Question

1. A quality controller measures tensile stress (kg per cm²) of a metal fastener in thirty samples of size 7. The following is a summary of the collected data.

i=1i=30xi = 12,780 and i=1i=30Ri=1530

where xi = average and Ri = range of sample i. The quality controller finds that R chart is in control and now wants to construct x-bar R chart.

1. Determine an unbiased estimate of the standard deviation of tensile stress of metal fasteners.

2. Determine the three-sigma upper control limit for the x-bar R chart.

Answer 1

we are given samples, m=30,

each sample size = 7

from sample size data for n=7 we see that

and

(i) unbiased estimate of the standard deviation of tensile stress of metal fasteners is given by the formula:-

hence unbiased estimate of the standard deviation of tensile stress of metal fasteners is 18.861.

(ii) three-sigma control limits for the -chart is given by the formula:-

hence

three-sigma upper control limit for the -chart is 482.583.