Question

Use 4 decimal places A control chart is to be established on a process producing refrigerators. The inspection unit is one refrigerator, and a chart for nonconformities is to be used. As preliminary data, 16 nonconformities were counted in inspecting 30 refrigerators. (a) What are the three-sigma control limits?

Answer 1

To establish the three-sigma control limits for a control chart on a process producing refrigerators, calculate the mean and standard deviation of the nonconformities. The lower control limit is Mean - 3 * Standard deviation and the upper control limit is Mean + 3 * Standard deviation.

Step-by-step explanation:

To establish the three-sigma control limits, we need to calculate the mean and standard deviation of the nonconformities. The mean is calculated by dividing the sum of the nonconformities by the number of inspections: 16 / 30 = 0.5333. The standard deviation is calculated using the formula sqrt(p(1-p)/n), where p is the proportion of nonconformities and n is the number of inspections. In this case, p = 16 / 30 = 0.5333 and n = 30. Plugging in these values, we get sqrt(0.5333(1-0.5333)/30) = 0.0992. The three-sigma control limits are then calculated as: lower control limit = mean - 3 * standard deviation = 0.5333 - 3 * 0.0992 = 0.2355, and upper control limit = mean + 3 * standard deviation = 0.5333 + 3 * 0.0992 = 0.8311.