IE 571 Homework #4 (due 11/8/2012 before 5:00 pm)

1. The following data represent individual observations on molecular weight taken hourly from

a chemical process.

Observation

Number

x Observation

Number

x Observation

Number

x Observation

Number

x

1 1045 6 1008 11 1139 16 1125

2 1055 7 1050 12 1169 17 1163

3 1037 8 1087 13 1151 18 1188

4 1064 9 1125 14 1128 19 1146

5 1095 10 1146 15 1238 20 1167

The target value of molecular weight is 1050 and the process standard deviation is thought to

be about σ = 25.

a) Set up a tabular cusum for the mean of this process. Design the cusum to quickly detect a

shift of about 1.0 σ in the process mean.

b) Set up a standardized cusum for the mean of this process to quickly detect a shift of about

1.0 σ.

c) Set up EWMA control chart with λ = 0.1 and L = 2.7. Compare your results to those

obtained with the cusum.

2. A process is in control with 05.1,100 Sx , and n = 5. The process specifications are at 95

± 10. The quality characteristic has a normal distribution.

a) Estimate the potential capability.

b) Estimate the actual capability.

c) How much could the fallout in the process be reduced if the process were corrected to

operate at the nominal specification?

3. In a study to isolate both gage repeatability and gage reproducibility, two operators use the

same gage to measure 10 parts three times each. The data are shown below.

Operator 1 Measurements Operator 2 Measurements

Part Number 1 2 3 1 2 3

1 50 49 50 50 48 51

2 52 52 51 51 51 51

3 53 50 50 54 52 51

4 49 51 50 48 50 51

5 48 49 48 48 49 48

6 52 50 50 52 50 50

7 51 51 51 51 50 50

8 52 50 49 53 48 50

9 50 51 50 51 48 49

10 47 46 49 46 47 48

a) Estimate gage repeatability and reproducibility.

b) Estimate the standard deviation of measurement error.

c) If the specifications are at 50 ± 10, what can you say about gage capability?

4. Two parts are assembled as shown in the figure. The distributions of x1 and x2 are normal,

with µ1 = 20, σ1 = 0.3 and µ2 = 19.6, σ2 = 0.4. The specifications of the clearance between the

mating parts are 0.5 ± 0.4. What fraction of assemblies will fail to meet specifications if

assembly is at random?