What is the probability of a false alarm

Reference no: EM131384601

The diameter of a part produced by an automatic machine is a characteristic of interest. Based on historical data, the process average diameter is 15 mm with a process standard deviation of 0.8 mm. If samples of size 4 are randomly selected from the process:

(a) Find the 1σ and 2σ control limits.

(b) Find the 3σ control limits for the average diameter.

(d) If the process mean shifts to 14.5 mm, what is the probability of not detecting this shift on the first sample plotted after the shift? What is the ARL?

(e) What is the probability of failing to detect the shift by the second sample plotted after the shift?

(f) Construct the OC curve for this control chart.

(g) Construct the ARL curve for this control chart.

Reference no: EM131384601

Questions Cloud

What are warning limits and what purpose do they serve : What are warning limits and what purpose do they serve?- What is the utility of the operating characteristic curve? How can the discriminatory power of the curve be improved?

Discuss the relationship between arl and type i and ii error : Discuss the relationship between ARL and type I and II errors.- How are rational samples selected? Explain the importance of this in the total quality systems approach.

What is the probability of an overall type i error : What is meant by an overall type I error rate? If Rules 1, 2, and 3 of this chapter are used simultaneously, assuming independence, what is the probability of an overall type I error if 3σ control limits are used?

Select a health care provided with which you are familiar : Select a health care provided with which you are familiar and write a four to six (4-6) page paper in which you:Determine the direct impact of marketing for the health care provider you selected.Outline a strategy for the health care provider you sel..

What is the probability of a false alarm : Find the 1σ and 2σ control limits.- Find the 3σ control limits for the average diameter.- What is the probability of a false alarm?

Find warning limits for control chart for the average length : Find the warning limits for a control chart for the average length.- Find the 3σ control limits. What is the probability of a type I error?

Probability of concluding that the process is out of control : Find the 1σ and 2σ control limits. For the 1σ limits, what is the probability of concluding that the process is out of control when it is really in control?

What is the overall probability of a type i error : Suppose that Rules 2 and 3 are used simultaneously to determine out-of-control conditions. What is the overall probability of a type I error assuming independence of the rules?

How many samples will be analyzed before detecting a change : On average, how many samples will be analyzed before detecting a change in the process mean? Assume that the process mean is now at 110 mm (having moved from 105 mm) and that the process standard deviation is 6 mm. Samples of size 4 are selected f..

User Account

All Pages