Final answer:
To calculate the total Taguchi Quality Cost, one would typically use the Taguchi Loss Function. However, we cannot complete the calculation without the cost coefficient (k) or the specific Taguchi Loss Function formula for this scenario. If these were available, the total cost would be the sum of the individual losses computed for each unit in the sample.
Step-by-step explanation:
The Taguchi Quality Cost is calculated using the Taguchi Loss Function, which quantifies the financial loss associated with a product's deviation from the target value, even within specified limits. The target length of a metal rod is 51.8 mm, with an upper specification limit (USL) of 52.9 mm and a lower specification limit (LSL) of 50.7 mm. The Taguchi Loss Function is usually expressed as L(x) = k(x - T)^2, where x is the actual measurement, T is the target value, and k is the cost coefficient.
To find the k value, we use the formula k = LSL/USL (USL - T)^2, which assumes the loss at the specification limits is equal to the scrap cost. With a USL of 52.9 mm, an LSL of 50.7 mm, a target, T, of 51.8 mm, and a scrap cost of $38.00, calculating k yields a value specific to the given limits and target. However, the k value or the exact formula for this specific case has not been provided in the question. Therefore, we cannot proceed with the exact calculation without knowing the value of k or having the full Taguchi Loss Function formula for this scenario.
Assuming we had the k value, we would apply the Taguchi Loss Function to each measured rod length to calculate individual losses, which would then be summed to provide the total Taguchi Quality Cost for the sample. For the measurements provided (52.1, 52.3, and 53.1 mm), only the last measurement falls outside the specification limits and would incur the full scrap cost.