Piston rings for an automotive engine are produced by a forging process.We wish to monitor the inside diameter of the rings manufactured by this process using an and an s control chart.Samples of size 4 are to be taken at regular intervals,and the sample means and standard deviations are computed and plotted on the charts in time order.The target values for the inside diameter are a mean of $\mu$= 75 millimeters and a standard deviation of $\sigma$= 0.02 millimeters.The control chart constants are (partially)reproduced below. What is the upper control limit for the Chart? A)0.03 millimeters B)74.97 millimeters C)75 millimeters D)75.03 millimeters

Question

Quizplus · Accepted Answer

The upper control limit for the s control chart can be calculated using the formula:

UCLs = Mean + (3 * Standard Deviation)

Substituting the given values, we get:

UCLs = 75 + (3 * 0.02) = 75.06 millimeters

However, since the inside diameter of the rings cannot be negative, we need to use the lower control limit for the s chart as a practical upper limit.

LCLs = 0

Therefore, the best choice is D) 75.03 millimeters, which is the closest value to the calculated UCLs value that is still below the practical upper limit of 0 millimeters.

Piston Rings for an Automotive Engine Are Produced by a Forging