10. Problem VI
We produce a flat part for one of our customers. The part has a rectangular grid of 44 holes, 4 rows of 11 holes each. All holes have the same nominal diameter. The thickness of the part is different for each row, but the same for all holes in any given row. A bushing (metal tube sized to fit tightly into a hole) must be installed in each hole. The bushing is inserted into the hole on the top side of the part, then pulled down through the hole towards the bottom side. After installation, a bushing must not protrude below the bottom surface, and the bushing must end no more than 0.008″ above the bottom surface (inside the part).
The length of a bushing prior to installation is called the Before
measurement. The After
measurement is the location of the end of the bushing relative to the bottom surface. A positive value of After
means that the bushing ends above the bottom surface. A negative value means that the bushing protrudes below the bottom surface. Thus, the lower specification limit (LSL) for After
is 0.000″ and the upper specification limit (USL) is 0.008″. The target value is 0.004″.
The bushings stretch when installed. We have been using a trial and error process in which bushings of various lengths are installed and removed until an acceptable value of After
is achieved. This is done for each of the 44 holes on each part. We are wasting a lot of time and money. We have collected data from which to develop an equation that will accurately predict After
as a function of Before
and the hole location. Such an equation would tell us what length bushing was needed for each hole. Bushings could then be cut to the specified lengths and installed without trial and error.19.
Open bushing installation data
.. This file contains the current state data we collected. Fit a Normal distribution to After
. If the current state continues as is, what percentage (2 decimals places) of future After
values are predicted to be out of spec?