10. (10 points) Your Company takes special information reports over the phone. Y
ID: 346496 • Letter: 1
Question
10. (10 points) Your Company takes special information reports over the phone. You are the manager responsible for five operators who take down the field data and they each take 600 calls per month. Given the data below on the number of incorrect reports each operator has taken this past month (you compare the actual hard data when it is received by mail) and using a “p" chart answer the questions below: Incorrect Reports Operator Operator A Operator B Operator C Operator D Operator E 17 19 32 21 What is the average failure rate for all instructors combined? a. b. What is operator B's failure rate? What is the standard deviation of sampling distribution for the above group of instructors? c. d. What is the 95.5% upper and lower control limits for this group? e. Is this process in our out of control and why?Explanation / Answer
Total number of incorrect reports = 22 + 17 + 19 + 32 + 21 = 111
Total number of calls taken by 5 operators together = 5 x 600 = 3000
= Total number of incorrect reports/ Total number of calls taken
= 111/300
= 0.037
AVERAGE FAILURE RATE OF ALL OPERATORS COMBINED = 0.037
= Number of incorrect reports for operator B / Number of calls taken by operator B
= 17 / 600
= 0.028
FAILURE RATE OF OPERATOR B = 0.028
Sample size= n = 600 calls
Average failure rate = pbar = 0.037
Therefore , Standard deviation of sampling distribution of above group of instructors
= Square root ( pbar x ( 1 – pbar)/n)
= Square root ( 0.037 x 0.963 /600)
= 0.0077
Upper control Limit ( UCL ) = Pbar + Z x Standard deviation = 0.037 + 1.695 x 0.0077 = 0.037 + 0.013 = 0.05
Lower Control Limit ( LCL ) = Pbar – Z x Standard deviation = 0.037 – 1.695 x 0.0077 = 0.037 – 0.013 = 0.024
Upper limit = UCL x Sample size = 0.05 x 600 = 30
Lower Limit = LCL x Sample size = 0.024 x 600 = 14.4
However , it is to be noted that Incorrect reports of operator D i.e. 32 is outside the range limit 14.4 – 30 as calculated above.
Therefore , the PROCESS IS OUT OF CONTROL
AVERAGE FAILURE RATE OF ALL OPERATORS COMBINED = 0.037
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