Exam 14: Statistical Process Control

Examine the given run chart or control chart and determine whether the process is within statistical control.

Which type of chart does not have control limits?

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.

A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.

Sketch a control chart that indicates that a process is not statistically stable due to the run of 8 rule.

Which of the following is not one of the criteria for determining if a control chart indicates that a process is not statistically stable?

Construct an R chart and determine whether the process variation is within statistical control. A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour.

Describe an R chart and give an example. What does it attempt to monitor?

A control chart for $\bar { x }$ is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour.

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below. What would be the value of the centerline that would be used in creating an R chart?

A control chart for attributes is to be constructed. Which process would have wider control limits, a process which has been having a 5% rate of nonconforming items, or a process which has been having a 10% of nonconforming items? Assume that both processes have the same sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a shift from 10% to 15%? Explain your reasoning.

Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.

Construct an $\bar { x }$ chart and determine whether the process variation is within statistical control. A machine that is supposed to produce ball bearings with a diameter of 7 millimeters yields the following data from a test of 5 ball bearings every 20 minutes.

A control chart for $\bar { x }$ is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.

An x chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at x and control limits at x + A3 s and x - A3 s where A3 is found in the Control Chart Constants table and s is the mean of the sample standard deviations. Construct an x chart based on standard deviations for the data below. A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality control. The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated. The results for 12 consecutive days are shown in the table below. Day Range 1 21.1 3.4 1.2 2 23.4 4.7 1.7 3 20.9 3.1 0.9 4 25.6 6.2 2.3 5 21.3 4.7 1.3 6 20.5 3.7 1.7 7 25.8 5.8 2.1 8 23.7 6.2 2.9 9 29.8 2.1 0.8 10 22.7 4.4 1.6 11 20.0 2.7 0.7 12 24.6 7.8 3.0

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.