Question

The Ace, Ltd. sporting goods factory is just launching a line of soccer balls to be used in FIFA events. The circumference of the soccer ball must be between 68 and 70 cm when the balls are inflated to 12.05 psi. The company determined that it should set the LSL as 68 cm and the USL as 70 cm. Their quality strategy was to become a six-sigma company, and they instituted training and new tools to achieve that goal, and so the intent was to control process capability such that C_p = 2.

1) What is the standard deviation of the circumference of the soccer balls in production?

2) On their first production batch, they determined that the mean circumference was 69.5. Assuming that the circumference is normally distributed, what is the dpmo?

3) The soccer-ball company has a sampling plan in which the circumference of 25 randomly-selection soccer balls is selected from each day’s production. The measurement system is crude (a tape measure) and the % GRR is 50 %. If the company employs 100% inspection (implies a measurement that is reliable) to cope with the poor GRR, what % of the balls will be rejected? (Note- assume there is no bias error.)

Answer 1

The details solution in given below.

Given that:

The circumference of the soccer ball must be between 68 and 70 cm when the balls are inflated to 12.05 psi.

USL= 70 and LSL = 68 cp = 2

1)

Ans: We know that , process capability index

Cp = (USL - LSL) / 6×σ

6×σ = (USL - LSL) / Cp = (70-68) / 2 = 1

sigma= σ = 1/6 = 0.16667

The standard deviation of the circumference of the soccer balls in production is 0.16667

2)

Ans:

Let On their first production batch, they determined that the mean circumference was 69.5.

The formula is the total number of defects divided by the total number of units inspected multiplied by the number of defect opportunities per unit.

DPO=12.05/69.5

Defects per million opportunities (DPMO) Six-Sigma is determined by evaluating the DPMO, Multiply the DPO by one million. DPMO= DPO X 106

                            = 0.171381 X 106