Question

15 17 (c) The time needed for checking in at a hotel is to be investigated. Historically, the process has had a standard deviation equal to 0.146. The means of 26 samples of n=14 are shown below. Sample Mean Sample Mean 1 3.86 14 3.81 2 3.90 3.83 3 3.83 16 3.86 4 3.81 3.82 5 3.84 18 3.86 6 3.83 19 3.84 7 3.87 20 3.87 8 3.88 21 3.84 9 3.84 3.92 10 3.80 23 3.89 11 3.88 24 3.86 3.86 25 3.88 13 3.88 26 3.90 Overall Mean = 3.856 Construct an appropriate control chart for this process with three- sigma limits. ii. Plot the information and look for points and patterns. What can you conclude? 22 12 i.

plz dont use hand write. thx!!

Answer 1

1)

Here, I have prepared X bar chart for the above data, I have used Minitab to construct such graph or chart, step- go to Stat> Control Charts> Variable charts for subgroups> X Bar Charts,

Here, we will select the available mean values as applicable for 26 samples, we will get the below graph:

based on below chart and using three sigma quality, UCL value is 4.294 and LCL value is 3.418

Xbar Chart of Mean 4.3 UCL=4.294 4.2 4.1 4.0 3.9 Sample Mean X=3.856 3.8 3.7 3.6 3.5 LCl=3.418 3.4 1 4 7 10 16 19 22 25 13 Sample

2)

Test Results for Xbar Chart of Mean

TEST 7. 15 points within 1 standard deviation of center line (above and below CL).
Test Failed at points: 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26

as, we have faced continuous up and down of the data

as, we have seen that there are assignable causes, so, we could conclude that process data are NOT in statistical control.