Exam 21: Statistical Process Control

The mean of the sample means and the pooled standard deviation of 40 samples of size 5 taken from a production process under control are found to be 400 and 15,respectively.The lower control limit for the chart is:

____________________ variation is caused by specific events or factors that are frequently temporary.

Control charts that are used to monitor a process whose results are categorized as either defective or non-defective are called p charts.

The chart is employed to determine whether the process distribution means have changed.To determine whether the process distribution standard deviation has changed,we use the S (which stands for standard deviation)chart.

What is the average run length (ARL)until an control chart signals a false alarm if the control limits are set at ±2.5 standard errors from the centerline?

40 Samples Manufacturing ​ The mean of the sample means and the pooled standard deviation of 40 samples of size 5 taken from a production process under control are ,and S = 11.5,respectively. ​ ​ -{40 Samples Manufacturing Narrative} Compute the zone boundaries for the chart.

30 Samples Production Thirty samples of size 4 were drawn from a production process.The data are shown below. ​ ​ -{30 Samples Production Narrative} Looking at the and S charts developed in a previous question,can you infer that the process is under control? If so,explain why.If not,explain what the problems are.

Diaper Delivery Wrap-M-Up,a Ft.Lauderdale diaper Service,has 10 delivery men who each deliver diapers to 50 customers every day.Wrap-M-Up decides to record the proportion of diapers delivered on time for a 10-day period and construct a p chart to see whether the proportion is too erratic.The data are shown below: ​ ​ -{Diaper Delivery Narrative} Find the numerical value of the center line for the p chart.

If the average run length of a process is 385,then the control chart will wrongly conclude that the process is out of control once every 385 samples on average.

Assume that the control limits of an chart are defined as 3 standard errors above and below the centerline.Calculate the probability that a sample mean falls outside the control limits when the process is in fact under control.

In statistical process control,a Type II error is usually expensive since it means stopping production to repair the cause of the variation.

If a machine part is slowly losing its ability to work,causing the standard deviation of the process to increase,this is an example of assignable variation called a trend.

The mean of the sample means and the pooled standard deviation of 40 samples of size 9 taken from a production process under control are ,and S = 12,respectively.The lower control limit and the upper control limit of the 3-sigma chart are 408 and 432,respectively.

30 Samples Production Thirty samples of size 4 were drawn from a production process.The data are shown below. ​ ​ -{30 Samples Production Narrative} Construct an S chart.

The ____________________ is the expected number of samples that must be taken on average,before the control chart indicates that the process has gone out of control.

30 Samples Production Thirty samples of size 4 were drawn from a production process.The data are shown below. ​ ​ -{30 Samples Production Narrative} Construct an chart.

The centerline of an control chart is the mean of the samples being collected.

Assume that the control limits of an chart are defined as 2.5 standard errors above and below the centerline.Calculate the probability that a sample mean falls outside the control limits when the process is in fact under control.

40 Samples Production ​ The mean of the sample means and the pooled standard deviation of 40 samples of size 8 taken from a production process under control are ,and S = 14.5,respectively. ​ ​ -{40 Samples Production Narrative} Calculate the centerline and control limits for the chart.

30 Samples Production Thirty samples of size 4 were drawn from a production process.The data are shown below. ​ ​ -{30 Samples Production Narrative} Calculate the mean and standard deviation of each sample.