Question

The Elon Company manufactures parts for an aircraft company using three computerized numerical controlled (CNC) turning centers. The company has to decide which machines are capable of producing a specific part with design specifications of 0.0970 inch ± 0.015 inch. The machines have the following parameters: Machine 1 (mean= 0.0995, s = 0.004); Machine 2 (mean = 0.1002, s = 0.009); Machine 3 (mean = 0.095, s = 0.005). Determine which machines (if any) are capable of producing the products within the design specifications.

Answer 1

Answer:

machine 1 with the mean  0.0995, s = 0.004  will only be capable of producing the products within the design specifications.

Step-by-step explanation:

Given that:

The company has to decide which machines are capable of producing a specific part with design specifications of 0.0970 inch ± 0.015 inch.

The upper limit of the specific part = 0.0970 inch +  0.015 inch = 0.112 inch

The lower limit of the specific part =  0.0970 inch -  0.015 inch = 0.082 inch

Th question continues by stating the following parameters for the machines.

Machine 1 (mean= 0.0995, s = 0.004);

Machine 2 (mean = 0.1002, s = 0.009);

Machine 3 (mean = 0.095, s = 0.005).

The main objective here is to determine  which machines (if any) are capable of producing the products within the design specifications.

Given that Cp is < 1

This process will be capable if Cpk is ≥ 1

To start with machine 1;

$Cpk = Min [ \dfrac{0.112-0.0995}{3*0.004} \ , \ \dfrac{0.995-0.082}{3*0.004} ]$

Cpk = Min[1.46, 1.04]

Cpk = 1.04

Thus this process is capable because Cpk ≥ 1  

Machine 2;

$Cpk = Min[\dfrac{(0.112-0.1002)}{(3*0.009)}, \dfrac{(0.1002-0.082)}{(3*0.009)}]$

Cpk =  Min[0.67, 0.44]

Cpk = 0.44

Thus this process is not  capable because Cpk < 1  

Machine 3

$Cpk = Min[\dfrac{0.112-0.095}{3*0.005}, \dfrac{0.095-0.082}{3*0.005}}]$

Cpk =  Min[0.87, 1.13]

Cpk = 0.87

Thus this process is not  capable because Cpk < 1  

In conclusion, machine 1 with the mean  0.0995, s = 0.004  will only be capable of producing the products within the design specifications.

Answer 2

Using the Empirical Rule, it is found that Machine 1 is capable of producing the products within the design specifications.

The Empirical Rule states that for a normal variable, 99.7% of the measures are within 3 standard deviations of the mean.

• In this problem, we want 99.7% of the machines in the interval $0.07 \pm 0.015$, that is, between 0.082 and 0.112 inches.

For Machine 1:

$0.0995 - 3(0.004) = 0.0875$

$0.0995 + 3(0.004) = 0.1115$

In the interval, so it is capable.

For Machine 2:

$0.1002 - 3(0.009) = 0.0732$

$0.1002 + 3(0.000) = 0.1272$

Values outside the interval, so it is not capable.

For Machine 3:

$0.095 - 3(0.005) = 0.08$

$0.095 + 3(0.005) = 0.11$

Values outside the interval, so it is not capable.

To learn more about the Empirical Rule, you can take a look at https://brainly.com/question/24537145