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mortgage company is interested in monitoring performance . fifteen samples of 5

ID: 385321 • Letter: M

Question

mortgage company is interested in monitoring performance . fifteen samples of 5 are completed mortgage transactions each were obtained and the transaction time ( days ) mean and process are as shown below ,

-construct control chart for mean and range

- if max. time for process is fixed as 16 days , and requore min. 5 days to complete , determine the process capability index, process capability ratio and plot the specification limit on control chart.

sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 mean 17 14 8 17 12 13 15 16 13 14 16 9 11 9 12 range 6 11 4 8 9 14 12 15 10 10 11 6 9 11 13

Explanation / Answer

Given are :

Sample size = n = 5

Xbar = Mean of mean values = Sum of all mean values / 15 = 13.07

Rbar = Mean of Range values = Sum of all range values / 15 = 9.93

As per the standard table of constants for Xbar and Range charts, following are the relevant values of constants :

A2 = 0.577

D4 = 2.114

D3 = 0

Thus Control chart for mean ( i.e. Xbar chart ) as follows :

Upper Control Limit = UCL = Xbar + A2.Rbar = 13.07 + 0.577x 9.93 = 13.07 + 5.73 = 18.8

Lower Control Limit = LCL = Xbar – A2.Rbar = 13.07 – 0.577x9.93 = 13.07 – 5.73 = 7.34

Control Chart for Range ( i.e. Range chart ) as follows :

Upper Control Limit = D4.Rbar = 2.114 x 9.93 = 20.99

Lower Control Limit= D3.Rbar = 0

Process Capability Ratio, Cp

=( Maximum time – Minimum time )/ 6 x Process Standard deviation

= ( Max time – Minimum time ) / 3 x A2.Rbar

= (16 – 5 ) / 3 x 5.73

= 11/17.19

= 0.64

Process capability index, Cpk

= Minimum ( ( Upper Control Limit – Xbar)/3x process standard deviation, ( Xbar – Lower control Limit )/3 x Process Standard deviation )

= Minimum ( (16 – 13.07) / A2x Rbar, , ( 13.07 – 5) /A2xRbar)

= Minimum ( 2.93/5.73 , 8.07/5.73)

= Minimum ( 0.511 , 1408)

= 0.511