Question

A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.15 mm and the mean is 23 mm.

Round your answer to 4 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.

The process capability index for the process is _________

The probability of producing a tire being too wide is ________

The probability of producing a defective tire is ______

Answer 1

The process capability index for the process is:
Cp = (USL - LSL) / (6σ)

= (23.2 - 22.8) / 6x0.15
= 0.4444

The probability of producing a tire being too wide is calculated by using excel formula in the following manner:

Probability{too wide}
= NORM.DIST(USL, mean, σ, 1)
= NORM.DIST(23.3, 23, 0.15., 1)
= 0.091211

The probability of producing a defective tire is calculated by using the excel formula in the following manner:

a. Probability{too narrow}
= NORM.DIST(LSL, mean, σ, 1)
= NORM.DIST(22.8, 23, 0.15, 1)
= 0.091211

b. Probability{defective}
= 0.091211 + 0.091211
= 0.182422