Design specifications require that a key dimension on a product measure 105 ± 12 units. A process being considered for producing

Question

3 years ago

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Design specifications require that a key dimension on a product measure 105 ± 12 units. A process being considered for producing

this product has a standard deviation of three units. a. What can you say (quantitatively) regarding the process capability? Assume that the process is centered with respect to specifications

Mathematics

1 answer:

marta [7] · Answer 1 · 2022-05-15T09:45:56+03:00

Answer:

Cpk = Cpu = Cpl = 0.4785

Step-by-step explanation:

Solution:-

- The capability of a process is determined using the capability index ( Cpk ). The index helps in determining the output of the process lies within the specification limits.

- The key dimension on a product measure is:

105 ± 12 units

- Process is producing this product at a 6-sigma quality standards i.e ( process is producing this product has a standard deviation (σ) of three units.)

Where, Standard Error in measured value = 12 units.

- The process capability (Cpu) is defined based on the Upper Specification Limit of the process (USL):

Cpu = (USL - u) / 3σ

- The process capability (Cpl) is defined based on the Lower Specification Limit of the process (LSL):

Cpl = ( u - LSL) / 3σ

- Assume that the process is centered with respect to specifications, then the given absolute value of u = 105 units.

Where the specification limits are defined as:

LSL = u - SE = 105 - 12

LSL = 93 units

USL = u + SE = 105 + 12

USL = 117 units

- Now evaluate the Process capability on each of the two limits specification limits:

Cpu = (USL - u) / 3σ

Cpu = (117 - 105) / 3σ

Cpu = 4 / σ

Cpl = ( u - LSL) / 3σ

Cpl = ( 105 - 99 ) / 3σ

Cpl = 4 / σ

- The minimum of Cpu and Cpl is denoted as the Cpk value:

Cpk = min ( Cpu , Cpl )

Cpk = Cpu = Cpl = 4 / 8.36

Cpk = Cpu = Cpl = 4 / 8.36 = 0.4785