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1. Problem I (5 points)                                                                                                                                                                                                                                Open PM schedule analysis. This file contains life data on the primary functional component in a family of devices we sell to certain customers. Currently this component receives preventive maintenance (PM) every 1000 hours of use. All other components receive PM every 1300 hours. Changing the primary functional component to the 1300 hour PM cycle would save us about $100K per annum in PM costs. However, this could also increase the cost of unplanned maintenance. To assess this risk, we want to determine the increase in the probability of failure between PM cycles.

1.  Identify the life distribution giving the best fit to this data. Use this distribution to answer questions 2 through 5. Express the failure probabilities to 4 decimal places.

 

2. 2. Give the most likely failure probability at 1000 hours.

3. 3. Give the worst-case failure probability at 1000 hours.

4. 4. Give the most likely failure probability at 1300 hours.

5. 5. Give the worst-case failure probability at 1300 hours

6. Problem II  (4 points)

Open msa 12 appraisers. This file contains pass-fail inspections of 6 samples of material by 12 appraisers. Each appraiser inspected each sample twice.

6. Convert the file to the format needed for this analysis. Which option below best describes this format.
7. 7. What is the agreement grand mean? (Round off to the nearest whole number.)

8. 8. Which sample would be most useful in a follow-up discussion aimed at understanding the causes of disagreement among the appraisers?

9. 9. Assuming % agreement is a good proxy for % correct, which appraiser represents the greatest opportunity for improvement?

10. Problem VI  (16 points)

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?