Question

12) An accounts department started an improvement project to try to reduce the number of internal purchase forms that its users completed incorrectly. As an overall measure of their success, they want to use a Control Chart to measure the number of purchase forms that were not completed correctly. Draw a detailed Control Chart showing the Mean, UCL, LCL and Target Value. UCL = Mean + σ, LCL= Mean-o, Target Values 8, (10 Points) Day of Number of month purchase forms, defective forms defective, p Number of 0.583 14 16 12 12 24 0.457 0.444 27 23 19 0.522 0.263 0.636 0.387 0.24 0.636 0.294 0.423 14 12 31 25 10 14 17 26 30 21 12 13 14 15 0 0.533 16 381

Answer 1

SOLUTION

First, calculate mean of all values

Mean = 11.1538

Std dev. = 3.9337

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R-code for getting the graph (all steps mentioned)

## CREATE DATA SET FROM GIVEN QUESTION

newd3 = data.frame(sno = c(1,2,3,4,5,6,7,10,11,12,13,14,15),tot = c(24,35,27,23,19,22,31,25,22,17,26,30,21), def = c(14,16,12,12,5,14,12,6,14,5,11,16,8))

## CALCULATE MEAN AND STANDARD DEVIATION OF 'NUMBER OF DEFECTIVE FORMS '

def_mean = mean(newd3$def)
def_mean

sd = sqrt(var(newd3$def))
sd

## CREATE TARGET VALUE, UCL AND LCL - AS PER QUESTION

t_val = 8
ucl = def_mean + 1*(sd)
lcl = 0

## PLOT GRAPHS LINES AND POINTS

ggplot(newd3, aes(x = sno, y = def)) + geom_point() + geom_hline(yintercept = t_val, col = "green") + geom_hline(yintercept = ucl, col = "red") + geom_hline(yintercept = lcl, col = "red") + geom_hline(yintercept = def_mean, col = "blue", linetype = "dotdash")

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15 10- 5 12 4 sno

The red lines are the UCL and LCL. The green line is the target value (8) and the dot-dash blue line is the mean of number of defective forms.

This is the detailed Control chart for the variable "number of defective forms".