Specification limits- USL and LSL

A standard letter sized envelope is 4 inches wide and 9.5 inches long. Normally 8.5 inch by 11-inch pages are folded in thirds before they are inserted into such envelopes for mailing. Considered page folding is a process whose measurable output is the width of the folded page.

a) What specification limits does the envelope size place on the page folding process?

                                      

Ans:   Upper specification limit (USL) = 4"

           Lower specification limit (LSL) = 3.7"   ∴ 11/3 = 3.7  

  

b)      What is the penalty for exceeding the upper specification?

Ans:  Loss (l) = K(Y-T) ²

T      = 3.7 + 0.15                                 ∴ 4 – 3.7/2

        = 3.85"

L_USL = K (4-3.85)²

                   = K (0.15)²

LUSL = 0.0225K