The EuroWatch CompanyThe EuroWatch CompanyWhere timing is everythingWhere timing is everything

Team 6Team 6

Watch Production AnalysisWatch Production Analysis

February 16, 2006February 16, 2006Quantative Business AnalysisQuantative Business Analysis

EuroWatch CompanyEuroWatch Company

Production Capabilities- Two lines running independently - Production = 500 watches per hour- Line 1 = older and less reliable with a 2% defect rate- Line 2 = newer and more reliable with a 1% defect rate

The task at hand- Analyze production lines for efficiency

Where Timing is Everything

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EuroWatch CompanyEuroWatch Company

Task #1Task #1– To determine the number of defect free watches

produced by each line in a given hour– Must have a 99% success rate– Not producing more than a given number of

defective watches per hour

Where Timing is Everything

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EuroWatch CompanyEuroWatch CompanyWhere Timing is Everything

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Number of defective items in a random sample of 500 items

Number of trials 500Defect Probability 2%

Cum Prob EVNumber of defectives (k) P(k) 0.00000000 10.00

0 0.0000410 0.00004102 01 0.0004186 0.00045964 0.0004192 0.0021315 0.00259114 0.0042633 0.0072210 0.00981216 0.0216634 0.0183104 0.02812259 0.0732425 0.0370693 0.06519187 0.1853466 0.0624126 0.12760443 0.3744757 0.0898886 0.21749308 0.6292218 0.1130487 0.33054182 0.904399 0.1261224 0.45666421 1.135102

10 0.1263798 0.58304401 1.26379811 0.1148907 0.69793472 1.26379812 0.0955469 0.79348160 1.14656213 0.0731976 0.86667920 0.95156914 0.0519639 0.91864310 0.72749515 0.0343598 0.95300290 0.51539716 0.0212557 0.97425865 0.34009217 0.0123503 0.98660892 0.20995518 0.0067632 0.99337217 0.12173819 0.0035015 0.99687366 0.06652820 0.0017186 0.99859224 0.03437221 0.0008017 0.99939392 0.01683522 0.0003562 0.99975013 0.00783723 0.0001511 0.99990122 0.003475

Line 1 old line

Task 1 : Production Line 1Task 1 : Production Line 1

Based upon this analysis we are 99% certain that:

Expected Value of 10 defective watches per hour

482 working watches

18 defective watches

EuroWatch CompanyEuroWatch CompanyWhere Timing is Everything

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Number of defective items in a random sample of 500 items

Number of trials 500Defect Probability 1%

Cum Prob EVNumber of defectives (k) P(k) 0 5.0000

0 0.0065705 0.0065705 01 0.0331843 0.0397547 0.03322 0.0836310 0.1233858 0.16733 0.1402298 0.2636156 0.42074 0.1759955 0.4396111 0.70405 0.1763510 0.6159621 0.88186 0.1469592 0.7629213 0.88187 0.1047588 0.8676801 0.73338 0.0652097 0.9328898 0.52179 0.0360081 0.9688979 0.3241

10 0.0178585 0.9867564 0.178611 0.0080355 0.9947920 0.088412 0.0033076 0.9980995 0.039713 0.0012541 0.9993537 0.016314 0.0004407 0.9997943 0.006215 0.0001442 0.9999385 0.002216 0.0000442 0.9999827 0.000717 0.0000127 0.9999954 0.000218 0.0000034 0.9999988 0.000119 0.0000009 0.9999997 0.000020 0.0000002 0.9999999 0.000021 0.0000000 1.0000000 0.000022 0.0000000 1.0000000 0.000023 0.0000000 1.0000000 0.0000

Line 2

Based upon this analysis we are 99% certain that:

Expected Value of 5 defective watches per hour

489 working watches

11 defective watches

Task 1 : Production Line 2Task 1 : Production Line 2

EuroWatch CompanyEuroWatch CompanyWhere Timing is Everything

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Task #2Task #2– Must be 99% positive – Customer receives 500 defect-free watches

