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"Servicios de Ingeniería", a technology firm based in Mexico, specialized in providing topography, mapping, and engineering services to the Construction, Mining, and Oil & Gas Industry. They are also using drones and satellite imageries to map their client’s assets and to carry out elevation profiling and volume estimation based works.
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2 If there are an upper and lower specification, where the upper thickness limit is 2.4 and the lower thick-ness limit is 1.4, what fraction of the output is expected to be out of tolerance?
The upper limit is given in a. The lower limit is 1.4 so Z = (1.4 – 1.9625)/.209624 = -2.68337. NORMSDIST(-2.68337) = .003644 fraction defective, so .3644 percent of the washers are expected to have a thickness lower than 1.4. The total expected fraction defective would be .018441 + .003644 = .022085 or about 2.2085 percent of the washers would be expected to be out of tolerance.
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4 What would be the Cpk for the process if it were centered between the specification limits (assume the process standard deviation is the same)?
The center of the specification limits is 1.9, which is used for X-bar in the following:
5 What percentage of output would be expected to be out of tolerance if the process were centered?
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Sample
1
2
3
4
5
6
7
8
9
10
X-bar
R
1
1.9
2
1.9
1.8
2.2
1.7
2
1.9
1.7
1.8
1.89
0.5
2
1.8
2.2
2.1
2.2
1.9
1.8
2.1
1.6
1.8
1.6
1.91
0.6
3
2.1
2.4
2.2
2.1
2.1
2
1.8
1.7
1.9
1.9
2.02
0.7
4
2.1
2
2.4
1.7
2.2
2
1.6
2
2.1
2.2
2.03
0.8
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0.65
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Let’s assume that, as a first step to improving the process, a sample of 40 washers coming from the machine that produces the washers was taken and the thickness measured in millimeters. The following table has the measurements from the sample:
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Questions
1 If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thick-nesses are distributed normally, what fraction of the output is expected to be greater than this thickness?
The average thickness in the sample is 1.9625 and the standard deviation is .209624. The probability that the thickness is greater than 2.4 is Z = (2.4 – 1.9625)/.209624 = 2.087068 1 - NORMSDIST(2.087068) = .018441 fraction defective, so 1.8441 percent of the washers are expected to have a thickness greater than 2.4.
2 If there are an upper and lower specification, where the upper thickness limit is 2.4 and the lower thick-ness limit is 1.4, what fraction of the output is expected to be out of tolerance?
The upper limit is given in a. The lower limit is 1.4 so Z = (1.4 – 1.9625)/.209624 = -2.68337. NORMSDIST(-2.68337) = .003644 fraction defective, so .3644 percent of the washers are expected to have a thickness lower than 1.4. The total expected fraction defective would be .018441 + .003644 = .022085 or about 2.2085 percent of the washers would be expected to be out of tolerance.
3 What is the Cpk for the process?
4 What would be the Cpk for the process if it were centered between the specification limits (assume the process standard deviation is the same)?
The center of the specification limits is 1.9, which is used for X-bar in the following:
5 What percentage of output would be expected to be out of tolerance if the process were centered?
Z = (2.4 – 1.9)/.209624 = 2.385221
Fraction defective would be 2 x (1-NORMSDIST(2.385221)) = 2 x .008534 = .017069, about 1.7 percent.
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Observation
Sample
1
2
3
4
5
6
7
8
9
10
X-bar
R
1
1.9
2
1.9
1.8
2.2
1.7
2
1.9
1.7
1.8
1.89
0.5
2
1.8
2.2
2.1
2.2
1.9
1.8
2.1
1.6
1.8
1.6
1.91
0.6
3
2.1
2.4
2.2
2.1
2.1
2
1.8
1.7
1.9
1.9
2.02
0.7
4
2.1
2
2.4
1.7
2.2
2
1.6
2
2.1
2.2
2.03
0.8
Mean:
1.9625
0.65
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Progress report
- 1. VHC Gas Station Progress Report 19 December 2019
- 2. Survey Data 1 2 3 4 5 6 7 8 9 > 9 50 m Fig. 1. Camera locations and image overlap. Number of images: 82 Flying altitude: 68.1 m Ground resolution: 1.82 cm/pix Coverage area: 0.0459 km² Camera stations: 82 Tie points: 37,081 Projections: 153,220 Reprojection error: 0.922 pix Camera Model Resolution Focal Length Pixel Size Precalibrated FC6310 (8.8 mm) 4864 x 3648 8.8 mm 2.61 x 2.61 μm No Table 1. Cameras.
