Question

Solve using Minitab.

The dataset represents sample data points from measurements of steel-concrete beam deflections from the center point. (a) Do the data appear to be normally distributed? (b) Plot individuals and moving range control charts of the time to deflection data with a moving range length of 2. Interpret the charts. (c) Using Minitab's calculator, create two transformed data columns, one for the square root of deflection and one for the natural log of deflection. Construct a normal probability plot for each transformed data set. Do the SQR1(deflection) or the Ln(deflection) data appear to be normally distributed? (d) Plot individuals and moving range control charts of the SqRt(deflection) and Ln(deflection) data transformed data sets with a moving range length of 2. Comment on any observed differences in the IM-R charts 24.04 12.97 20.93 16.59 9.57 18.92 26.64 96.11 17.24 30.54 44.90 38.57 63.10 86.19 31.48 22.64 23.42 8.37 70.73 16.70 28.56 53.42 40.86 65.12 36.34 16.97 11.19 29.98 8.58 37.22 46.85 45.62 52.97 37.76 24.17 38.58 5.79 11.23 54.19 38.73 43.83 44.08 9.47 26.00 59.93 98.34 39.30 62.26 35.59 9.53

Answer 1

a. Data is not normal as p value is < 0.05, thus we reject null hypothesis and data fails normality test.

Probability Plot of Deflections Normal 99 Mean 35.84 StDev 22.45 N 50 95 AD 0.912 90 P-Value 0.019 80 70 60 50 40 30 20 10 1 0 25 50 75 100 Deflections Percent 2un

b.

TEST 1. One point more than 3.00 standard deviations from center line.

Test Failed at points: 50

TEST 2. 9 points in a row on same side of center line.

Test Failed at points: 25, 26, 27, 28, 29

Pt. 50 have some special cause.

pt. 25,26,27,28,29 failed test 2 means - also a special cause and deflections of beams for

I-MR Chart of Deflections 100 UCL=100.0 BAw 50 X -35.8 0 LCL-28.3 46 1 6 11 16 21 26 31 36 41 Observation 80 UCL-78.81 40 MR-24.12 20 0 LCL-0 46 6 11 16 21 26 31 36 41 Observation anleAlenpipu

c. Yes, both data for sqrt & log are normal as for both of them p value is > 0 .05

Probability Plot of Sqrt Normal Mean 5.698 StDey 1.857 N 50 95 AD 0.268 90 P-Value 0.671 80 70 60 50 40 30 20 10 5 2 4 5 6 7 8 10 Sqrt LO 99 Percent

Probability Plot of Log Normal 99 3.368 Mean StDey 0.6929 50 95 AD 0.561 90 P-Value 0.139 80 70 60 50 40 30 20 10 5 2,0 2,5 3.0 3,5 4,0 4,5 5.0 Log Percent

d.

TEST 2. 9 points in a row on same side of center line.

Test Failed at points: 24, 25, 26, 27, 28, 29

I-MR Chart of Sqrt UCL 11.29 10.0 7.5 X-5.70 5.0 2.5 LCL-0.10 0.0 46 1 6 11 21 26 31 36 41 Observation UCL-6.876 60 4.5 3.0 MR-2.104 1.5 0.0 LCL 0 46 1 11 16 21 26 31 36 41 Observation 16 NO anleAl enpipu

TEST 2. 9 points in a row on same side of center line.

Test Failed at points: 24, 25, 26

I-MR Chart of Log UCL-5474 |Artunatanpdia| X-3.368 3 2 LCL-1.263 16 46 1 6 11 26 31 36 Observation UCL-2.587 2.4 1.8 1.2 MR-0.792 0.6 0.0 LCL 0 46 6 11 16 21 26 31 36 41 Observation 41 21 anjeAjenpiNpu Moving Range