Improve Quality Control Process

Oct 13, 2025 by wbrum.org 82 views

Understanding the Distribution of Defective Light Bulbs in a Randomly Selected Box

Let ${$ x $}$ denote the number of defective light bulbs in a randomly selected 20-count box from a local hardware store. The variable ${$ x $}$ has the following distribution:

X	0	1	2
P(X)	0.6	0.3	0.1

In this article, we will delve into the distribution of defective light bulbs in a randomly selected box and explore the implications of this distribution on the quality control of the light bulbs.

The distribution of defective light bulbs in a randomly selected box is a discrete probability distribution, where the random variable ${$ x $}$ takes on the values 0, 1, and 2. The probability of each value is given in the table above.

The probability of 0 defective light bulbs is 0.6, which means that 60% of the boxes have no defective light bulbs.
The probability of 1 defective light bulb is 0.3, which means that 30% of the boxes have one defective light bulb.
The probability of 2 defective light bulbs is 0.1, which means that 10% of the boxes have two defective light bulbs.

The expected value of a discrete random variable is the sum of the product of each value and its probability. In this case, the expected value of ${$ x $}$ is:

E(X) = 0(0.6) + 1(0.3) + 2(0.1) = 0 + 0.3 + 0.2 = 0.5

This means that on average, a randomly selected box will have 0.5 defective light bulbs.

The variance of a discrete random variable is the sum of the product of each value and its squared probability. In this case, the variance of ${$ x $}$ is:

Var(X) = (0-0.5)^2(0.6) + (1-0.5)^2(0.3) + (2-0.5)^2(0.1) = 0.15 + 0.09 + 0.09 = 0.33

This means that the variance of the number of defective light bulbs in a randomly selected box is 0.33.

The distribution of defective light bulbs in a randomly selected box has several implications for the quality control of the light bulbs.

Quality Control: The distribution suggests that the quality control process is not effective in detecting defective light bulbs. The high probability of 0 defective light bulbs suggests that the quality control process is not catching all the defective light bulbs.
Supply Chain Management: The distribution suggests that the supply chain management process is not effective in ensuring that only high-quality light bulbs are shipped to the customers. The high probability of 1 and 2 defective light bulbs suggests that the supply chain management process is not catching all the defective light bulbs.
Customer Satisfaction: The distribution suggests that the customer satisfaction level is low. The high probability of 1 and 2 defective light bulbs suggests that customers are likely to be dissatisfied with the quality of the light bulbs.

In conclusion, the distribution of defective light bulbs in a randomly selected box is a discrete probability distribution with values 0, 1, and 2. The probability of each value is given in the table above. The expected value of the distribution is 0.5, and the variance is 0.33. The distribution has several implications for the quality control of the light bulbs, including the need for improved quality control and supply chain management processes.

Based on the analysis of the distribution, the following recommendations are made:

Improve Quality Control Process: The quality control process should be improved to detect all the defective light bulbs.
Improve Supply Chain Management Process: The supply chain management process should be improved to ensure that only high-quality light bulbs are shipped to the customers.
Monitor Customer Satisfaction: The customer satisfaction level should be monitored to ensure that customers are satisfied with the quality of the light bulbs.

By implementing these recommendations, the quality of the light bulbs can be improved, and the customer satisfaction level can be increased.
Frequently Asked Questions (FAQs) about the Distribution of Defective Light Bulbs

In our previous article, we discussed the distribution of defective light bulbs in a randomly selected box from a local hardware store. We explored the implications of this distribution on the quality control of the light bulbs and made several recommendations to improve the quality of the light bulbs. In this article, we will answer some frequently asked questions (FAQs) about the distribution of defective light bulbs.

A: The probability of a box having no defective light bulbs is 0.6, which means that 60% of the boxes have no defective light bulbs.

A: The probability of a box having one defective light bulb is 0.3, which means that 30% of the boxes have one defective light bulb.

A: The probability of a box having two defective light bulbs is 0.1, which means that 10% of the boxes have two defective light bulbs.

A: The expected value of the distribution of defective light bulbs is 0.5, which means that on average, a randomly selected box will have 0.5 defective light bulbs.

A: The variance of the distribution of defective light bulbs is 0.33, which means that the variance of the number of defective light bulbs in a randomly selected box is 0.33.

A: The distribution of defective light bulbs suggests that the quality control process is not effective in detecting defective light bulbs. The high probability of 0 defective light bulbs suggests that the quality control process is not catching all the defective light bulbs.

A: The distribution of defective light bulbs suggests that the supply chain management process is not effective in ensuring that only high-quality light bulbs are shipped to the customers. The high probability of 1 and 2 defective light bulbs suggests that the supply chain management process is not catching all the defective light bulbs.

A: The distribution of defective light bulbs suggests that the customer satisfaction level is low. The high probability of 1 and 2 defective light bulbs suggests that customers are likely to be dissatisfied with the quality of the light bulbs.

A: The quality of the light bulbs can be improved by improving the quality control process, improving the supply chain management process, and monitoring customer satisfaction.

A: The recommendations for improving the quality of the light bulbs are:

Improve Quality Control Process: The quality control process should be improved to detect all the defective light bulbs.
Improve Supply Chain Management Process: The supply chain management process should be improved to ensure that only high-quality light bulbs are shipped to the customers.
Monitor Customer Satisfaction: The customer satisfaction level should be monitored to ensure that customers are satisfied with the quality of the light bulbs.

By implementing these recommendations, the quality of the light bulbs can be improved, and the customer satisfaction level can be increased.