Combining Std Dev and Mean Values

Jul 2016
1
0
Phoenix
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?
 

romsek

MHF Helper
Nov 2013
6,725
3,030
California
for independent normal rv's means add and variances add.

so square your standard deviations, sum them, and take the square root to obtain the standard deviation of the sum