Problem Set 3 - Control Charts#
(Check Canvas for due dates and office hours)
Datasets are here (same PW as the course notes)
For handwritten-questions, submit as usual (screenshot/picture/export) For excel-based questions, directly submit the excel sheet.
Give the name of distributions (most likely) and relevant sample statistics to monitor and control the following CTQs parameters.
CTQ: Width of soft drink cans.
CTQ: Pencil - broken or not.
CTQ: Concentration of an active ingredient (in grams per liter) in a chemical process.
CTQ: Number of customer complaints per day.
CTQ: Number of defective welds per meter of pipeline.
CTQ: Survival of a packaging in a drop test.
CTQ of the product/service/software you told on the First Day of Class (check the class notes on Canvas homepage) (come up with one if you were not there on the first day).
On a two-sided hypothesis testing on mean of a normal distribution with known \(\sigma^2\),
Given Type-I error rate \(\alpha = 0.1\), what will be the control limit \(L\)?
Given Type-I error rate \(\alpha = 0.01\), what will be the control limit \(L\)?
Given 3-sigma control limits, what will be the probability of false alarm in the control chart? Write the probability as number of expected alarms per 1000 subgroups.
Given 6-sigma control limits, what will be the probability of false alarm in the control chart? Write the probability as number of expected alarms per 1000 subgroups.
Draw the appropriate pair of charts (in excel sheets) on the subgroups to monitor the measured widths of soft drink cans (a normal CTQ, data attached) for both the cases. Consider \(L=3\).
The mean and variance of width of the softdrink cans are known to be 1.5 and 0.0064, respectively.
The mean and variance of width of the softdrink cans are unknown.
Draw the appropriate pair of charts (in excel sheets) on the subgroups to monitor nominal voltage measured from a high voltage power supply over consecutive days (a normal CTQ, data attached) for both cases. Consider \(L=3\).
The mean and standard deviation of the nominal voltage are known to be 350 and 10, respectively.
The mean and standard deviation of the nominal voltage are unknown.
Draw the appropriate chart (in excel sheet) to monitor and control the fraction of defective capacitors in a production facility (data attached) for both cases. \(1\) in the dataset denotes that the capacitor failed the quality test (defective) and \(0\) denotes the capacitor passed the quality test. How many subgroups are “out-of-control”?
The defective fraction is known to be \(5\%\) (consider \(L=3\)).
The defective fraction is not known.
Fungal spores appear in paper manufacturing affect the quality of paper and are a hazard to workers. Assume that these fungal spores appear as countable dark spots for every roll of paper manufactured. Draw the appropriate chart (in excel sheet) to monitor and control the fungal spores, through the data on the number of spots measured every minute (data attached, consider \(L=3\)) for both cases. There is at least one paper roll with 7 spots (from the dataset at Time 31), is that a cause for concern?
The mean number of spots per roll is 1.75.
The mean number of spots per roll is unknown.