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Sma2110:Applied Mathematics Ii Question Paper
Sma2110:Applied Mathematics Ii
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2011
QUESTION ONE (30 MARKS)
(a) Briefly explain five reasons why control charts are popular tools in quality control. (5 Marks) (b) The following data were collected from a process manufacturing power supplies. The variable of interest is output voltage and = 5. Sample number R 1 104 4 2 105 5 3 104 2 4 106 11 5 102 4 6 105 3 7 106 7 8 105 2 9 106 4 10 104 3 11 105 4 12 103 2
2
13 102 3 14 105 4 15 104 5 16 105 3 17 106 5 18 102 2 19 105 4 20 103 2
(a) Set up the and R charts on this process. (8 Marks) (b) If the specifications on the characteristics were 103 ± 4, Calculate the fraction of non conforming terms. (4 Marks) (c) Discuss the advantages and disadvantages of acceptance sampling. (6 Marks) (d) Draw the Type-B OC curve for the single sampling plan = 50 = 1 (7 Marks)
QUESTION TWO (20 MARKS)
(a) A production manager at a tire manufacturing plant has inspected the number of defective tires in twenty random samples with twenty observations each. Following are the number of defective tires found in each sample. Sample number number of defective tires sample Number of defective tires 1 3 11 3 2 2 12 2 3 1 13 2 4 2 14 1 5 1 15 1 6 3 16 2 7 3 17 4 8 2 18 3 9 1 19 1 10 2 20 1
(i) Construct the P-chart with the above information and comment on the constructed chart. (5 Marks) (ii) What do you say about the control chart pattern? (1 Marks) (b) Explain the three sampling plane used in acceptance sampling. (6 Marks) (c) Discuss the dimensions of quality. (8 Marks)
3
QUESTION THREE (20 MARKS)
(a) An chart has a centre line of 100, uses a three sigma control limits and is based on sample size of four. The process standard deviation is known to be six. If the process mean shifts from 100 to 92. (i) Calculate the probability of detecting this shift on the first sample following the shift? (7 Marks) (ii) Find 1 and give interpretation. (2 Marks)
(b) A process that produces bearing focusing is controlled with a fraction conforming control chart, using sample size = 100 and a centre line = 0.02. (i) Find the three-sigma limits for this chart. (5 Marks) (ii) Analyze the ten new samples ( = 100) shown here for statistical control Sample number Number of Nonconforming 1 5 2 2 3 3 4 8 5 4 6 1 7 2 8 6 9 3 10 4
What conclusions can you draw about the process now? (6 Marks)
QUESTION FOUR (20 MARKS)
Samples of = 4 items are taken from a manufacturing process at regular intervals. A normally distributed quality characteristics is measured and and s values are calculated for each sample. After 50 sub groups have been analyzed we have
1000
50
1 i ix
72
50
1 i is
(a) Compute the control limits for and s control charts. (4 Marks) (b) If the specifications are 19 ± 4, What are your conclusions regarding the ability of the process to produce items conforming to specifications? (4 Marks)
4
(c) Assuming that if an item exceeds the upper specification limit it can be reworked and it is below the lower specification limit is must be scrapped, What percentage crap and rework is the process producing? (4 Marks) (d) If the process were centred at = 19, find the effect it will have on the percent of scrap and rework. (4 Marks)
QUESTION FIVE (20 MARKS)
(a) and R-charts with = 4 are used to monitor a normally distributed quality characteristics. The control chart parameters are given below.
- Chart R- Chart UCL = 815 UCL = 46.98 Centre line = 800 Centre line = 20.59 LCL = 785 LCL =0
Both charts exhibit control. Calculate the probability that a shift in the process mean to 790 will be detected on the first sample following the shift. (7 Marks) (b) A process is being controlled with a fraction non conforming control chart the process average has been shown to be 0.07. Three sigma control limits are used and the procedure calls for taking daily samples of 400 items. (i) Calculate the upper and lower limits. (4 Marks) (ii) If the process average suddenly shits to 0.1, find the probability that the shift would be detected on the first subsequent sample. (9 Marks)
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