Statistical or Machine Learning Approach for Simulating Variable (proportion)

Question

I am currently facing a challenge in analyzing customer satisfaction data from an electric drive production facility. During a specific period of the month, we encountered technical issues with our machinery, resulting in lower-than-expected customer satisfaction values.

To provide context, we operated optimally from the 1st to the 11th of the month, and for each of these days, we recorded the percentage of satisfied customers. However, from the 12th to the 19th, technical issues arose, impacting customer satisfaction. In essence, we experienced 8 days of "non-optimal performance" and 22 days of optimal performance.

I am seeking advice on the most suitable statistical or machine learning methods to simulate or infer the overall satisfaction for the entire month had the technical issue not occurred.

Methods I am considering:

1. Bootstrap resampling with a 95% confidence interval, resampling customer satisfaction survey data from the period of normal operation to infer our expected performance.
2. Monte Carlo simulation, assuming a binomial distribution for the theoretical distribution of satisfaction percentages, using input data from the optimal performance period.

I have also heard about machine learning or time series forecasting using data from other months. I would appreciate a well-informed and academically-backed perspective on the best approach to address this question.

My desired output will be a confidence interval of the proportion of customer satisfaction for that particular month, where it is simulated, inferred, forecasted, etc. The objective is to obtain this information under the assumption that the technical difficulty did not occur

Answer 1

I think you have a couple of options.

Since you're only interested in the average customer satisfaction for the month, you could simply ignore the corrupted dates. The estimate would have lower precision due to smaller sample size, but there is no need to model the daily customer satisfaction. You can use the bootstrap or any other technique to estimate the confidence interval for the average rating.

If you needed to answer "what would our satisfaction have been on those days where the machines were malfunctioning" you could model the data using an appropriate regression model. The choice of regression model will depend on a lot of things, so I won't get into it here.