Data Exercises on Control Charts



Data Exercises on Control Charts

1. A production process has been running for a long time, during which data has been gathered and analysed. The conclusion is that under stable conditions, the process has a mean of 64 and a standard deviation of 0.02. Consider the data of last month’s production. Your task is to report to the Quality Supervisor. What should you report? Give a clear motivation for your report. Use the data set ccex1.sf3.

2. Recently there have been an increasing number of complaints from customers about the diameter of a certain product. The target value of the diameter equals 631 mm with allowed maximal deviations of size 12.3 mm. The Quality Supervisor of the firm, who has a longstanding responsibility for quality issues, investigates this and concludes that everything is in order with the production process. The same conclusion is reached by a young employee who has just received some statistics training. Their analyses are based on the files supervisor.sgp and youngemp.sgp.

Comment on both replies. Give an analysis of your own and compare to the above analyses. Use the data set ccex2.sf3.

3. In an injection moulding process it is important to keep part weight consistent over time. Therefore control charts are applied to monitor part weight. The data collection consists of taking 5 consecutive parts per shift and obtaining the weight of each part.

a) Report through appropriate control charts on the moulding process. Do not forget to check the assumptions on which your control charts are based. Use the data set ccex3.sf3.

b) Subsequent investigations of the process revealed nothing unusual on the conditions during the data collection. Moreover, subsequent runs with the same unchanged process turned out parts that were consistently acceptable. How can this be explained?

c) Use the sample averages as individual observations and construct a control chart for individual observations . Interpret this new control chart. Compare your results with the previous control charts.

4. In a plant one takes each 2 hours a sample from a production process. Each sample consists of 3 measurement of pressure in psi (pounds per square inch). The results are reported in the table below.

|8.00 a.m. |10.00 a.m. |12.00 a.m. |2.00 p.m. |

|37 |142 |66 |94 |

|33 |144 |61 |96 |

|35 |145 |60 |99 |

a) Estimate the standard deviation of the process by using ranges. What do you conclude about the process based on these numbers?

b) Estimate the standard deviation of the process by using the sample standard deviation.

Explain the huge difference between a) and b). Which method is more appropriate here? What is your final assessment on this process?

5. A plant would like to monitor diameters of aluminium pipes. The data set ccex4.sf3 contains means and ranges of 20 rational subgroups of size 5 of a pilot run. Use Shewhart control charts to check whether the process is in statistical control. Remove subgroups that appear to be out of control.

6. The data set ccex5.sf3 contains measurements of the yield of a chemical process. It is known from earlier measurements that when the process is in control, the values for mean and standard deviation are 45 and 1, respectively. We would like to monitor the process in order to detect changes of size 1.

a) Set up Shewhart control charts and check whether there is an out-of-control situation

b) Set up CUSUM control charts with the same in-control ARL as the Shewhart control charts of a). Does the process appear to be in-control?

c) Explain the different behaviour of the control charts in a) and b).

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