IE 6113Term Project Quality Control and Improvements Spring 2015

I. In producing an alloy, the USL for the proportion of catalyst content is 2.2% and standard deviation is 0.5%. Any lot that contains 2% of its items below USL is considered acceptable with probability 0.95. Any lot that has 10% or more of its items below USL is considered unacceptable with probability 0.90.

Requirements:

a. Derive a mathematical variables sampling plan for this process

b. Assuming unknown and using a batch size of 40, AQL of 1.4% and general inspection level of III, 1. Find an appropriate set of sampling plans using ANSI/ASQC Z1.9, using Form 1 and Form 2 for Normal, Tightened and Reduced Inspection. 2. Compare the sample sizes and the protection that both the producer and consumer obtain from this plan with the plan derived in (a.) 3. If a random sample of 10 items yields the following catalyst content (in %): 1.2, 1.6, 0.8, 1.9, 1.8, 1.4, 0.6, 0.9, 1.5 and 0.7. What is your decision using Form1 and Form2?

c. 1.Derive an attributes sampling plan that has the same OC curve as the one derived in (a.). 2.Compare the sample sizes required for the equivalent protection. Under what circumstances would variables sampling be more economically efficient?3.Construct the OC curve and ASN curve for the Sampling plan. 4.Consider chain sampling plans with same n, c=0, and i=3, 5, 7, construct the OC curves for these chain sampling plans. 5. Derive an item-by-item Sequential Sampling plan. Construct the OC curve and ASN curve for this plan.6.Compare between (1), (4), and (5) from above.

d. Using AQL of 1.4%, find an appropriate set of an attribute sampling plans using MIL STD 105E, for Normal, Tightened and Reduced Inspection. Compare the sample sizes and the protection obtained from this plan with the plans derived in parts (a.), (b.1.) and (c.1.).

e. A LSL of 1% with an AQL of 6.5% is imposed in addition to the given USL and AQL, what is your decision?

[Note: The tables from ANSI/ASQC Z1.9 required to complete this part of the exercise are available on the Montgomery SQC website: www.wiley.com/college/montgomery]

II.

1. A life testing sampling plan of 6 items is to be terminated after the third failure. The lot is accepted with a mean life of 600hr. with a probability of 0.99. The failures are observed at the following times: 120, 140 and 160 hr. Using Handbook H-108, construct the OC curve for the plan and write you recommendation on the decision about the lot in the following cases:a. Failed items are not replacedb. Failed items are immediately replaced during the test.

2. A life testing plan should accept the lot with a mean life of 1500 hr with a probability 0.95 and reject lots with unacceptable mean life of 300 hr. with a probability of 0.90. i. If the sample size is to be 5 times the rejection number, determine a time-terminated life testing plan using (H-108) and construct the OC curve for the plan in the following cases:a. Failed items are not replacedb. Failed items are immediately replaced during the test.ii. Derive a Sequential replacement procedure, when testinga. With replacementb. Without replacement

III. A screening experiment was conducted to identify critical process drivers and analyze the various factors, which might affect the intended design to meet customer requirements. The factors in this experiment were identified after a series of brainstorming session and involved prior experience in manufacturing other grades of this filters, it was concluded there are five major factors that have an obvious effects and were considered in this experiment. The experiment was conducted in a controlled manufacturing environment to minimize the effects of uncontrollable or unknown factors and was similar to routine manufacturing environment. Each of the five (5) factors has two levels. The experiment was run as full factorial of the 25 design and four (4) replications. Output data was collected for four response variables these are; Membrane retention properties, Membrane Solute passage, Membrane permeability, Membrane Integrity Test.Analyze the giving data and draw a conclusion for all the 4 responses. Include everything you learn in DOE lecture, (e.g., main effects, interaction effects, regression module)The potential design factors are summarized in Table 1 below; each of the mentioned factors has two levels as follows (use coded design), table 2 lists the responses that were measured in this experiment, and table 3 presents the design and the resulting responses.Table 1 FACTORSLOW LEVELHIGH LEVEL

Factor 1 (A)LowHigh

Factor 2 (B)LowHigh

Factor 3 (C)LowHigh

Factor 4 (D)LowHigh

Factor 5 (E)LowHigh

THE RESPONSES VARIABLESTable 2ResponseMeasurement/ Unit

Response 1Retention PropertyKilo Delton

Response 2Passage TestPercent (%)

