Table of Contents

- 1 What is the probability of getting all the 5 rejected items or all the 5 accurate items?
- 2 What is defective unit?
- 3 How do you calculate the DPMO given the value of the defective rate?
- 4 How is defect per unit calculated?
- 5 What is the probability that a sample of 200 contains no defective?
- 6 What is the cumulative probability of a product failure?

## What is the probability of getting all the 5 rejected items or all the 5 accurate items?

→ The probability of getting all five accurate is = (0.08)⁵ = {(0.08)*(0.08)*(0.08)*(0.08)*(0.08)} ≈ 0.00000328. (Ans.)

## What is defective unit?

A defective unit is a unit that has one for more defects. Many prefer to use the term nonconforming units to clarify that a unit that fails to meet the requirements does not necessarily imply that it is unfit for use. For example, a requirement may have been set for a particular dimension.

**What is the probability of choosing first two non defective bulbs followed by a defective bulb?**

If you chose a non-defective and a defective bulb you did so by either choosing a non-defective and then a defective or a defective and then a non-defective. Each possibility has probability 1/3 so the probability of choosing a non-defective and a defective bulb is 1/3 + 1/3 = 2/3.

### How do you calculate the DPMO given the value of the defective rate?

DPMO = Total Number of Defects found in Sample / (Sample Size * Number of Defects Opportunities per Unit in the Sample) * 1000000

- DPMO = 156 / (80 * 100) * 1000000.
- DPMO = 19500.

### How is defect per unit calculated?

Defects Per Unit (DPU) It’s found by dividing the total number of defects found by the number of units. For example, if 30 units are produced and a total of 60 defects have been found, the DPU equals 2.

**What is the percentage of defective products in a manufacturing process?**

Question 913255: A manufacturing process produces 5 percent defective items. What is the probability that in a sample of 50 items: a. 10 percent or more will be defective?

## What is the probability that a sample of 200 contains no defective?

If 1.5 \% of items produced by a manufacturing unit are known to be defective, what is the probability that a sample of 200 would contain no defective item? If the items are independent then the probability is ( 1 – 0.015) 200 = 0.049.

## What is the cumulative probability of a product failure?

The cumulative probability that r or fewer failures will occur in a sample of n items is given by: where q = 1 – p. For example, a manufacturing process creates defects at a rate of 2.5\% (p=0.025). A sample of 20 parts is randomly selected (n=20).

**How do you find the probability of a defect?**

One can easily find the probabilities of 1 defective, 2 defectives, …, 8 defectives and, since they are mutually exclusive outcomes, add them up. Applying the idea of complementarity – that the sum of those = 1 – P {0 defectives} results in an easier to calculate answer.