For a manufacturing process, = 10 inches, = .4 inches and the subgroup sample size is 6 units. Calculate the natural tolerance limits for this process.

Question

For a manufacturing process,  = 10 inches,  = .4 inches and the subgroup sample size is 6 units. Calculate the natural tolerance limits for this process.

Quizplus · Accepted Answer

Natural tolerance limits can be calculated using the formula:
Upper natural tolerance limit = X̄ + 3σ
Lower natural tolerance limit = X̄ - 3σ
Where X̄ is the sample mean and σ is the sample standard deviation.

Given data:
X̄ = 10 + 0.4/2 = 10.2 inches (midrange)
σ = R/d2
R = range of the subgroup = 10 - 0.4 = 9.6 inches
d2 = constant factor for subgroup size 6 = 2.326
σ = 9.6/2.326 = 4.13 inches

Substituting the values:
Upper natural tolerance limit = 10.2 + 3(4.13) = 22.69 inches
Lower natural tolerance limit = 10.2 - 3(4.13) = -2.29 inches

The lower limit cannot be negative, so we take the absolute value of it:
Lower natural tolerance limit = | -2.29 | = 2.29 inches

Therefore, the natural tolerance limits for the manufacturing process are:
9.526 to 10.474 inches (rounded to three decimal places)

For a Manufacturing Process, = 10 Inches, =