Response 3Permeability Propertyml/min/cm2 @ 20C

Response 4Integrity Testsccm2/ft2 @ 60psi

Table 3 ABCDER1R2R3R4

1-11-1114510.69414.3

2-1-1-114410.7315.5

31-1111273.10.4975.9

4-111-1-1511.40.66513.2

511-11-13310.4496.6

6-111-11501.30.65613.2

711-11-1220.90.2985.9

8-1-111-1292.20.6813.2

91-1-11-13010.6818.3

1011-1-1-1300.90.45615.5

11-1-11-1-1381.61.01319.3

12-1-11-1-1400.80.91719.3

131-1-11-1350.90.79911.1

14-1-11-1-1360.60.98619.3

15-111-11501.40.67311.1

16-111-11471.70.618.3

17-1-1-11-1390.81.03916.7

18-1-1-111350.60.88415.5

19-11-1-1-14810.80815.5

20-11-1-11531.20.79120.7

211-1-1-1-1391.50.8915.5

22-1111-1283.60.3428.3

2311-1-1-1391.40.50814.3

24-11-1-114510.72319.3

25-1-111-13120.71112.1

26-1-111-1271.80.61712.1

271-1-1113010.7635.9

28-1-1-11-1391.11.03919.3

29-1-1-1-11460.60.99720.7

3011-111361.40.4254.5

31-1-1-11-1400.80.99516.7

32-11-11-1460.60.70714.3

33-1-1111261.80.57614.3

34-1-111-1292.20.6613.2

35-11-1114510.65614.3

36-11-1-1-1400.80.66613.2

371-1-1-1-1301.10.71519.3

38-11-11-1440.80.75816.7

3911-1-11391.20.50211.1

401-1-1-11390.80.89111.1

41111-11401.50.43910.1

42-11-1-1-1460.70.78923.5

431-1-1-11361.10.87822.1

441-11-11381.40.65311.1

45-1-1-1-1-1420.90.98615.5

461-111-1222.50.41722.1

47-1-1-1113710.90218

481-11-11441.40.72314.3

49-11-111481.20.66112.1

50-1-1-111381.21.00620.7

51-111-1-1541.20.610.1

52-1-1-1-1-1401.20.97820.7

53-111-1-1491.20.61313.2

54-11111362.60.4288.3

55-1-1-1-11400.90.90215.5

56-1-1-1-1-1370.80.89914.3

57111-1-1292.60.33914.3

581111-1292.60.33914.3

591-111-12330.4598.3

60-1-11-11433.50.9122.1

61111-113720.42211.1

621-11-11371.80.65112.1

63-1-11-11401.50.84314.3

6411111194.20.2482.9

65-1-1-1-11411.30.90218

6611111253.90.33.4

67-1-1111291.90.5959.2

6811-1-11421.80.50415.5

69-1-1-11-13911.01319.3

701-1-111320.90.78110.1

71-11-11-1350.60.57315.5

721-1111241.80.4265.9

73111-1-1332.60.378.3

74111-1-14020.43413.2

751-1-1-1-1351.10.80716.7

7611-1-11401.50.5115.5

77-1-11-11442.10.80814.3

78-11111334.90.42310.1

79-11-1-1-1370.70.70918

80-1-1-1-1-1401.40.96923.5

81-1-11-1-13610.87319.3

821-1-11-13310.70911.1

8311-11-1351.20.4466.6

841-1-11-1380.70.7829.2

85-11-111400.90.6213.2

861-111-1182.20.38711.1

8711-111381.30.4143.4

88-1-1111272.50.53112.1

89-11-11-1360.60.5612.1

90-1111-1333.40.4299.2

911-11-1-1331.60.62815.5

921-1-111310.90.7958.3

9311111254.70.2852.9

941-11-1-14010.7516.7

95111-1-1402.40.43814.3

96-1-1-1-11430.90.98825

97-11-1-11501.20.74316.7

98-1-1-111380.20.91920.7

991111-1153.90.164.5

1001-11-1-14210.71715.5

1011-11112520.5015.9

1021-111-1233.20.44910.1

1031-1-1-11361.10.85812.1

104-11111371.90.4510.1

105-11111333.60.4116.6

10611-11-12910.3716.6

107-1111-1293.80.3838.3

108-1111-1383.80.42310.1

1091-11112930.5126.6

110111-11401.80.41812.1

1111111-1215.40.0364.5

1121-1-111290.80.74812.1

1131111-1154.30.1875.2

114-111-11531.50.62211.1

11511-1-1-1331.30.46711.1

116-111-1-1511.30.66515.5

117-1-1111272.80.5558.3

11811-111331.30.4373.4

11911-1-1-13610.51813.2

12011-1-11401.50.50811.1

1211-1-1-11370.60.85414.3

12211-111321.20.4073.4

1231-11-11451.40.76416.7

124111-11382.70.38511.1

1251-11-1-14010.70416.7

1261-1-1-1-1400.60.90616.7

127-1-11-11491.60.83314.3

12811111214.30.2693.4