Question: A process has mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is

A process has mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ control limits on an X̅ chart.

a. If the process mean shifts to 9, what is the average number of samples that will be drawn before the shift is detected on an X̅ chart?

b. An upward shift to what value will be detected with an ARL of 8?

c. If the sample size remains at 4, to what value must the standard deviation be reduced to produce an ARL of 8 when the process mean shifts to 9?

d. If the standard deviation remains at 2, what sample size must be used to produce an ARL no greater than 8 when the process mean shifts to 9?

Step by Step Solution

★★★★★

3.42 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a X has a normal distribution with 9 and X 24 1 The 3 limits are 8 31 or 5 and 11 The probability th... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics Engineers Scientists Questions!

One graph in the ï¬gure at the top of the next column represents a normal distribution with mean µ = 8 and standard deviation Ï = 2. The other graph represents a normal...

In the book Foundations of Financial Management ( 7th ed.), Stanley B. Block and Geoffrey A. Hirt discuss risk measurement for investments. Block and Hirt present an investment with the possible...

A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes-vibrations, temperature, wear and tear, and the like-the lengths of the pins...

A process has mean 1 2 and standard deviation 3 . 0 . The process is monitored by taking samples of size 5 at regular intervals. Required information A process has mean 1 2 and standard deviation 3 ....

6. A process has mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the...

A process has mean 12 and standard deviation 3. The process is monitored by taking samples of size 5 at regular intervals. The process is declared to be out of control if a point plots outside the 3...

5. A process has mean 12 and standard deviation 3. The process is monitored by taking samples of size 5 at regular intervals. The process is declared to be out of control if a point plots outside the...

1 2 Sampling and Data Collection Plan The scenario is to research whether in Maranon company the \"on my way\" method of shipping when used to leads to low shipment costs. The two variables used will...

When a certain manufacturing process is in control, it produces items whose values are normally distributed with mean 10 and standard deviation 2. The following simulated data represent the values of...

Please help me with these questions C webassign.net water my lonestar lonestar's mail Facebook Apple Bing Google Yahoo MY NOTES ASK YOUR TEACHER 3. [-/5 Points] DETAILS MENDSTAT14 7.E.045. An...

Stock Y has a beta of 1.35 and an expected return of 14.2 percent. Stock Z has a beta of .75 and an expected return of 9.1 percent. If the risk-free rate is 4.3 percent and the market risk premium is...

What are the four methods used in by-product costing, and how do they differ? Which is the preferred method and why?

The risk that a financial institution may be forced to borrow emergency funds excessive cost to cover its immediate cash needs is known as: A . credit risk B . liquidity risk market risk interest -...

4. Shorten the duration of critical path tasks. This option must be explored carefully. The underlying issue here must be to first examine the assumptions that guided the original activity duration...

In a recent semester at a local university, 500 students enrolled in both Statistics I and Psychology I. Of these students, 82 got an A in statistics, 73 got an A in psychology, and 42 got an A in...

The General Social Survey asked 32,201 people how much confidence they had in educational institutions. The results were as follows. a. What is the probability that a sampled person has either some...

Charles has six songs on a playlist. Each song is by a different artist. The artists are Drake, Beyonce, Taylor Swift, The Weeknd, Calvin Harris, and Rihanna. He programs his player to play the songs...

Question 15 1.5 pts Today you observe the folowing quotes: Spot GBPUSD - $1.06 60 Day Forward GBPUSD - $1.26 In 60 day you expect to receive 171,078 British Pounds. In 60 days you expect the GBPUSD...

Assume our bank issued a $50 million, one-year-maturity CD, denominated in British pounds. Later that day, the bank invested $25 million in a US Treasury Bill and $25 million in a pound-denominated...

Which one of the following statements is false? A) Numerical measures can help investors decide if it is time to buy or sell a stock. B) Future earnings may be one of the most significant factors to...