Question

Listed in the following table are the number of bolts of cloth produced on a daily basis in a small textile mill and the corresponding number of imperfections found in these bolts. Use these data to estimate the averageu Bolts of Cloth roduced #of Imperfections DAY Bolts of Cloth roduced 20 20 20 21 0 DAY imperfections 37 23 30 28 6 7 8 31 37 24 36 27 23 2 3 23 21 10 Compute for the 1. u bar [a] 2. Upper control limit and [b] 3. Lower control limit. [c] 4. Is the data in control? [d] 5. If NOT, u bar new, [e] 6. Upper control limit new and [f] 7. Lower control limit new. [g]

The U Chart versus the C Chart The C chart is used when a single unit will be examined for nonconformities at each time point. The U chart is used when a number of units will be sampled at each time point, and a per unit average number of nonconformities will be obtained. U Chart Formulas Suppose we have k samples, each of size ni. Let Di represent the total number of nonconformities in the i th sample. Formulas for the Points on the Chart The i th per unit number of nonconformities ui is calculated using i i i n D u = , Estimating the U Chart Center Line In the U Charts procedure, the center line proportion may be input directly, or it may be estimated from a series of samples. If it is estimated from the samples the formula for the centerline proportion is ∑ ∑ = = = k i i k i i n D u 1 1 If all the samples are the same size, this formula reduces to k u kn D u k i i k i ∑ i ∑ = = = = 1 1 U Chart Limits The lower and upper control limits for the U chart are calculated using the formulas ni u LCL = u − m ni u UCL = u + m where m is a multiplier (usually set to 3) chosen to control the likelihood of false alarms (out-of-control signals

Answer 1