Though only seven averages and range values are available, the engineers studying the olive bottle filling process have decided to create X-bar and R charts for the samples measuring the air gap in the bottle. Upon viewing the charts, it became obvious that the 4^th point has an assignable cause. Investigation revealed that the corks for this batch had not been placed at the correct depth in the bottle, thus resulting in the large air gap exhibited by the 4^th point. Adjustments have been made to the machinery and this problem is not expected to reappear. Revise the control chart. Assume an assignable cause has been found for the 4^th point and remove this point from the chart. Calculate the new limits.

Question

Quizplus · Accepted Answer

The Answer is Sum of x-bars = 66.34 Sum of R's = 3.5 n = 5
Point 4, X-bar = 9.92, R = 0.6

\begin{array} { l } \mathrm{XDB} ext { new }=-\frac{66.34-0.92}{7-1}=\frac{56.42}{6}=9.4\\mathrm{R} ext { -barnew }=-\frac{3.5-0.6}{7-1}=\frac{2.9}{6}=0.5\ ext { Sigma }=-\frac{ ext { Rbarnew }}{ ext { d } 2}=-\frac{0}{2.326}=0.2\U C L x = 9.4 + 1.324 ( 0.2 ) = 9.7 \\operatorname { LCL } x = 9.4 - 1.324 ( 0.2 ) = 9.1 \ ext { UCLr } = 4.918 ( 0.2 ) = 0.98 \ ext { LCLr } = 0 \\end{array}

Though Only Seven Averages and Range Values Are Available, the Engineers