Problem on x̄ Chart - Quality Engineering - Metrology and Quality Engineering

TL;DR

Analysis of an X-Bar chart problem for determining acceptance of a lot based on sample dimensions measured through a vernier caliper.

Transcript

hello students today we will solve one more problem that is the x bar problem so here they have given the components need to be turned to a diameter of 25 mm on a cnc turning machine so a sample of 15 has been drawn and table below shows the dimensions which are measured using a vernier caliper so sample number that is small n is 15 and they have g... Read More

Key Insights

• 🗳️ The problem involves using an X-Bar chart to determine acceptance of a lot based on sample dimensions.
• ☺️ The X-Bar value is calculated by summing up the dimensions and dividing by the sample size.
• ☺️ The standard deviation (sigma) is calculated using the differences between each dimension and the X-Bar value.
• 🎮 Plotting the dimensions on the chart reveals points outside the upper and lower control limits, indicating the process is not under statistical control.

Questions & Answers

Q: What is the purpose of the X-Bar chart in this problem?

The X-Bar chart is used to determine if the lot can be accepted based on the sample dimensions, by comparing them to control limits and assessing the statistical control of the process.

Q: How is the X-Bar value calculated?

The X-Bar value is calculated by summing up all the given dimensions (xi) and dividing the sum by the sample size (n), which in this case is 15.

Q: How is the standard deviation (sigma) calculated?

The standard deviation (sigma) is calculated by finding the sum of the square of the differences between each dimension (xi) and the X-Bar value, dividing it by the sample size (n), and taking the square root of the result.

Q: What do the upper and lower control limits represent?

The upper and lower control limits determine the acceptable range of dimensions on the X-Bar chart. Any points falling outside these limits indicate the process is not under statistical control.

Summary & Key Takeaways

• The problem involves drawing an X-Bar chart for determining the acceptance of a lot based on the dimensions of 15 sample components measured with a vernier caliper.

• The X-Bar chart requires calculating the X-Bar value and the standard deviation (sigma) using the given dimensions.

• By plotting the dimensions on the chart and comparing them to the upper and lower control limits, it is determined that the process is not under statistical control, requiring further investigation.