hts dld determine whether it is in control. sons is a fictional Indian manufactu

Question

hts dld determine whether it is in control. sons is a fictional Indian manufacturer of high-quality cricket balls. The balls are erials To maintain its reputation as a high-quality producer, the company has strict quality control standards. the a 3 Madan Lal & 100% handmade and consist of high-quality leather and producer, the company has strict quality control standards. The weight of a cricket ball has a mpact on day and records its quality. Typically, a ball weighs between 156 grams and 163 grams. Every day the company weighs a sample of ds ther weights. The following table shows the weights of the balls sa pedang a 20-day pe d weights Weight (in grams) 155.3, 156.0, 160.1, 154.9, 158.7 155.0, 156.9, 162.1, 159.9, 157.7 61.3, 159.0, 158.6, 164.2, 160.5 165.3, 164.0, 160.9, 161.9,159.7 160.0, 158.0, 164.1, 158.9, 157.7 155.8, 157.5, 159.1, 157.9, 160.3 158.4, 153.0, 157.1, 158.2,156.5 60.0, 155.5, 162.7, 161.5, 156.2 157.8, 159.0, 163.3, 158.9, 156.7 165.7, 162.9, 156.1, 159.9, 163.7 Sample Sample 12 13 14 15 16 17 18 19 20 Weight (in grams) 154.9, 155.8, 160.7, 155.9, 158.1 156.3, 157.0,158.1, 159.9, 162.7 164.3, 162.8, 158.1, 156.4, 157.7 158.3, 157.4, 162.4, 163.1, 156.4 165.3, 159.4, 159.1, 162.5,163.5 161.3, 159.1, 161.1, 153.9, 154.9 56.7, 162.0, 154.1, 157.9, 166.7 159.3, 164.5, 162.8, 156.3, 158.0 165.3, 159.5, 162.8, 157.9, 163.7 158.0, 156.7,160.8, 157.9, 160.3 10 a Design a mean and a range chart for the cricket-ball production process using 3 control limits. b. For the month of May, the company recorded the following 10 sample means and sample ranges Sample means: 158.3, 164.0, 158.3, 159.0, 161.5, 157.8, 160.3, 155.9, 163.1, and 158.6 Sample ranges: 4.1, 6.3,5.4,5.9,6.1,6.4,6.6,6.7,6.9, and 7.0 Was the process in control during the month of May? :How would increasing the sample sie frofiv to 20 affect he control chart? Would it change your conclusion in part b

Explanation / Answer

a) For x bar chart

CL = x bar = 159.47

for n= 20, d3 = 9.960, d2 = 3.735 from table used in control chart

UCL = xbar + 3* R bar /( 3.735*4.5 )= 159.47 +(3* 6.6 /(3.735*4.5))= 160.65

LCL = xbar - 3* R bar /(3.735* 4.5) = 159.47 +(3* 6.6 /(3.735*4.5)) = 158.29

R-chart

CL= 6.6

UCL = Rbar + (3*d3 *Rbar /d2) = 6.6 + (3* 9.960*6.6/3.735) = 59.4

LCL =  Rbar - (3*d3 *Rbar /d2) = 6.6 - (3* 9.960*6.6/3.735) = -46.2 = 0

(being negative)

b)

For the month may for mean char process is out of control because sample points falls beyond the control limits.

For the month may for Range char process is in control because sample points falls within the control limits.

c) If we increase the sample size from 5 to 20 then mean chart comes to be in control for the sample of month may.

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