Over several weeks of normal, or in-control, operation, 20...

Over several weeks of normal, or in-control, operation, 20 samples of 150 packages each of synthetic-gut tennis strings were tested for breaking strength. A total of 141 packages of the 3000 tested failed to conform to the manufacturer's specifications. a. What is an estimate of the process proportion defective when the system is in control? b. Compute the upper and lower control limits for a $p$ chart. c. With the results of part (b), what conclusion should be made about the process if tests on a new sample of 150 packages find 12 defective? Do there appear to be assignable causes in this situation? d. Compute the upper and lower control limits for an $n p$ chart. e. Answer part (c) using the results of part (d). f. Which control chart would be preferred in this situation? Explain.

Over several weeks of normal, or in-control, operation, 20 samples of 150 packages each of synthetic-gut tennis strings were tested for breaking strength. A total of 141 packages of the 3000 tested failed to conform to the manufacturer's specifications.
a. What is an estimate of the process proportion defective when the system is in control?
b. Compute the upper and lower control limits for a $p$ chart.
c. With the results of part (b), what conclusion should be made about the process if tests on a new sample of 150 packages find 12 defective? Do there appear to be assignable causes in this situation?
d. Compute the upper and lower control limits for an $n p$ chart.
e. Answer part (c) using the results of part (d).
f. Which control chart would be preferred in this situation? Explain.

Key Concepts

Process Proportion Defective

This concept involves estimating the fraction of items in a process that do not meet quality standards, based on historical data from when the process is in control. It establishes a baseline measure of quality against which future samples are compared.

Statistical Process Control

A methodology used to monitor a process through various types of control charts to distinguish between common cause variation (inherent to the process) and special or assignable cause variation (indicative of process issues). It is an essential tool for maintaining process quality over time.

p Chart

A control chart used to monitor the proportion of defective items in a sample. It plots the sample proportion of defects and uses calculated control limits to determine if the process is in controlled condition or if there are indications of special causes of variation.

Control Limits

These are predetermined boundaries calculated using the statistical properties of a process, typically set at plus and minus three standard deviations from the process mean. They are used to decide whether a process is operating normally or if intervention is needed.

np Chart

A variant of the p chart that displays the number of defective items in a sample rather than the proportion. It is particularly useful when sample sizes are constant, offering a direct count-based interpretation of process defects.

Assignable Cause

A term referring to specific, identifiable factors that cause variation in a process beyond the normal, random variation. Detecting an assignable cause implies that the process is out of control and corrective actions are required.

Transcript

Please give Ace some feedback