You are testing a requirement for the thickness of a rubber coating on the undercarriage of an uncrewed ground vehicle. The system specification states the rubber coating shall be 5.7 +/- 0.06 mm think. You know from your experience with the manufacturing process that the process could produce a coating +/- 0.28 mm thick.Since there is variation in the coating process you decide to collect a sample to estimate the mean thickness of the coating. You want to estimate the possible range of process thickness with 95% confidence.What sample size should you inspect? Remember you cannot inspect a fraction of a unit, round up.
Question
You are testing a requirement for the thickness of a rubber coating on the undercarriage of an uncrewed ground vehicle. The system specification states the rubber coating shall be 5.7 +/- 0.06 mm think. You know from your experience with the manufacturing process that the process could produce a coating +/- 0.28 mm thick.Since there is variation in the coating process you decide to collect a sample to estimate the mean thickness of the coating. You want to estimate the possible range of process thickness with 95% confidence.What sample size should you inspect? Remember you cannot inspect a fraction of a unit, round up.
Solution
To determine the sample size needed, we can use the formula for the sample size of a population mean:
n = (Z^2 * σ^2) / E^2
where:
- n is the sample size
- Z is the Z-score (for a 95% confidence level, Z = 1.96)
- σ is the standard deviation (in this case, the variation in the coating process, which is 0.28 mm)
- E is the margin of error (in this case, the tolerance in the system specification, which is 0.06 mm)
Substituting the given values into the formula, we get:
n = (1.96^2 * 0.28^2) / 0.06^2
Solving this equation will give us the required sample size. However, since we cannot inspect a fraction of a unit, we will need to round up to the nearest whole number.
Similar Questions
Small thickness is measured by using
The mean diameter of a certain part from a manufacturing process is 5 mm and the standard deviation is 0.01 mm. The Lower Specification Limit 4.95 mm and the Upper Specification Limit (USL) is 5.03 mm.REQUIRED:Determine the value of the Process Capability Index.
The mean length of a certain part from a manufacturing process is 12 mm and the standard deviation is 0.03 mm. The lower specification limit is 11.99 mm and the upper specification limit is 12.03 mm.REQUIRED:Determine the value of the Process Capability Ratio.
A sheet metal manufacturer is making 10-gauge sheet metal, which is supposed to be 3.416 mm thick. One of the pieces of manufacturing equipment was suspected of malfunctioning, so the manufacturer tested a random sample of 100 pieces of steel to make sure the average steel thickness is 3.416 mm.Which of the following is a statement of the null hypothesis?
A sheet metal manufacturer is making 10-gauge sheet metal, which is supposed to be 3.416 mm thick. One of the pieces of manufacturing equipment was suspected of malfunctioning, so the manufacturer tested a random sample of 100 pieces of steel to make sure the average steel thickness is 3.416 mm.Which of the following is a statement of the null hypothesis? The equipment is working properly. The average average steel thickness is 3.416 mm. The equipment is not working properly. The average average steel thickness is not 3.416 mm. The equipment is making the sheet metal too thick. The average average steel thickness is greater than 3.416 mm.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.