LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2004

ST 6602/STA 602 – STATISTICAL PROCESS CONTROL

07.04.2004                                                                                                           Max:100 marks

1.00 – 4.00

SECTION – A

 

Answer ALL the questions                                                                          (10 ´ 2 = 20 marks)

 

1. Explain Statistical Process Control.
2. What are control limits?
3. Describe Total Quality Management (TQM).
4. Define ‘Chance’ and ‘Assignable’ causes of variation.
5. Discuss rational subgroup concept.
6. What information is provided by the operating characteristic curve of a control chart?
7. Define Process Capability Ratio (PCR).
8. Define Average Run Length Concept.
9. Why is np-chart not appropriate with variable sample size?
10. Explain Demerit Scheme.

 

SECTION – B

 

Answer any FIVE questions                                                                          (5 ´ 8 = 40 marks)

 

11. What is quality? What are different dimensions of quality?

 

12. A quality characteristic is monitored by a control chart designed so that the probability that a certain out-of-control condition will be detected on the first sample following the shift to that state is 1 -b.

Find the following:

1. The expected number of subgroups analyzed before the shift is detected.
2. The probability that the shift is not detected on m -th subsequent sample.

 

13. Samples of n = 8 items each are taken from a manufacturing process at regular intervals. A quality characteristic is measured and  and R values are calculated for each sample.  After 50 samples, we have

Assume that the quality characteristic is normally distributed.  Compute control limits for

the and R control charts.

 

14. Statistical monitoring of a quality characteristic uses both an and S charts.  The charts are to be based on the standard values m = 200 and s = 10, with n = 4.  Find 3 – sigma control limits for the S-chart and – chart.

 

15. Distinguish between c and u charts.

 

 

16. In designing a fraction non-conforming chart with center line at p = 0.20 and 3 – sigma control limits, what is the sample size required to yield a positive LCL?

 

17. Define the terms i) Specification Limits and ii) Natural Tolerances with an illustration.

 

18. How is lack of control of a process determined using control chart technique?

 

 

SECTION – C

 

Answer any TWO questions                                                                        (2 ´ 20 = 40 marks)

 

19. a) Explain ‘Stem – amd – Leaf plot’ with an illustration.

 

1. b) A normally distributed quality characteristic is monitored by a control chart with L –

sigma control limits.  Develop a general expression for the probability that a point will

plot outside the control limits when the process is really in control.                    (10+10)

 

20. Suppose each automobile produced on an assembly between 9 a.m. and 10 a.m. is examined for paint blemishes on the left front door, with the results given in the following Table. These blemishes may not be easily seen with the naked eye, but a trained inspector with a special light source and magnifying glasses can spot them.

 

Automobile No.	1            2         3          4         5         6          7         8        9       10   0.84    0.62    0.84     1.08    0.62     0.84     1.08    0.84   1.08    0.62     3         2         4          5         4          2          12       6        7          4
Surface Area in Sq.Mt.
No. of Blemishes

 

For the above case, state:

1. Which control chart (s) would be appropriate to use for ongoing SPC?
2. Why do you suggest the chart (s) in a) ?
3. What assumptions are you making in suggesting the chart (s) in a) ?      (8+6+6)

 

21. a) Mention the theoretical base of p-chart and set up its control limits:

 

1. Explain the procedure of obtaining the OC curve for a p-chart with an illustration.

(8+12)

22. Write short notes on:-
23. Six – Sigma quality

 

1. Single Sampling Plan.      (10+10)

 

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 24

SIXTH SEMESTER – APRIL 2006

                                           ST 6602 – STATISTICAL PROCESS CONTROL

(Also equivalent to STA 602)

 

 

Date & Time : 24-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

Section A

 

Answer all questions                                                                         ( 10 ´ 2 = 20 )

 

1. What are the chief aspects of quality?
2. What are quality costs?
3. What is the difference between conformity and non – conformity?
4. Mention any two ways of detecting the stability of a process using control charts.
5. What is the ARL for a process that is in – control? How is it interpreted?
6. What are ‘Specification Limits’?
7. Mention the difference between c – chart and u – chart.
8. Mention the advantage of acceptance sampling plan procedures.
9. What is the use of probability plots?
10. Give the control limits for EWMA control chart.

