Analyzing Producti

on Efficiency in Manufacturing

Objective: To use hypothesis testing concepts to compare the production efficiency of two types of machine tools in a

manufacturing plant.

Background:

A manufacturing company is considering the introduction of a new type of machine tool $($Machine Tool $Y)$ to work alongside its

existing machine tool $($Machine Tool X$).$ The project's goal is to assess the efficiency of the new machine tool in terms of operation

time, wear rate, and variability in operation time.

Data Collection:

Randomly select products manufactured using Machine Tool Xand Machine Tool Y$.$

Record the operation time for each selected product.

Record the number of products showing wear from the samples.

Calculate the sample mean and sample standard deviation of operation time for both machine tools.

Sample Data for $n=10$ :

Hypothesis Testing:

Population Mean $($Operation Time$)$:

a$.$ Compare the average operation time between Machine Tool $x$ and Machine Tool Y$.$

b$.$ Perform a two$-$sample t$-$test to test if there is a significant difference in average operation time.

Population Proportion $($Wear Rate$)$:

a$.$ Compare the wear rates between Machine Tool X and Machine Tool Y$.$

b$.$ Perform a two$-$sample z$-$test to test if there is a significant difference in wear rates.

Population Standard Deviation $($Variability in Operation Time$)$:

a$.$ Compare the variability in operation time between Machine Tool $x$ and Machine Tool Y$.$

b$.$ Perform an F$-$test to test if there is a significant difference in the variability of operation time.

Analysis and Conclusion:

Analyze the results of the hypothesis tests for each population parameter $($mean$,$ proportion, and standard deviation$).$

Determine if the new machine tool $($Machine Tool Y$)$ is more efficient than the existing machine tool $($Machine Tool $x)$ based on

the results.

Provide recommendations for the company on whether to continue using both machine tools, replace Machine Tool X with

Machine Tool Y$,$ or implement further enhancements based on the findings.