Respuesta :
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, Â Â Â Â 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  Â
- 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     Â
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