Kate Drew has been handpainting wooden Christmas ornaments f

Kate Drew has been hand-painting wooden Christmas ornaments for several years. Recently, she has hired some friends to help her increase the volume of her business. In checking the quality of the work, she notices that s ome slight blemished occasionally are apparent. A sample of 20 pieces of work resulted in the following number of blemished on each piece: 0, 2, 1, 0, 0, 3, 2, 0, 4, 1, 2, 0, 0, 1, 2, 1, 0, 0, 0, 1. Develop upper and lower control limits for the number of blemishes on each piece.

Solution

Mean no.of defectives = (1+0+0+.....+1)/20 =20/20 = 1

LCL - Mean-3*sqrt(mean) =1-3*Sqrt(1) = 0 (since it is negative)

UCL = Mean+3*sqrt(mean) = 1+3*1 = 4

The Lower and upper control limits for the number of blemishes on each piece = (0,4)