Question

an auto repair shop has a four-part tire installation process with the following ftys for each step: .998, .984, .989, and .986.

what is the rty of the complete tire installation procedure?

.985
.968
.958
.989

Explanation:

Identify the given values and target metric

We are given the First Time Yield (FTY) for each of the four steps in a tire installation process:

• \(FTY_1 = 0.998\)
• \(FTY_2 = 0.984\)
• \(FTY_3 = 0.989\)
• \(FTY_4 = 0.986\)

Our goal is to find the Rolled Throughput Yield (RTY) of the complete procedure.

Apply the Rolled Throughput Yield formula

Using the First Time Yield concept, the Rolled Throughput Yield (RTY) represents the probability that a single unit will pass through the entire multi-step process defect-free. It is calculated by multiplying the individual yields of each step:

$$ RTY = FTY_1 \times FTY_2 \times FTY_3 \times FTY_4 $$

Calculate the final product

We substitute the given values into the formula:

$$ RTY = 0.998 \times 0.984 \times 0.989 \times 0.986 $$

Let's compute the product step-by-step:

$$ 0.998 \times 0.984 = 0.982032 $$

$$ 0.982032 \times 0.989 \approx 0.971230 $$

$$ 0.971230 \times 0.986 \approx 0.957632 $$

Rounding to three decimal places, we get:

$$ RTY \approx 0.958 $$

Answer:

• (A) .985
• (B) .968
• (C) .958 (Correct answer)
• (D) .989