Chapter 5 Control Charts For Variables

Section 2. Control Charts For ¯x and R (ATTENDANCE 4) 85(i) Normal probability plotThe SAS normal probability plot is more or less linear and so indicates theweights of the ice cream treats (choose one) are / are not more or lessnormally distributed.(j) New samples in process control?Five new samples from the ice cream process are plotted on the previouslydetermined control charts above.sample x 1 x 2 x 3 x 41 17 19 22 242 19 14 16 213 16 20 21 174 19 18 15 245 17 18 21 22From SAS, it appears the ice cream process has gone out of control and,more specifically, has shifted (choose one) downwards / upwards althoughthe range of the process still appears to be in control.(k) Probability in control if there is a shift in mean?The probability the process remains in control if the mean shifts from 10.55to 12 ounces, is equal to the probability ¯x falls between the upper controllimit and the lower control limit,P (in control) = P (LCL ≤ ¯x ≤ UCL)= P (5.78 ≤ ¯x ≤ 15.32; µ = 12, ˆσ¯x = 1.59) =(choose one) 0.47 / 0.78 / 0.98Assuming normality, it is 2nd DISTR normalcdf(5.78, 15.32, 12, 1.59)(l) More probability in control if there is a shift in mean?The probability the process remains in control if the mean shifts to 4ounces, is equal to the probability ¯x falls between the upper control limitand the lower control limit,P (in control) = P (LCL ≤ ¯x ≤ UCL)= P (5.78 ≤ ¯x ≤ 15.32; µ = 4, ˆσ¯x = 1.59) =(choose one) 0.13 / 0.68 / 0.87Hint: 2nd DISTR normalcdf(5.78, 15.32, 4, 1.59)(m) Different ways of saying the same thingThe probability the process remains in control if the mean shifts to 4ounces, is another way of saying (choose none, one or more)i. the probability of not detecting a mean shift to 4 ounces.