# Combining Std Dev and Mean Values

#### jtstien

I'm wondering if there is a way to combine the data for Machine A and Machine B in the problem below to come up with one data set, i.e. 1 std deviation value and 1 mean value for Machine A and Machine B combined. I was thinking I could just add the mean/std deviation values and get mean = 3,002mm / std dev = 5 but i'm not sure if that is correct. Any insight into this would be greatly appreciated! Thanks.

PROBLEM:
Assume that your company has received an order for 100,000 assemblies each consisting of two subassemblies. The two subassemblies are assembled end-to-end to create an assembly that is to be 3,000 mm in length with a lower specification limit of 2,995 mm and upper specification limit of 3,003 mm. Your company has two machines to make these subassemblies. Machine A makes Subassembly A. Measurements of Machine A found that the subassemblies produced had a mean length of 1,000 mm with a standard deviation of 3 mm. Machine B makes Subassembly B. Measurements on Machine B have found it makes parts with a mean of 2,002 mm and a standard deviation of 2 mm. The order is for 100,000 assemblies.

THE QUESTION I WILL ULTIMATELY BE ANSWERING:
Given the current situation, if 100,000 assemblies are manufactured, how many will not meet the specifications?

MHF Helper