Answer :
To calculate the Taguchi Quality Cost for each metal rod, we need to determine the deviation from the target value and apply the Taguchi parameter T.
Given data:
- Target value (T) = 51.8 mm
- Upper specification limit (USL) = 52.9 mm
- Lower specification limit (LSL) = 50.7 mm
- Scrap cost = $38.00
a) The Taguchi parameter T is given in $/mm². To calculate T, we need to determine the total allowable deviation from the target value within the specification limits:
- Total allowable deviation = (USL - LSL) / 6
- T = Scrap cost / (Total allowable deviation)²
- Total allowable deviation = (52.9 - 50.7) / 6 = 0.36 mm
- T = 38.00 / (0.36)² = 348.77 $/mm²
b) The Taguchi Quality Cost of the first metal rod is the squared deviation from the target value multiplied by the Taguchi parameter T:
- Deviation of the first rod = 51.7 - 51.8 = -0.1 mm
- Quality Cost of the first rod = (-0.1)² * T = 0.01 * 348.77 = $3.49
c) The Taguchi Quality Cost of the second metal rod:
- Deviation of the second rod = 52.4 - 51.8 = 0.6 mm
- Quality Cost of the second rod = 0.6² * T = 0.36 * 348.77 = $125.56
d) The Taguchi Quality Cost of the third metal rod:
- Deviation of the third rod = 53.3 - 51.8 = 1.5 mm
- Quality Cost of the third rod = 1.5² * T = 2.25 * 348.77 = $781.98
To calculate the total Taguchi Quality Cost of the sample of three units, we sum up the individual costs:
- Total Taguchi Quality Cost = Quality Cost of the first rod + Quality Cost of the second rod + Quality Cost of the third rod
- Total Taguchi Quality Cost = 3.49 + 125.56 + 781.98 = $910.03
Therefore, the total Taguchi Quality Cost of the sample of three units is $910.03.
About Taguchi
The Taguchi method is a quality improvement effort known as the off-line quality control method. This method aims to produce products that are more robust (robust) so that it is often referred to as the Robust Design method.
Learn More About Taguchi at https://brainly.com/question/16006199
#SPJ11
Final answer:
The Taguchi Loss Function calculates quality costs due to deviation from target specifications. The costs for the provided sample of metal rods can only be partially calculated without the Taguchi parameter value. The definite cost for the out-of-spec third rod is $38, but the other costs remain unknown.
Explanation:
The Taguchi Loss Function is a method of measuring the cost of quality-related losses due to deviation from target specifications in manufacturing processes. Given a target length of 51.8 mm for a metal rod, with specification limits of 50.7 mm and 52.9 mm respectively, we calculate the loss for each rod outside this range using the formula L = k(y - t) extsuperscript{2}, where L is the loss, k is the Taguchi parameter (cost per mm extsuperscript{2} of deviation), y is the actual measurement of the rod, and t is the target value. In case the rods are out of spec, they must be scrapped at a cost of $38. In this scenario, the measurements are 51.7 mm, 52.4 mm, and 53.3 mm, and the Taguchi parameter must be calculated assuming the cost for scrapping is equivalent to the loss at the specification limits.
The Taguchi Quality Costs for the rods are calculated as follows:
- For the first rod (51.7 mm), the deviation from target is -0.1 mm, which would imply no loss since it's within the spec limits.
- For the second rod (52.4 mm), the deviation from target is 0.6 mm. Assuming a quadratic loss function, the cost is k(0.6) extsuperscript{2}.
- For the third rod (53.3 mm), the deviation from target is 1.5 mm, which is beyond the upper spec limit. The loss would then be $38, as it has to be scrapped.
However, without the Taguchi parameter k value provided, the actual costs for the first two rods cannot be specifically calculated. We can only definitively state the cost of the third rod out of spec, which is $38.00. The total Taguchi Quality Cost for these three rods would be the sum of the individual costs for each rod.
