3- (12 pts.) After a number of co er a number of complaints about its directory
ID: 378324 • Letter: 3
Question
3- (12 pts.) After a number of co er a number of complaints about its directory assistance, a telephone company observed 16 operator assistance personnel by observing 200 calls from each to deternine the frequency of wrong mumber given to a caller. Sample2 Errors Proportion 1 23 5678 10 1112 13 14 1516 89 29 Compute the control limits for a P-chart for this process. Use Z 3. Round all P-Chart control limits to three decimals a- b- Based on above control limits, which operator's performance is out of control?Explanation / Answer
Total number of errors ( wrong numbers ) in 16 observations = 155
Total number of observations = 200 calls/ operator x 16 operators = 3200 calls
Hence, proportion errors = pbar = 155/3200 = 0.0484
Sample size = n = 200
Thus control limits for p charts using Z = 3 as follows :
Upper Control Limit = UCL
= pbar + 3x Square root ( pbar x ( 1 – pbar)/n)
= 0.0484 + 3 x Square root ( 0.0484 x ( 1 – 0.0484) /200)
= 0.0484 + 3 x Square root ( 0.0484 x 0.9516/200)
= 0.0484 + 3 x 0.0151
= 0.0484 + 0.0453
= 0.0937
Lower Control Limit = LCL = Maximum ( 0 , pbar – 3 x Square root( pbar x (1- pbar)/n)
= Maximum ( 0 , 0.0484 – 0.0453)
= Maximum ( 0, 0.0031)
= 0.0031
Thus Control limits for proportion of errors are within range 0.0031 and 0.0937
CONTROL LIMITS : LCL = 0.0031 AND UCL = 0.0937
Converting above range of proportion of errors into number of errors by multiplying with 200 , we get following control limits for permissible range of number of errors for an operator.
Thus,
Minimum permissible number of errors = 0.0031 x 200 = 0.62
Maximum permissible number of errors = 0.0937 x 200 = 18.74
However , errors for sample 8 is 26 and error for sample 16 is 29 . Both of these are beyond maximum permissible error of 18.74 ,
PERFORMANCE OF OPERATOR 8 AND OPERATOR 16 are out of control
CONTROL LIMITS : LCL = 0.0031 AND UCL = 0.0937
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