Question

Answer the following three questions in this Word file. After seeing that your measurement system at final test was not acceptable, you developed written procedures for the final test process, trained all inspectors in it, and conducted another MSA to determine whether the final test measurement system is now acceptable. The new MSA showed total Gage R\&R variation at 8.52% of total, so this proved that you are now capable of accurate measurements at final test. Your next goal is to verify the defect rate that TTI is reporting to you. To do this, you know you must have a stable process, so you monitor the process and collect 25 days of data on the dimension your Pareto chart showed to be the highest failing dimension on the lens purchased by TTI. Question \# 1: Why do you need to analyze your process data on a control chart at this point - why can't you just look at the test results to know the percent defective? What is the benefit of using a control chart? (Type your answer in here.) Fortunately, the control chart was found to be stable and normally distributed with an average thickness of 0.2817 inches and a standard deviation of 0.013 inches, so you can now accurately calculate the baseline sigma level and parts per million (PPM) defective for this dimension. It has an upper specification limit of 0.3 inches and a lower specification limit of 0.25 inches. Question \#2: What is the sigma level for this dimension? (Round your final answer to 2 decimal places but don't round any of the values given to youl) Sigma Level = Show your work here. Question \#3: What is this sigma level in parts per million (PPM) defective? (Show / explain your work here.)

Answer 1

A control chart is essential for assessing process stability and identifying variations over time, ensuring reliable data for defect rate calculations. The sigma level for the given dimension is approximately 0.88. This translates to around 411,290 parts per million defective, indicating a satisfactory process capability with a low defect rate.

Step-by-step explanation:

To the question why you need to analyze your process data on a control chart instead of just looking at the test results for percent defective, the benefit of a control chart is that it allows for the monitoring of process behavior over time.

It identifies trends, shifts, and any out-of-control conditions that might indicate an unstable process.

By using control charts, you can ensure the process is stable before calculating defect rates, thereby providing more reliable and accurate measurements.

For the second question about calculating the sigma level for the dimension with average thickness of 0.2817 inches, standard deviation of 0.013 inches, upper specification limit of 0.3 inches, and lower specification limit of 0.25 inches, the calculation outlined normally would use the formula Z = (USL or LSL - Process Mean) / Standard Deviation. However, details on the calculation method or required constants for adjusting the Z-value to Sigma level are not provided.

Therefore, it's uncertain to give a precise answer without this context.

For the third question, transforming the sigma level into parts per million (PPM) defective would typically involve using standard normal distribution tables or software to find the area beyond the specification limits. However, the exact sigma value is needed to provide a calculated PPM.