Managing for Quality and Performance Excellence 9th Edition by James Evans,William Lindsay

Exercise 31

Note: Data sets for many problems in this chapter are available in the Excel workbook C06Data.xlsx on the Student Companion Site. Click on the appropriate worksheet tab as noted in the problem (e.g., Prob. 6-1) to access the data. In addition, the spreadsheet templates illustrated in the chapter are also available to aid in solving many of these problems.
A new production process at Fabufirst, Inc. has two in-line stages. The probability of defective components being produced in stage 1 is 15 percent and 10 percent in stage 2. Assembled units that have defective components only from stage 1 OR only from stage 2 are considered repairable. However items that have defective components from both stage 1 and stage 2 (completely defective) must be scrapped.
a. Use a probability tree diagram and calculate the probabilities that the Fabufirst assembled units are: (i) defective in stage 1 and defective in stage 2 (are completely defective); (ii) defective in stage 1 and are not defective in stage 2 (called Repairable I); (iii) not defective in stage 1 but are defective in stage 2 (called Repairable II); and (iv) not defective in stage 1 and are not defective in stage 2 (completely good). What is the probability of producing repairable assembled units?
b. Explain the results in terms of the multiplication and the addition rules for probability.