Question #190475

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




1
Expert's answer
2021-05-10T13:28:55-0400

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


Given, i=125Xiˉ=4010\sum_{i=1}^{25}\bar{X_i}=4010


    and i=125Ri=71\sum_{i=1}^{25}R_i=71


A2=0.729,d3=0,d4=2.8282A_2=0.729,d_3=0,d_4=2.8282


Number of sample=25


Xˉˉ=i=125Xiˉn=401025160.4\bar{\bar{X}}=\dfrac{\sum_{i=1}^{25}\bar{X_i}}{n}=\dfrac{4010}{25}160.4


and Rˉ=i=125Rin=7225=2.88\bar{R}=\dfrac{\sum_{i=1}^{25}R_i}{n}=\dfrac{72}{25}=2.88


Therefore Control limit for Xˉ\bar{X} are


UCLxˉ=xˉˉ+A2Rˉ=160.4+(0.729)(2.88)=162.49952UCL_{\bar{x}}=\bar{\bar{x}}+A_2\bar{R} =160.4+(0.729)(2.88)=162.49952


and LCLxˉ=xˉˉA2Rˉ=160.4(0.729)(2.88)=158.30048LCL_{\bar{x}}=\bar{\bar{x}}-A_2\bar{R} =160.4-(0.729)(2.88)=158.30048

      

and control limit for R-chart


UCLRˉ=d4Rˉ=2.282×22.88=6.5721LCLRˉ=d3Rˉ=0×2.88=0UCL_{\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


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