- 3. Camera Calibration 1 pix Fig. 2. Image residuals for FC6310 (8.8 mm). FC6310 (8.8 mm) 82 images Type Resolution Focal Length Pixel Size Frame 4864 x 3648 8.8 mm 2.61 x 2.61 μm Value Error P1 P2 F 3372.58 P1 -0.000393745 6.2e-006 1.00 -0.03 P2 -0.000823451 6.4e-006 1.00 Table 2. Calibration coefficients and correlation matrix.
- 4. Ground Control Points B1 B2 B3 B4 B5 -20 cm -16 cm -12 cm -8 cm -4 cm 0 cm 4 cm 8 cm 12 cm 16 cm 20 cm x 300 Control points Check points 50 m Fig. 3. GCP locations and error estimates. Z error is represented by ellipse color. X,Y errors are represented by ellipse shape. Estimated GCP locations are marked with a dot or crossing. Count X error (cm) Y error (cm) Z error (cm) XY error (cm) Total (cm) 5 2.14035 1.45301 12.6806 2.58695 12.9417 Table 3. Control points RMSE. X - Easting, Y - Northing, Z - Altitude.
- 5. Label X error (cm) Y error (cm) Z error (cm) Total (cm) Image (pix) B1 0.611024 -2.27288 -15.0781 15.2607 0.622 (7) B2 -2.68352 0.695733 18.8062 19.0094 1.013 (12) B3 2.91854 1.41832 -9.57428 10.1092 0.583 (11) B4 -2.21485 -0.933666 -5.08037 5.62027 0.558 (8) B5 1.38108 1.42225 10.2705 10.4601 0.260 (8) Total 2.14035 1.45301 12.6806 12.9417 0.688 Table 4. Control points. X - Easting, Y - Northing, Z - Altitude.
- 6. Digital Elevation Model -60 m 210 m 50 m Fig. 4. Reconstructed digital elevation model. Resolution: 7.26 cm/pix Point density: 190 points/m²
- 7. Processing Parameters General Cameras 82 Aligned cameras 82 Markers 6 Coordinate system Mexico ITRF2008 / UTM zone 12N (EPSG::6367) Rotation angles Yaw, Pitch, Roll Point Cloud Points 37,081 of 40,503 RMS reprojection error 0.151514 (0.922371 pix) Max reprojection error 0.456324 (31.8877 pix) Mean key point size 5.56055 pix Point colors 3 bands, uint8 Key points No Average tie point multiplicity 4.28472 Alignment parameters Accuracy Medium Generic preselection Yes Reference preselection Yes Key point limit 20,000 Tie point limit 2,000 Adaptive camera model fitting Yes Matching time 9 minutes 49 seconds Alignment time 27 seconds Dense Point Cloud Points 15,050,120 Point colors 3 bands, uint8 Depth maps generation parameters Quality Medium Filtering mode Aggressive Processing time 1 hours 8 minutes Dense cloud generation parameters Processing time 4 minutes 44 seconds Model Faces 981,865 Vertices 493,159 Vertex colors 3 bands, uint8 Depth maps generation parameters Quality Medium Filtering mode Aggressive Reconstruction parameters Surface type Height field Source data Dense cloud Interpolation Enabled Processing time 58 seconds DEM Size 5,087 x 5,337 Coordinate system Mexico ITRF2008 / UTM zone 12N (EPSG::6367) Reconstruction parameters Source data Dense cloud Interpolation Enabled Processing time 1 minutes 27 seconds
- 8. General Orthomosaic Size 17,747 x 19,275 Coordinate system Mexico ITRF2008 / UTM zone 12N (EPSG::6367) Colors 3 bands, uint8 Reconstruction parameters Blending mode Mosaic Surface DEM Enable hole filling Yes Processing time 7 minutes 58 seconds Software Version 1.5.3 build 8407 Platform Windows 64