Datastor Case Study - Stats Probabilitiy and Binomials

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  • Topic: Standard deviation, Probability theory, Arithmetic mean
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  • Published : November 12, 2012
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DataStor Case Study|
Team 1

Case Study for DataStor

DataStor, a data storage device and media manufacturer, produces a compact hard drive called DS1000, which stores 1GB of data. Their primary customer is Four-D, a national reseller of the drives.

Four-D 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 8-hour 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.

Four-D 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 Four-D 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 Four-D? 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 X-bar 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 Four-D? That is, what is the probability of Four-D rejecting a shipment of drives from DataStor?

The probability of Four-D rejecting a shipment of drives from DataStor, if there process is “in control”, is 3.8%.

Four-D 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 Four-D’s quality standard of 6.2, was gained from Question 1.

Outcomes 1 – 10 were queried because there are 10 possible scenarios of Four-D rejecting the sample. The cumulative probability of Four-D 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| 6.6E-06| |
| 4| 4.4E-08| |
| 5| 2E-10| |
| 6| 6.5E-13| |
| 7| 1.4E-15| |
| 8| 2.1E-18| |
| 9| 1.8E-21| |
| 10| 6.8E-25| |
| | | |
| | 0.03765| |

3. What is the probability of DataStor having four or more shipments rejected in twenty days by Four-D, assuming that their production process has been “in control”?

The probability of Four-D rejecting a...
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