Two parts in an assembly are in constant contact and have frequent sliding movem

Question

Two parts in an assembly are in constant contact and have frequent sliding movements relative to each other. Because of this, it is necessary to have a certain surface roughness so that the pieces are able to move easily upon application of the proper lubricant. Therefore, in the machining operation that produces these parts, the surface roughness needs to be between 110 and 140 micro-inches, with a nominal of 125 micro-inches. If the loss for parts made with a roughness of 106 micro-inches is $3.29, find the value of k for the loss function. Assume quadratic loss function. What would be the loss for a part with a surface roughness of 150 micro-inches? If the process is in control, approximately normally distributed, and centered at the nominal with a Cpk value of 1.2, what is the average loss incurred by the assembly?

Explanation / Answer

a)   assume a loss function of the form

     L = C (d - x)^2

     3.29 $   = C * (125 - 106)^2

     C = 0.009   $/micro-inch^2

b)   L   = 0.009 * (125 - 150)^2

           = 5.6267 $

c)   Cp   = USL - LSL / 6 * sigma

      1.2 = 140 - 110    / 6 * sigma

      sigma = 4.16667

      Lspec   = 0.009 * ((140 - 110) / 2)^2   = 2.025 $

      Average loss = Lspec / 9*Cp^2   = 2.025 / 9 * 1.2^2   = 0.15625 $

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