Question:

Describe a situation in an administrative or services business where this sort of defect probability analysis may appropriately be used.

Case information:

A new production process at MakeIt 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.

Let,

1 – item produced in stage 1

2 – item produced in stage 2

D – Defective unit

ND – Not defective unit

The probability of item to be defective produced in stage 1 = P(D/1) = 0.15

The probability of item to be not-defective produced in stage 1 = P(ND/1) = 1 - 0.15 = 0.85

The probability of item to be defective produced in stage 2 = P(D/2) = 0.10

The probability of item to be not-defective produced in stage 2 = P(ND/1) = 1 - 0.10 = 0.90

The decision tree is as follows:

a. defective in stage 1 and defective in stage 2 (are completely defective) = 0.015

b. defective in stage 1 and are not defective in stage 2 (called Repairable I) = 0.135

c. not defective in stage 1 but are defective in stage 2 (called Repairable II) = 0.085

d. not defective in stage 1 and are not defective in stage 2 (completely good) = 0.765

e. What is the probability of producing repairable assembled units? = P(repairable 1) + P(repairable II) = 0.135 + 0.085 = 0.22.