Question

Problem 2 The thickness of a printed circuit board is an important quality characteristic. Data on board thickness (in inches) are given in Table 5E.1 (The table has been uploaded to Folio) for 25 subgroups of three boards each. (a) [Pencil version] Set up an R chart by computing the initial set of seven lines (USL, UWL, UOL, CL, LOL, LWL, and LCL). Is the process variability in statistical control? Use the 9 rules. Note: You are not asked to revise the R chart. (b) [Minitab version) Repeat part (a) using Minitab and show your Minitab output. (c) (Pencil version] Estimate the process standard deviation (6).

Answer 1

solution:

Given that

Given that X -0.062952, R -0.000936 and n-3 (a) 30 - control limits for - chart: CL,X = 20.82 UCL = X+AJĀ Where A, is = 0.062952 + (1.023) X(0.000936) a constant taken from tables for n=3 = 0.063909528 LCL - 8-AR Where A is =0.062952 -1.023) (0.000936) taken from tables for n=3 = 0.061994 (6) 30 - control limits for R-chart: CLR = R = 0.000936 CLR - DR Where D, is a - (2.574)*(0.000936) constant based upon n =0.002409264

LCL, DR =0x(0.000936) -0 (Since D, - O forn<7) Xbar-R Chart of Boardı, ..., Board3 1. 161222 The process standard deviation, a = - R Where d, is a constant dy taken from tables for n 0.000936 1.693 -0.0005529

_USL-LSL and the process capability, c,= 60 0.0645-0.0615 6x0.0005529 -0.904323

C).

What are the limits you would expected to contain all the process measurements ? ( Approximately 99.73%)

6-0 limit: Ã + 3a = 0.06295 +0.000486)3

= [0.061492, 0. 064408]

X without Samples 14,15; 22 = 0,06295)

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