses are discrete. For example counting of defect is discreate measure. 

Responses can be discrete, but there can be various limitations and risks with discrete responses. Below three are major point to mention for discreate response DOE 

 

1. Loss of details:- Granule details of continuous data is advantage, with discrete data, these details are missed out. For Example, when we measure defect count in a batch, we losses details of exact size of defect and specification of defect.
2. Analysis complexity: For discrete data, logistic / poisson regression has to be performed, which is complex compared to linear regression. This Makes analysis complex. Example : No of student passed final exam. 
3.  Sample size: Discrete data often requires a larger sample size for analysis. This increases cost and time required for the experiments. 

 

Below are some examples of the discrete response:

• No of defect in manufacturing.
• No of customer identified by a survey.
• No of student passed in unit test.
• No of patients facing side effect of a medicine

This was a slightly tricky and a difficult one to answer. Mohammad Riyadh Al Kamal has provided the best answer to this question. Well done!!