EuroWatch CompanyEuroWatch Company

Order for 500 watches

Using only Line 2 for production

Guarantee of 99% certainty that customer will receive 500 defect-free watches

Where Timing is Everything

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1%

NProd2 Probability500 0.006570483042501 0.039422898254502 0.121718198361503 0.259425667205504 0.432592809277505 0.607145288486506 0.754060291819507 0.860258851372508 0.927562188489509 0.965551183217510 0.984887581533511 0.993852638934512 0.997670259211513 0.999173814274514 0.999724759808515 0.999913550477516 0.999974317474517 0.999992762045518 0.999998059735519 0.999999504053520 0.999999878854521 0.999999971661522 0.999999993640523 0.999999998628

Probability of Defects (p)

Number of Watches made (n)

Task 2 : Production Line 2Task 2 : Production Line 2

EuroWatch CompanyEuroWatch Company

Task #3Task #3– Using both Line 1 & Line 2 for production– Order for 1000 watches– Containing the same number of watches from

each Line– Guarantee of 99% certainty that customer will

receive 1000 defect-free watches

Where Timing is Everything

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EuroWatch CompanyEuroWatch CompanyWhere Timing is Everything

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Watches to be Shipped 513 Watches to be Shipped 513Number of defectives (k) P(k) Cum Prob Vlookup Number of defectives (k) P(k) Cum Prob Vlookup

0 0.0057657 0 0 0 0.0000315 0 01 0.0298770 0.00576574 1 1 0.0003303 0.00003155 12 0.0772577 0.03564274 2 2 0.0017256 0.00036184 23 0.1329249 0.11290044 3 3 0.0059985 0.00208745 34 0.1711911 0.24582530 4 4 0.0156084 0.00808599 45 0.1760329 0.41701641 5 5 0.0324273 0.02369443 56 0.1505466 0.59304929 6 6 0.0560309 0.05612178 67 0.1101402 0.74359593 7 7 0.0828212 0.11215270 78 0.0703673 0.85373611 8 8 0.1069070 0.19497391 89 0.0398827 0.92410345 9 9 0.1224218 0.30188089 9

10 0.0203039 0.96398617 10 10 0.1259196 0.42430270 10

Line 2 Line 1

Task 3 : Production Lines 1 & 2Task 3 : Production Lines 1 & 2

Snapshot of Defective Watches

EuroWatch CompanyEuroWatch CompanyWhere Timing is Everything

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Watch Runs 2000 Prob >= Prob <=Watches to create 1026 1000 1000lots of 1000 or more 1990 0.995 0.005

Task 3 : Production Run SimulationTask 3 : Production Run Simulation

Simulation Equals

- 2 Independent simulation lines- Calculated defect-free probability values- Lines 1 & 2 total defect-free watches- Probability of acceptable shipments

Simulation Findings

Line 2 Defects Line 1 Defects Total watches0.994578665 12 0.54079988 10 10040.284625814 4 0.22074379 8 10140.470410265 5 0.29821609 8 10130.826488291 7 0.37622075 9 10100.863743051 8 0.75918028 12 10060.885132184 8 0.27482214 8 10100.088907743 2 0.9166087 15 10090.548934515 5 0.51970778 10 10110.341364714 4 0.8658449 14 10080.111667954 2 0.6375040 11 10130.734145861 6 0.06294852 6 10140.453036600 5 0.53071365 10 10110.960224539 9 0.9923810 19 9980.443281747 5 0.6439185 11 10100.181946903 3 0.64482591 11 10120.514814284 5 0.34010346 9 1012

Findings & Recommendations– Line 2 orders must be shipped with 511 watches in

order to guarantee 500 defect-free watches reach the client

– Combined shipments from Line 1 & Line 2 should contain 1016 watches in order for the client to receive 1000 defect-free watches

– Therefore, it is beneficial to send combinations, as opposed to only using Line 2 to fulfill shipments

EuroWatch CompanyEuroWatch CompanyWhere Timing is Everything

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The EuroWatch CompanyThe EuroWatch CompanyWhere timing is everythingWhere timing is everything

Questions???Questions???

The EndThe End

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