# Question: The weight of connecting rods used in an automobile engine

The weight of connecting rods used in an automobile engine is to be closely controlled to minimize vibrations. The specification is that each rod must be 974 ± 1.2 grams. The half-width of the specified interval, namely, 1.2 grams, is known as the tolerance. The manufacturing process at a plant produces rods whose weights are normally distributed with a mean µ of 973.8 grams and a standard deviation σ of 0.32 grams.

a. What proportion of the rods produced by this process will be acceptable according to the specification?

b. The process capability index, denoted by Cp, is given by the formula Calculate Cp for this process.

Cp = Tolerance / 3 * σ

c. Would you say a larger value or a smaller value of Cp is preferable?

d. The mean of the process is 973.8 grams, which does not coincide with the target value of 974 grams. The difference between the two is the offset, defined as the difference and therefore always positive. Clearly, as the offset increases, the chances of a part going outside the specification limits increase. To take into account the effect of the offset, another index, denoted by Cpk, is defined as

Cpk = Cp = Offset / 3 * σ

Calculate Cpk for this process.

e. Suppose the process is adjusted so that the offset is zero, and σ remains at 0.32 gram. Now, what proportion of the parts made by the process will fall within specification limits?

f. A process has a Cp of 1.2 and a Cpk of 0.9. What proportion of the parts produced by the process will fall within specification limits?

a. What proportion of the rods produced by this process will be acceptable according to the specification?

b. The process capability index, denoted by Cp, is given by the formula Calculate Cp for this process.

Cp = Tolerance / 3 * σ

c. Would you say a larger value or a smaller value of Cp is preferable?

d. The mean of the process is 973.8 grams, which does not coincide with the target value of 974 grams. The difference between the two is the offset, defined as the difference and therefore always positive. Clearly, as the offset increases, the chances of a part going outside the specification limits increase. To take into account the effect of the offset, another index, denoted by Cpk, is defined as

Cpk = Cp = Offset / 3 * σ

Calculate Cpk for this process.

e. Suppose the process is adjusted so that the offset is zero, and σ remains at 0.32 gram. Now, what proportion of the parts made by the process will fall within specification limits?

f. A process has a Cp of 1.2 and a Cpk of 0.9. What proportion of the parts produced by the process will fall within specification limits?

## Answer to relevant Questions

A restaurant has three sources of revenue: eat-in orders, takeout orders, and the bar. The daily revenue from each source is normally distributed with mean and standard deviation shown in the table below. a. Will the total ...When sampling is from a population with standard deviation σ = 55, using a sample of size n = 150, what is the probability that will be at least 8 units away from the population mean µ? According to a recent article in Worth, the average price of a house on Marco Island, Florida, is $2.6 million. Assume that the standard deviation of the prices is $400,000. A random sample of 75 houses is taken and the ...The data points in a sample of size 9 are 34, 51, 40, 38, 47, 50, 52, 44, 37. a. If you can take the deviations of these data from any number you select, and you want to minimize the sum of the squared deviations (SSD), what ...The average value of $1.00 in euros in early 2007 was 0.76. If σ = 0.02 and n = 30, find P(0.72 < x̄ < 0.82).Post your question