Question

Lake Mead Elevations What does the R chart tell us about Lake Mead?

Short answer

The R-chart shows that variation in the process is out of control.

Step-by-step solution

Given information

Refer to Exercise 3 for the description of R-chart.

The data is given for monthly elevations of a lake recorded for 75 years.

Define a R-chart

One of the control chartsthat monitors the variation in the process is R-chart. It is graphed for sample range measures over the given period of time.It includes three values along with the observations in sequential form:

• Centerline\(\left( {\bar R} \right)\): mean of all sample ranges.
• Lower control limit (LCL)
• Upper control limit (UCL)

Describe the given R-chart

By observing the chart, the following values are obtained:

The observations for sample ranges marked with blue.

The three lines show:

\(\begin{array}{c}\bar R = 21.27\;{\rm{ft}}\\UCL = 36.52\;{\rm{ft}}\\LCL = 6.02\;{\rm{ft}}\end{array}\)

There are many values that lie beyond the upper control limit in the initial times as compared to the recent one, which lies beyond the lower control limit.

Thus, the R-chart shows that the variation in the process is statistically out of control.