1. Set up 3-sigma control limits with the given data. Is the process in control?
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1. Set up 3-sigma control limits with the given data. Is the process in control? Why?
ore: ts an adjusthent heeded? Total 85 Case: Scharadin Hotels Scharadin Hotels is a national hotel chain started in hotel bill is left under the guest's door in the early morning 1957 by Milo Scharadin. What started as one upscale hours and, if all is in order, does not require any additional hotel in New York City turned into a highly reputable action on the guest's part. Express checkout is a service national hotel chain. Today, Scharadin Hotels serveswelcomed by busy travelers who are free to depart the over 100 locations and is recognized for its customer hotel at their convenience. However, the increased num- service and quality. Scharadin Hotels are typically ber of billing errors began creating unnecessary delays located in large metropolitan areas close to convention and frustration for the guests who unexpectedly needed centers and centers of commerce. They cater to both to settle their bill with the front desk. The hotel staff often business and nonbusiness customers and offer a wide had to calm frustrated guests who were rushing to the air- array of services. Maintaining high customer service port and were aggravated that they were getting charged has been considered a priority for the hotel chain for items they had not purchased. Identifying the Source of the Problem A Problem with Quality The Scharadin Hotel in San Antonio, Texas, had recently Larraine Scharadin, Milo Scharadin's niece, had recently been experiencing a large number of guest complaints due been appointed to run the San Antonio hotel. A recent to billing errors. The complaints seemed to center around business school graduate, Larraine had grown up in guests disputing charges on their final hotel bill. Guest the hotel business. She was poised and confident and complaints ranged from extra charges, such as meals or understood services that were not purchased, to confusion for the for not hotel. When she became aware of the billing problem, charged at all. Most hotel guests use express check- she immediately called a staff meeting to uncover the the importance of high quality source of the problem. out on their day of departure. With express checkout, theExplanation / Answer
It is given that sample size = n = 50
Total number of incorrect bills in 30 days
= 2 + 2 + 1 + 2 + 2 + 3 +2 +2 + 1 +2 + 1 + 2 + 3 + 3 +2 + 3 + 2 + 2 + 1 +3 + 3 +3 +3+4+5+5 + 6 +5+5+5
= 85
Average number of defects per sample = 85/ Number of sample = 85/30
Therefore, proportion of defects per sample = Pbar = 85/ ( 50 x 30) = 0.057 ( rounded to 3 decimal places )
We need to draw p chart which will be the appropriate chart in this case which will determine upper and lower control limits on proportion of incorrect bills
Accordingly , Control Limits for P Chart:
Upper Control limit ( UCL ) = Pbar + 3 x Square root ( pbar x ( 1- pbar/n)= 0.057 + 3 x Square root ( 0.057 x 0.943 / 50)
= 0.057 + 3 x 0.0328 = 0.057 + 0.0984 = 0.1554
Lower Control Limit = Maximum ( 0, Pbar – 3 x Square root ( pbar x ( 1 – Pbar)/n ) )
= Maximum ( 0, 0.057 – 0.0984 )
= Maximum ( 0, - 0.041)
= 0
Therefore the control limit range for proportion of incorrect bills is 0 to 0.1554
Or, control limit range for number of incorrect bills per sample ( of sample size = 50 ) will be :
O to 0.1554 x 50
= 0 to 7.77 bills
As it can be seen from the data provided, all the number of data pertaining to incorrect number of bills per sample are within range 0 – 7.77 bills
Therefore , the process is in control
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