Question

The Long Life Insurance Company receives applications to buy insurance from its salespeople, who are specially trained in selling insurance to new customers. After the applications are received, they are processed through a computer. The computer is programmed so that it prints messages whenever it runs through an item that is not consistent with company policies. The company is concerned with the accuracy of the training that its salespeople receive, and it contemplates recalling them for more training if the quality of their performance is below certain limits. Five samples of 50 applications received from specific market areas were collected and inspected with the following results: Sample Applications with Errors 3 2 2 . 3 4 2 5 Determine the lower control limit for a p-chart.

Answer 1

Sample size(n) = 50

Number of samples = 5

Total number of observation ($\sum$n ) = Sample size x number of samples = 50 x 5 = 250

Sum of number of errors($\sum$np)= 3+2+1+2+2 = 10

P-bar = np/ n = 10/250 = 0.04

Sp = √ {[P-bar(1-P-bar)] / n}

= √ {[0.04(1-0.04)] / 50}

= √[(0.04 x 0.96) /50]

= √(0.0384/50)

= √0.000768

= 0.028

Lower Control Limit = P-bar - 3(Sp)

= 0.04 - (3x0.028)

= 0.04 - 0.084

= -0.044

= 0 (when the LCL value is negative it is taken as 0)