2 Larrys boat shop wants to monitor the number of blemishes

2) Larry\'s boat shop wants to monitor the number of blemishes in the paint of each boat. Construct a 3-sigma c-chart and determine if their paint process is in control using the following data. Show your work. Sample Number Number of Defects 1 3 2 4 3 2 4 1 5 3 6 2 7 1 8 4 9 2 10 3

Solution

The given information is represented in the tabular form as follows:

The c-chart is meant for controlling the number of defects. The central line is the average value of number of defects, say C and the 3-sigma control limits are: U.C.L. = C + 3 SQRT(C ) & L.C.L = C - 3 SQRT(C ) or 0

In the present case there are 10 samples with total number of defects as 25, therefore C=2.5 and 3-sigma limits are:

U.C.L. = 2.5 + 3*SQRT(2.5) = 2.5 + 3*1.58 =7.24

L.C.L. = 2.5 - 3*SQRT(2.5) = 2.5 - 3*1.58 = -2.24 or 0

As the number of defects (Maximum 4) for all samples are found to be less than the value of Upper Control Limit of 7.24, therefore the paint process may be considered in control.