A powder metal manufacturing company is producing sleeves for a locking mechanism.The target (nominal)value for the inside diameter is 1 inch.The inside diameter specifications are 1 $\pm$ .005 inches.Assume that the process is in statistical control with = 1.0002 inches, = .003 inches and subgroup size of 5. What are the natural tolerance limits for this process? Is the process capable?

Question

A powder metal manufacturing company is producing sleeves for a locking mechanism.The target (nominal)value for the inside diameter is 1 inch.The inside diameter specifications are 1 $\pm$ .005 inches.Assume that the process is in statistical control with  = 1.0002 inches,  = .003 inches and subgroup size of 5. What are the natural tolerance limits for this process? Is the process capable?

Quizplus · Accepted Answer

The natural tolerance limits for a process in statistical control can be calculated using the formula:
NTL = x̄ ± (k*σ)
Where x̄ is the process mean, σ is the process standard deviation, and k is a constant based on the sample size (subgroup size) and the desired probability of the process falling within the specification limits.
For this process, x̄ = 1.0002 inches and σ = 0.003 inches (calculated using the range method), and the subgroup size is 5, which corresponds to a k value of 1.96 for a 95% confidence level.
Plugging in the values, we get:
NTL = 1.0002 ± (1.96*0.003) = 0.99633 to 1.004 inches
Therefore, the correct answer is C, and we can conclude that the process is capable since the natural tolerance limits fall within the specification limits.

A Powder Metal Manufacturing Company Is Producing Sleeves for a Locking