Problem 1 CPK: The specifications for a product are 6 mm +/- 0.1 mm. The process

Question

Problem 1 CPK: The specifications for a product are 6 mm +/- 0.1 mm. The process is known to operate at a mean of 6.05 with a standard deviation of 0.01 mm. What is the CPK for this process?

Problem 2 Defects: The housekeeping supervisor of a hotel has been concerned about the number defects in rooms recently cleaned. In order to evaluate the true magnitude of the problem the supervisor has selected a random sample of 20 rooms each over a ten week period. The number of rooms with defects are as follows:

Determine the center line, the upper and lower control limits

Week Number of Defects 1 1 2 3 3 2 4 1 5 4 6 1 7 2 8 0 9 3 10 1

Explanation / Answer

1. USL= (6+0.1) = 6.1 mm

LSL = (6 – 0.1) = 5.9 mm

Mean(X) = 6.05

Standard deviation (= 0.01 mm

CPK = Min (CpU, CpL)

CpU = (USL- X)/3

CpU= (6.1 - 6.05)/ 3*0.01

CpU = 1.66

CpL = (X - LsL)/3

CpL = (6.05 – 5.9)/ 3*0.01

CpL = 5

CpK = min (1.66, 5)

2. Mean = number of defects / N

N= 10 ( given)

Mean (x)= (1+3+2+1+4+1+2+0+3+1) = 18/10

Mean=1.8

Standard deviation:- 1/N ( xi- mean)2

SD = 1/10 * ( (1-1.8)2 + (3-1.8)2 + (2-1.8)2+ (1-1.8)2+(4-1.8)2+ (1- 1.8)2 +(2-1.8)2+ (0-1.8)2+( 3-1.8)2+(1-1.8)2)

SD= 1.16

UCL= mean + Z*SD

Z= 3 (given)

UCL = 1.8 +3*1.16

UCL= 5.28

LCL= mean - Z*SD

LCL = 1.8- 3*1.16

LCL = - 1.68

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