Packem Case Questions 1

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Packem Case Questions

1. If the Packem DS1000 hard drive production process at Packem Company is in control, what percentage of the drives produced would be considered in nonconformance by Four-D?

This chart shows the averages PDQ test score recorded for the eight drives tested during the shirt compared to the upper and lower control limits. As shown, all data points fall within the control limits, indicating that the hard drive production process has been in control for the past 150 shifts.

 

A drive is considered to be noncomforming if its performance test score is below 6.2. The probability of a score being noncomforming in this distribution is =(NORM.DIST(6.2,7,0.3,1) = 0.00383038, or P(noncomforming)= .0038. There is a .38% chance that an individual item will be noncomforming.

 

 

2. If the Packem DSIOOO hard drive production process at Packem Company is in control, how often would shipments be found unacceptable by Four-D?

 

10 out of 1000 drives are randomly selected to be inspected by Four-D at each shipment. A shipment is found to be unacceptable if 1 or more out of those 10 are noncomforming (scores below 6.2). In order to be considered acceptable, we want to see 0 defective drives. The probability of this is 1-binomdist =1-(BINOMDIST(0,10,J17,1))= .03765027.

This is the probability of at least one drive being found noncomforming, and therefore the shipment found to be unacceptable. (3.765% chance). Based on this probability, there should be an unacceptable shipment once every 26 days (3.765/100= 26.5). However, there have been 4 in the past 20 days. It is possible that this is just a coincidence, because sometimes there will be a 26 day period where there is more than 1 unacceptable shipment, and some 26 day periods wont have any unacceptable shipments, but it should average out to once every 26 days. This leads to question 3, what is the probability of four rejected shipments in twenty days?

 

3. What is the probability of four rejected shipments in the past twenty days assuming that the process has been in control all this time?

 

P(>=4 rejected)= 1-binom.dist(4-1,20,.0377,1)= .005998

The chance that there will be four rejected shipments in 20 days is .59%. This is very low. So why have there been so many rejections in this time period? T

 

4. Speculate as to the source of the problem at Packem Company. Has the problem with unaccepted shipments been due to an increase in drive non conformances at Packem, to increased quality requirements by Four-D Office Products, to damage during shipment, or is it simply due to random variation? Be as specific as possible. What evidence leads you to your conclusion? Attach any supporting evidence from your data analysis.

 

 

the fact that the PDQs being compared is an average of 8 samples may throw the data off. Upper and lower limits are set on a mean and Standard deviation of each individual data point, however we are looking at the average of 8 data points.

 

Upper and lower control should be tighter if you are looking at the averages of 8 samples, because the standard deviation would lower (upper and lower limits are 2 sigma above/below the mean).

It is possible that for each average of 8 samples, there are a couple of outliers pulling the average of the 8 up, while most of the scores are below 6.2. There are probably more non conformances at Packem than their current data suggest. Packem needs to improve the quality of their product, as well as improve the way they look at their data. Packem needs to look at each individual PDQ score, rather than the average of 8 per shift.

 

STEPS:

 

1. Identifying the business analysis questions

 

2. Converting business questions into statistical questions

 

3. Performing a descriptive analysis of the data

 

4. Applying formal analysis procedures

 

5. Developing conclusions and recommendations

 

6. Identifying unusual outcomes and future analysis

Sections:

· Executive Summary: 1-3 paragraphs, ** Last part written *** identify the problem, indicate your approach to solving it and concisely state conclusion

· Introduction: ~1 Paragraph, intro to the case, project scope.

· BODY: indicate how you developed your conclusions and recommendations

· Part 1: Begin with concise presentation of the question from the business perspective and explain how you conducted the analysis

· Part 2: Define the data set and specify the statistical procedures used

· Include specific statements of statistical models and hypothesis tests

· Results: Discuss the statistical results, indicating how they provide a solution to the case problem

· Include additional observations and extensions of your results

· Identify unusual outcomes, go into detail on the unexplored questions in the study (Questions for future work), might be important enough to justify another study.

· Document the additional questions and suggest how they might be answered and decide whether or not additional work should be taken

· Conclusion