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

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          

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

htrhyjk

step-by-step explanation:

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