Question

1. (5 points)A bottling plant wants to control the amount of soft drink it puts in each can. They decide to periodically sample batches of cans to measure the average amount of soft drink put in each can, and track that data over time to see if the filling process is behaving the way they would expect. Identify which type of quality tool would be appropriate to use, and briefly explain why you think that tool is the best choice. (If a process control chart is appropriate, specify which type.)

B.The intense care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.25 minutes. The target service performance in turnaround time is 25±5 minutes. Is the lab process capable?

C.

MANCHY are fast food chains providing similar items. BurgerMan offers food from a standard menu, while Jeffrey’s positions itself as providing more customized products. Consider two franchises, one of each chain.  You have just conducted an analysis of the two franchises, and your conclusion is that both places have similar capacities and average demand.  

At which location would you expect a longer line before being served? WHY

4. In Kristen’s Cookie Company, both you and your roommate become more productive as the order size increases, which is shown in the table below. So, as your capacity increases, your idle time should be

            Higher             Lower              The Same.                   

		Capacity (dozen/hour)
Source	Time (min)	1-dozen order	2-dozen order	3-dozen order
You	8	7.5	12	15
Oven	10	6	6	6
Roommate	4	15	17.14	18

Answer 1

1

Here we take sample batches periodically. Each sample batch consists of a number of cans . we measure the volume of drink in each can. The volume can be 50 ml , 55.5 ml etc . This data is continuous. Charts used are -> x- Chart, R –chart, Individuals & moving R( I-MR)

We want to check

• whether the averages of batches are closer together
• whether within each batch, there is to wide spread of values(wide range)

We use X-bar(mean ) and R chart (range )

1. x-bar chart is used for controlling the variations in the average quality
2. R bar chart is used for controlling the variation in the dispersion of the quality  

Contrast with Discrete Data/ Attribute data

• Attribute data consists of categories. Usually two discrete categories are there. e.g. Defects or no defects, Yes or No.
• No fractions- we don’t use 1.5 defect. It is either a defect or no defect
• Attribute data is qualitative data

  

B.

Capability

Process capability determines whether a process is capable of meeting product specifications. It is measured using Cp and Cpk

Cp shows where process can produce with a particular spread i.e. within a particular range (range=USL-LSL)

   If Cp =1, the process is just capable.

If Cp< 1, the process is incapable.

If Cp is >1, the process is capable.

A Cp value of 1 is 3 sigma quality. A Cp value of 2 is 6 sigma quality.

Specifications/requirements

LSL = mean-tolerance = 25-5=20

USL = mean+ tolerance= 25+5=30

Process

Mean= 26.2

Standard deviation = 1.25

Cp

= (USL-LSL) /( 6* process S.D)

= (30-20) / (6*1.25)

=1.33

   Cp is >1, the process is capable of producing within 3 sigma limits. The process has the potential to produce within a spread required. But this does not show whether the process is centred (around mean= 25).

The process may be centered around 20, which is way beyond what the customer wants. Cp does not show where the process mean is centered (where the mean is positioned)

CpK

The CpK shows whether the mean of the process is centred between the specification limits.          (Close to the specification mean           =25)                                         

The mean is centred when Cp and Cpk are equal.                                                             

If Cpk <1, the mean is off-center and defects will occur.                                                               

If Cpk >1, the mean may be off-center but it is still capable of meeting product specs.                                                      

Process capability index, or Cpk,

=min ( (USL-mean )/ ( 3*S.D) , (mean- LSL)/ ( 3*S.D) )

= min ((30-26.2 )/ ( 3*1.25) , (26.2-20)/ ( 3*1.25) )

=Min (1.01, 1.65)

= 1.01

If Cpk >1, the process is capable

1 Process Capability 0.350 0.300 0.250 0.200 0.150 0.100 0.050 0.000 Process distribution -Upper Spec Limit Lower Speo Limit Mesn Design target 25.00 Design tolerance5.00 4 Input: Process mean26.20 Process standard deviation1.25 Input the design target and tolerance, the process mean and standard deviation. 12 13 14 15 16 Output: 17 18 19 20 21 0.000 10.000 20.000 30.000 40.000 Upper spec limit 30.00 Lower spec limit 20.00 Process Capability Ratio Cp1.33 Cpk-1 1.01 upper specification li lower specification limit Process Capability Inder 23 24 25 26 lower specifi ication upper specification- pminimum3

C.

Expect a longer line in Jeffrey

For standardised production since we also know the demand, we can have several products prepared in advance

In Jeffrey, Offering customize products requires more service time. Several items have to prepared only after the customer makes a request