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 20 applications received from specific market areas were collected and inspected with the following results: Applications with Errors 2 2 1 4 3 3 2 Determine the lower controllimit for a p-chart 1 2 3

Answer 1

Answer:

We will find the Upper Control Limit (UCL) and Lower Control Limit (LCL) for P-Chart as mentioned in the below steps:

Col 1 Col 3 Col2 D P n 20 Col No >> Sample No. 1 2 3 4 NIN 20 0.100 0.100 0.050 1 20 20 3 0.150 5 20 N Total 10 0.100 0.500 0.100 0.067 P- = Sp = Z= UCL = LCL = 1.96 0.231 -0.031

Where , n = Sample Size = 20 and D = No. of applications with errors,

Calculation Steps:

Step 1: P = Fraction Defectives = Col 2 / Col 1

Step 2: P- = Central Line = Average of P =  Σ P / Total Samples = 0.5 / 5 = 0.1

Step 3: Sp = Standard Deviation = SQRT {[P- X [1-(P-)]] / Sample Size } = SQRT {[0.1 X (1 - 0.1) ] / 20} = 0.067 (Rounded to 3 decimal places)

Step 4: Find the values of CL, UCL and LCL as mentioned below:

CL = P- = 0.100

UCL=

= P- + (Z X Sp)

(Note: As no specific information is mentioned in the question, we assume that the confidence level is 95%)

Where Z = Value of Z at 95% confidence level = 1.96

Hence, UCL = 0.1 + (1.96 X 0.067)

= 0.231 (Rounded to 3 decimal places)

LCL=

= P- - (Z X Sp)

Where Z = Value of Z at 95% confidence level = 1.96

Hence, UCL = 0.1 - (1.96 X 0.067)

= -0.031 (Rounded to 3 decimal places) = 0

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