A Quality Analyst Wants to Construct a Sample Mean Chart

question 135

Essay

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that when the process is operating as intended, packaging weight is normally distributed with a mean of twenty ounces, and a process standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below.
(a) If he sets an upper control limit of 21 and a lower control limit of 19 around the target value of twenty ounces, what is the probability of concluding that this process is out of control when it is actually in control?
(b) With the UCL and LCL of part a, what do you conclude about this process-is it in control?

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Definitions:

Output

The amount of something produced by a person, machine, or system.

Double-Entry Bookkeeping System

An accounting method that records each transaction as both a debit and a credit in different accounts, ensuring the accounting equation stays balanced.

Single-Entry System

A rudimentary accounting method where entries are made in a single record, typically focusing only on cash flow and personal accounts.

Computerized Ledger System

A digital system for recording the financial transactions of a business or organization, providing an organized way to store, manage, and report financial data.