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Probability Analysis of Production Processes at Michigan Molding Co.

Analyzing the probability results of different machines at Michigan Molding Co. to enhance quality control of legend plates for aircraft cockpits. Understanding probability outcomes and independence of variables.

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Probability Analysis of Production Processes at Michigan Molding Co.

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  1. Problem # 50 Dr. Ali Moshtagh Probability Problems

  2. The Michigan Molding Co. The Michigan Molding Co. produces two-color legend plates for aircraft cockpits using four machines ( W, X, Y, and Z ). After quality-control inspection, the plates are graded as A, acceptable; B, needs repair; and C, can be scrapped. 1

  3. A sample of 1,000 legend plates revealed the following results: 2

  4. State in symbols, the probability that a legend plate selected at random • was produced by machine W. • was produced by machine X and needs repair. • Needs repair given that it was produced by machine Y. • (restricted to plates produced by machine W) is acceptable. • was either produced by machine Z or can be scrapped. 3

  5. State in words the meaning of each of the following • P ( B | Z ) • P ( A  Y ) • P ( B U X ) 4

  6. Compute the probability that a plate selected at random • was produced by machine Z. • was produced by machine X and is acceptable. • is acceptable, given that it was produced by machine X. • is either in need of repair or was produced by machine W. 5

  7. Use the addition theorem or multiplication theorem, as appropriate, to compute the following probabilities • P ( Y  B ) • P ( C U X ) • P ( A  C ) 6

  8. Determine if the variables (machine and grade) are statistically independent and show why or why not. 7

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