Question

A recent Living at Southeast post suggested that the vending machines on campus are error-prone (i.e., don't give change, fail to vend product, etc.). You conduct a study during which each day of the week you test 20 vending machines, and you tabulate the number of problems or errors encountered Friday Saturday Sunday Monday TuesdayWednesday Thursday Construct (sketch & label) control chart(s) having 85% control limits for the percentage of vending machine problems and indicate whether the chart(s) are in control.

Answer 1

The mean for the above set of data points is,

$\mu = 2.8571$

The standard deviation for the above set of data points is,

$\sigma = 1.8070$

The upper control limits (UCL) and lower control limits (LCL) for a 100(1-$\alpha$) % control are given by,

$UCL = \mu + z_{\alpha/2} \sigma ~~~~~~ LCL = \mu - z_{\alpha/2} \sigma$

For the given problem, $\alpha=0.15$ and $z_{\alpha/2} = z_{0.075} = 0.7580$

Therefore, the control limits are UCL=4.226 and LCL = 1.487.

The following plot depicts the control chart for this:

6 4 0 4 6 Days of Week

The numbers 0 to 6 on the x-axis correspond to the days Sunday, Monday, and so on till Saturday. Clearly, the chart was not in control on Monday and Saturday since the errors fell below the LCL. Also, the chart was also not in control on Tuesday and Thursday since the errors were higher than UCL.