Answer to Question #190475 in Statistics and Probability for sagun poudel

Question

A cricket ball manufacturing company wants to check the variation in the weight of the balls. For

this, 25 samples each of size 4, are selected and the weight of each ball is measured (in grams). The

sum of the sample average and the sum of Sample ranges were found to be ∑25 1 xi = 4010 Grams

and ∑25 ri = 72 grams, respectively. Computer the control limits for the X and R-charts. It is

given that A2 = 0.729, D3 = 0 and D4 = 2.282

Answer 1

To find the control limit for $\bar{X}$ and R charts.

Given, $\sum_{i=1}^{25}\bar{X_i}=4010$

    and $\sum_{i=1}^{25}R_i=71$

$A_2=0.729,d_3=0,d_4=2.8282$

Number of sample=25

$\bar{\bar{X}}=\dfrac{\sum_{i=1}^{25}\bar{X_i}}{n}=\dfrac{4010}{25}160.4$

and $\bar{R}=\dfrac{\sum_{i=1}^{25}R_i}{n}=\dfrac{72}{25}=2.88$

Therefore Control limit for $\bar{X}$ are

$UCL_{\bar{x}}=\bar{\bar{x}}+A_2\bar{R} =160.4+(0.729)(2.88)=162.49952$

and $LCL_{\bar{x}}=\bar{\bar{x}}-A_2\bar{R} =160.4-(0.729)(2.88)=158.30048$

      

and control limit for R-chart

$UCL_{\bar{R}}=d_4\bar{R}=2.282\times 22.88=6.5721 \\[9pt] LCL_{\bar{R}}=d_3\bar{R}=0\times 2.88=0$