INEN 395 -Quality Control -Spring 2017 Classwork 10 Chapter 8-Review- October 20

Question

INEN 395 -Quality Control -Spring 2017 Classwork 10 Chapter 8-Review- October 20, 2017 A c chart is used to monitor the number of surface imperfections on sheets of photographic fim ·The chart presently is set based on of 2.6. a) Find 3-sigma control limits for this process isson Table to determine the probability that a point will all outside these control limits while the process is actually operating at a ' of 2.6. c) If the process average shifts to 4.8, what is the probability of not detecting the shift on the first sample taken after the shift occurs? Page 4 of 4

Explanation / Answer

Here The lower and upper control limits for the C chart are calculated using the formulas

LCL = C 3C

UCL =C 3C

where C = 2.6

so,

LCL = 2.6 -3 * 2.6 = 2.6 - 4.837 = 0

UCL = 2.6 + 3 * 2.6 = 7.44

so Control Limits are (0, 7.44)

(b) Here the process will be outside the control limits of it has c > 7.44

so Pr(C > 7.44) = POISSON (C > 7.44) where = 2.6 conformities

Pr(C > 7.44) = POISSON (C > 7.44) = 0.00534

(c) Process avaree shifts to 4.8

We will not detect the shift if it is under the control limit of the earlier 3-sigma control limits.

so now new process mean = 4.8

Pr(C < 7.44) = POISSON (C < 7.44 ; 4.8) = 0.8867

so there are 88.67% probability that we will not observe any process mean shift.

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