If each step resulted in 1% defects

After 20 steps, only 81.2% of the product would be good quality.

At 10,000 tires per hour, this would be 1,880 defective tires per hour.

Tolerance on the machines and the SPC program

Extruder, rubber thickness spec of 400 +/- 10 thousandth of an inch (thou).

If settings were accurate, the output produced by the extruder had a thickness that was normally distributed with a mean of 400 thou and a standard deviation of 4 thou

1.If the extruder setting is accurate, what proportion of the rubber extruded will be within specifications?

2.Douglas has asked operators to take a sample of 10 sheets of rubber each hour from the extruder and measure the thickness of each sheet. Based on the average thickness of this sample, operators will decide whether the extrusion process is in control or not. Given that Douglas plans Three Sigma control limits, what upper and lower control limits should she specify to the operators?

3.If a bearing is worn out, the extruder produces a mean thickness of 403 thou when the setting is 400 thou. Under this condition, what proportion of defective sheets will the extruder produce? Assuming the control limits in question 2, what is the probability that a sample taken from the extruder with the worn bearings will be out of control? On average, how many hours are likely to go by before the worn bearing is detected?