0021// F-test & t-test for flatness control

F-test and t-test are common hypothesis testing use in manufacturing to compare two set of samples' variance and mean. Below is one of the examples to shown step by step how to use F-test and t-test in your manufacturing daily application.

Example:

One of the supplier developed a new process to machine a flat surface. Our supplier claim that the new process will produce with at least 10 micron better flatness control than old process.

To test the claim, our manufacturing engineer selects a simple random sample of 141 pieces of parts from new process and 616 pieces of parts from old process. The flatmess of parts from new process have mean 57.55 micron with a standard deviation of 24.51 micron; the flatness of parts from old process have a mean 69.83 micron with a standard deviation 0.41 micron.

Step 1: State the hypotheses.

These hypotheses are one-tailed test.

Step 2: Use F-test check the variances between two set of samples

By using data analysis in excel, we get the report below,

Note: Please choose the range of cells that can give you higher variance of variable 1 than variance of variable 2.

Because F = 59.34 > F critical one tailed. So, The variances of the two set of samples are unequal.

Step 3: Formulate analysis plan.

We set significance level is 0.05. Using our data, we will conduct two sample t-test with unequal variance of the null hypothesis.

Step 4: Analyse sample data.

By using data analysis in excel, we get the report below,

Logic behind the scene,

We want to know the condition to reject the null hypothesis. So, we want to know whether observe different in sample mean is large enough to cause rejection of null hypothesis (ie suffuciently larger than 10)

The observed different in sample means when mean different = 12.28 produced a t-score of 5.46. From the report we know P(T<=5.46) one tailed = 1.06E-07.

This tell us that we would expect to observe sample mean different of 12.28 or larger than 12.28 in 0.0000106% of our samples, if the true different were actually 10.

Step 5: Interpret results

Since 5.46> 1.66 (i.e. t stat > t critical one tailed), we can reject null hypothesis. At the same time, P(T<=t) one tailed < significant level (i.e. 0.000000106 < 0.05), we reject the null hypothesis too.

All in all, our supplier claim that the new process will produce with at least 10 micron better flatness control than old process is NOT TRUE.

Important Note:

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