# Step-by-Step Solution Let's break down the to find the **Rolled Through Yield (RT)**. --- **Step : Understand the** - **Y** is the that a unit passes through all process steps without defects. - You are given a process with 4 steps. - The numbers above the arrows (3, 2, 10, 4) represent defects at each step. - The input is **100 units**, and the output is **95 units**. --- ## **Step 2: Find the Yield at Each Step** Yield at each step is calculated as: \[ \text{Yield} = 1 - \frac{\text{Defects at Step}}{\text{Units Entering Step}} \] Let's compute for each step: ### **Step 1** - **Input:** 100 - **Defects:** 4 - \(\text{Yield}_1 = 1 - \frac{4}{100} = .96\) ### **Step 2** - **Input:** 100 (all units move to next step even if defective) - **Defects:** 2 - \(\text{Yield}_2 = 1 - \frac{2}{100} = .98\) ### **Step 3** - **Input:** 100 - **Defects:** 10 - \(\text{Yield}_3 = 1 - \frac{10}{100} = .90\) ### **Step 4** - **Input:** 100 - **Defects:** 4 - \(\text{Yield}_4 = 1 - \frac{4}{100} = .96\) --- ## **Step 3: Calculate RTY** RTY is the product of all yields: \[ \text{RTY} = \text{Yield}_1 \times \text{Yield}_2 \times \text{Yield}_3 \times \text{Yield}_4 \] \[ \text{RTY} = .96 \times .98 \times .90 \times .96 \] \[ \text{RTY} = .96 \times .98 = .9408 \] \[ .9408 \times .90 = .84672 \] \[ .84672 \times .96 = .8128512 \] \[ \boxed{.813} \] (Rounded to 3 decimal places) --- ## **Final Summary** - **RTY** for the given process is **.813**. - This means **81.3%** of units are expected to pass through all steps without any defects.

# Step-by-Step Solution Let's recalculate the **Rolled Through Yield (RTY)** based on the provided defects at each step. --- ## **Step 1: Understand the Process** - **Y** represents the yield of a unit passing through all process steps without defects. - The process has 4 steps, with defects at each step represented as follows: - Step 1: 4 defects - Step 2: 2 defects - Step 3: 10 defects - Step 4: 4 defects - The input is **100 units**. --- ## **Step 2: Calculate the Yield at Each Step** The yield at each step is calculated using the formula: \[ \text{Yield} = 1 - \frac{\text{Defects at Step}}{\text{Units Entering Step}} \] ### **Calculations for Each Step** 1. **Step 1** - **Input:** 100 - **Defects:** 4 - \[ \text{Yield}_1 = 1 - \frac{4}{100} = 0.96 \] 2. **Step 2** - **Input:** 100 (all units move to next step) - **Defects:** 2 - \[ \text{Yield}_2 = 1 - \frac{2}{100} = 0.98 \] 3. **Step 3** - **Input:** 100 - **Defects:** 10 - \[ \text{Yield}_3 = 1 - \frac{10}{100} = 0.90 \] 4. **Step 4** - **Input:** 100 - **Defects:** 4 - \[ \text{Yield}_4 = 1 - \frac{4}{100} = 0.96 \] --- ## **Step 3: Calculate RTY** RTY is calculated as the product of all yields: \[ \text{RTY} = \text{Yield}_1 \times \text{Yield}_2 \times \text{Yield}_3 \times \text{Yield}_4 \] \[ \text{RTY} = 0.96 \times 0.98 \times 0.90 \times 0.96 \] ### **Performing the Calculations** 1. \[ 0.96 \times 0.98 = 0.9408 \] 2. \[ 0.9408 \times 0.90 = 0.84672 \] 3. \[ 0.84672 \times 0.96 = 0.8128512 \] Therefore, rounding to three decimal places gives: \[ \boxed{0.813} \] --- ## **Final Summary** - The **Rolled Through Yield (RTY)** for the process is **0.813**. - This indicates that **81.3%** of the units are expected to pass through all steps without any defects.