4. A hospital is using X and R charts to record the time it takes to process pat
ID: 331398 • Letter: 4
Question
4. A hospital is using X and R charts to record the time it takes to process patient account information. A sample of five applications is taken each day. The first four weeks' (20 days') data give the following values: (15 Points) Xbar - 16 Minutes and Rbar 7 Minutes If the upper and lower specifications are 21 minutes and 13 minutes, respectively, calculate and interpret the indices: Estimate of the Population Standard Deviation (Sigma), 6 Sigma, Cp.and Cpk. Interpret the results. 5. Explain what is meant by variation and what occurs when a process is in control or out of control. The text refers to this as chance or assignable cause. Give examples of an assignable cause and a chance cause. (10 points) 6. Using the data in Question 1 prepare a XmR Control Chart (20 points) a. What is the Mean and the Moving range for the data. b. Interpret the control chart 7. What do control limits represent? What do Specification limits represent? (15 points) a. Describe the three cases that compare specification limits to control limits. b. What is the impact of each on quality?Explanation / Answer
(4)
The sample size (n) is 5. For n=5, from the standard coefficient table for 3-sigma charts, we note the value for the coefficient d2 which is -
d2 = 2.326
An unbiased estimate of the population standard deviation (sigma) is (R_bar / d2) = 7/2.326 = 3.00
On the other hand, X_bar gives us an estimate for the process mean which is 16 munites
The center of the specification = (USL+LSL)/2 = (21+13)/2 = 17. Therefore the process is off-centered.
Cp = (USL - LSL) / 6*sigma = (21 - 13)/(6*3) = 0.44
Cpk = Min{(USL - Mean)/3*sigma, (Mean - LSL)/3*sigma} = Min{(21 - 16)/9, (16 - 13)/9} = 0.333
Since this is an off-cented process, we are more concerned about the Cpk value. Since this is less than 1.0, the process is incapable of producing results within the given specification.
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