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 ± .005 inches.Assume that the process is in statistical control with = 1.0002 inches, = .003 inches,and subgroup size of 5.What is the sigma level capability for this process?

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 ± .005 inches.Assume that the process is in statistical control with  = 1.0002 inches,  = .003 inches,and subgroup size of 5.What is the sigma level capability for this process?

Quizplus · Accepted Answer

First, we need to calculate the process capability index Cpk using the following formula:
Cpk = min((USL - mean) / 3sigma, (mean - LSL) / 3sigma)
where USL = 1.005 (upper specification limit), LSL = 0.995 (lower specification limit), mean = 1.0002 (process mean), and sigma = 0.003 / d2 = 0.003 / 2.326 = 0.00129 (estimated process standard deviation based on subgroup size of 5 and d2 constant from the control chart factors).

Cpk = min((1.005 - 1.0002) / (3 x 0.00129), (1.0002 - 0.995) / (3 x 0.00129))
= min(2.909, 1.550)
= 1.550 (rounded to 3 decimal places)

Next, we can convert Cpk to sigma level using a standard table or equation. For example, we can use the following formula:
Sigma = (Cpk x process spread in specification limits) / 6
where process spread in specification limits = (USL - LSL) / 2 = 0.005 / 2 = 0.0025.

Sigma = (1.550 x 0.0025) / 6
= 0.00065 (rounded to 3 decimal places)

Using a sigma conversion table, we can find that 0.00065 corresponds to approximately 3.72 sigma level. Therefore, the process capability for this process is 3.72 sigma or choice B.

A Powder Metal Manufacturing Company Is Producing Sleeves for a Locking