Derive an expression for true strain as a function of D and Do for a tensile test specimen of round cross section, where D = the instantaneous diamete

A laser triangulation system is used to determine the height of a steel block. The system has a photosensitive detector that is located 750.000 mm above the working surface and the laser is mounted at a 30.00° angle from the vertical. With no part on the worktable, the position of the laser reflection on the photo sensor is recorded. After a part is placed on the worktable, the laser reflection shifts 70.000 mm toward the laser. Determine the height of the object.

A laser triangulation system has the laser mounted at a 35° angle from the vertical. The distance between the worktable and the photodetector is 24.0000 in. Determine (a) the distance between the laser and the photodetector when no part is present and (b) the height of a part when the distance between the laser and photo-detector is 12.0250 in.

The additional operation in the preceding problem will add $2.00 to the current cost of the part, which is $13.50. If the rate of returns from the customer at the tolerance of ±0.025 in is 2.1%, and it is expected to drop to zero returns using the new tolerance, should the company add the finish grinding operation to the manufacturing sequence for the part? Answer this question using the basic cost and return rate data without consideration of the Taguchi loss function.

A company produces a certain part whose most important dimension is 37.50 ±0.025 in. If the tolerance is exceeded, the customer will return the part to the manufacturer at a cost of $200 in rework and replacement expenses. (a) Determine the constant k in the Taguchi loss function, Eq. (42.13). (b) The company can add a finish grinding operation that will allow the tolerance to be reduced to ±0.010 in. Using the loss function from part (a) what is the value of the loss associated with this new tolerance?

The inspection department in an automobile final assembly plant inspects cars coming off the production line against 55 quality features considered important to customer satisfaction. The department counts the number of defects found per 100 cars, which is the same type of metric used by a national consumer advocate agency. During a one-month period, a total of 16,582 cars rolled off the assembly line. These cars included a total of 6045 defects of the 55 features, which translates to 36.5 defects per 100 cars. In addition, a total of 1955 cars had one or more of the defects during this month. Determine DPMO, DPM, and DUPM in a Six Sigma program for these data and convert each to its corresponding sigma level.

In the previous problem, if the foundry desired to improve its quality performance to the 5.0 sigma level in all three measures of DPM, how many defects and defective units would they produce in an annual production quantity of 15,000 castings? Assume the same eight features are used to assess quality.

A foundry that casts turbine blades inspects for eight features that are considered critical-toquality. During the previous month, 1,236 castings were produced. During inspection, 47 defects among the eight features were found, and 29 castings had one or more defects. Determine DPMO, DPM, and DUPM in a Six Sigma program for these data and convert each to its corresponding sigma level.

Twelve cars were inspected after final assembly. The number of defects found ranged between 87 and 139 defect per car with an average of 116. Determine the center and upper and lower control limits for the c chart that might be used in this situation.

The upper and lower control limits for a p chart are: LCL = 0 and UCL = 0.20. Determine the minimum possible sample size n that is compatible with this control chart.

The upper and lower control limits for a p chart are: LCL = 0.19 and UCL = 0.24. Determine the sample size n that is used with this control chart.

The yield of good chips during a certain step in silicon processing of integrated circuits averages 91%. The number of chips per wafer is 200. Determine the center, LCL, and UCL for the p chart that might be used for this process.

Ten samples of equal size are taken to prepare a p chart. The total number of parts in these ten samples was 900 and the total number of defects counted was 117. Determine the center, LCL and UCL for the p chart.