Datastor Case Study  Stats Probabilitiy and Binomials

Team 1

Case Study for DataStor
Background
DataStor, a data storage device and media manufacturer, produces a compact hard drive called DS1000, which stores 1GB of data. Their primary customer is FourD, a national reseller of the drives.
FourD has rejected four shipments of drives from DataStor in the past 20 days. DataStor wants to understand why their shipments are being rejected.
DataStor operates three 8hour shifts, five days a week. Each shift produces approximately 120 drives for a daily average total of 360 drives per day. The company runs quality checks called PDQ tests on one of their drives every hour of production. The test takes up to 20 minutes. Their historical “in control” process is defined with a mean of 7.0 and a standard deviation of .3.
FourD performs their own PDQ tests on the drives that DataStor ships them. They sample ten drives at random. If any of the drives have a PDQ score of 6.2 or below, then the entire shipment will be rejected. Penalties are assessed for each unacceptable shipment.
DataStor wants to determine why their shipments are being rejected. To do this, they first want to look at their internal processes before approaching FourD to see if there are problems/issues on their side.
Case Study Questions
1. If the DataStor DS1000 hard drive production process at DataStor Company is “in control”, what percentage of the drives produced would be considered to be in nonconformance by FourD? In other words, what is the likelihood (probability) that the PDQ test score of a drive tested at DataStor will fall below 6.2?
The probability that a PDQ test score of a drive tested at DataStor will fall below 6.2 is .38%.
We arrived at this conclusion based on DataStor’s “in control” standard: Mean = 7.0
Std Dev = .3
Coincidentally, the mean and the Xbar of the data sample are the same, 7.0 (6.96).
Using Normal Probabilities feature in PhStat, we determined: Common Data
Mean 7
Standard Deviation 0.3
 
Probability for X <=
X Value 6.2
Z Value 2.666667
P(X<=6.2) 0.0038304
2. If the DataStor DS1000 hard drive production at DataStor Company is “in control”, how often will the shipments be found unacceptable by FourD? That is, what is the probability of FourD rejecting a shipment of drives from DataStor?
The probability of FourD rejecting a shipment of drives from DataStor, if there process is “in control”, is 3.8%.
FourD conducts the PDQ test on 10 random samples of each shipment.. We used this as the sample size in the Binomial Probability Distribution feature of PhStat.
The probability of the event, that a drive would fall below FourD’s quality standard of 6.2, was gained from Question 1.
Outcomes 1 – 10 were queried because there are 10 possible scenarios of FourD rejecting the sample. The cumulative probability of FourD rejecting a shipment from DataStor’s “in control” process is 3.8%. See the table below for the calculation.
The binomial probability feature was used because this is a decision with two conditions: acceptable or unacceptable.
Binomial Probabilities  
   
Data  
Sample size 10  
Probability of an event of interest 0.0038304  
   
Statistics  
Mean 0.0383038  
Variance 0.0381571  
Standard deviation 0.1953384  
   
Binomial Probabilities Table  
 X P(X) 
 1 0.037 
 2 0.00064 
 3 6.6E06 
 4 4.4E08 
 5 2E10 
 6 6.5E13 
 7 1.4E15 
 8 2.1E18 
 9 1.8E21 
 10 6.8E25 
   
  0.03765 
3. What is the probability of DataStor having four or more shipments rejected in twenty days by FourD, assuming that their production process has been “in control”?
The probability of FourD rejecting a...
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