 

Section B

Answer any five  questions                                                               ( 5 ´ 8 = 40 )

 

1. Draw the phase diagram of quality improvement and explain it.

12. What are 3 sigma limits? Explain the logic behind their usage in control charts.
13. The number of nonconforming switches in samples of size 150 is shown below. Construct a fraction nonconforming control chart for these data. Does the process appear to be in control? If not, assume that assignable causes can be found for all points outside the control limits and calculate the revised control limits.

Sample number:1        2          3          4          5          6          7          8

Number of

Nonconforming

Switches          :8         1          3          0          2          4          0          1

 

Sample number:9        10        11        12        13        14        15

Number of

Nonconforming

Switches          :10       6          6          0          4          0          3

14. A control chart is to be established on a process producing refrigerators. The inspection unit is one refrigerator and a control chart for nonconformities is to be used. As preliminary data, 16 nonconformities were counted in inspecting 30 refrigerators.
    • What are the 3 – sigma control limits?
    • What is the probability of Type I error for this control chart?
    • What is the probability of Type II error for this control chart?
    • Find the average run length if the number of defects is actually 2.
15. Explain the different approaches in the construction of u – chart with variable sample size.
16. Explain the procedure for constructing a cumulative sum control chart.
17. What is meant by acceptance sampling? Mention its advantages.
18. Derive an expression for ‘Average Outgoing Quality’ with reference to single sampling plan.

Section C

Answer any two  questions                                                               ( 2 ´ 20 = 40 )

 

1. a.) Explain the role of designed experiments in quality improvement.

b.) The data below represent the results of inspecting all units of a personal computer produced for the last 10 days. Construct a standardized

fraction nonconforming control chart for these data. Does the process appear to be in control? If not, find the revised control limits.

Day:1     2     3     4     5     6     7     8     9     10

Units Inspected:80  110 90  75   130  120 70   125  105 95

Nonconforming

Units:4     7     5    8     6      6     4      5      8     7               (8+12)

20. ) Explain the statistical basis of a p – chart and derive its control limits.

b.) Construct probability plot to verify whether the following data has been generated from a normal population.

15,10,18,20,22,14,16,17.                                                        (10+10)

 

21. ) Derive the control limits for and R chart.

b.) Bath concentrations are measured hourly in a chemical process. The following data shows the concentration observed on the past 10 days each on a 4 hourly period.

Day                             Concentration

1                      160      186      190      206

2                      158      195      189      210

3                      150      179      185      216

4                      151      184      182      212

5                      153      175      181      211

6                      154      192      180      202

7                      158      186      183      205

8                      162      197      186      197

9                      169      205      185      188

10                    173      203      187      183

Analyze the data using the cumulative – sum control chart if the target mean concentration is 170.                                                                            ( 10 + 10 )

 

22. a) What are rectifying inspection plans? Mention its advantages.

b)Consider a single sampling plan with n = 100 , c = 2. Find the OC function corresponding to the incoming lot fraction defective p = 0.05 , 0.10 , … , 0.30

( 10 + 10 )

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc.  DEGREE EXAMINATION –STATISTICS

AC 24

SIXTH SEMESTER – APRIL 2007

ST 6602 – STATISTICAL PROCESS CONTROL

 

 

Date & Time: 20/04/2007 / 9:00 – 12:00       Dept. No.                                                                 Max. : 100 Marks

 

 

PART-A

Answer all the questions:                                                     10×2=20

 

1. Mention any 4 advantages of a control chart.
2. Write the 3-σ control limits for a c-chart with the process average equal to 4 defects.
3. The control limits for a p-chart are given below

UCL=.161,CL=.08,LCL=0,n=100

Find the equivalent control limits for an np chart.

1. Write the need for an EWMA control chart.
2. Define consumers risk,producers risk.
3. Mention any 4 advantages of acceptance sampling.
4. Write the expression for AOQ of a double sampling plan.
5. Write the control limits for an s-chart when σ is given.
6. Explain the term process capability.
7. What are the uses of a stem and leaf plot?

 

PART-B

 

Answer any 5 questions:                                            5×8=40

 

1. The number of defective switches in samples of size 150 are shown  below. Construct a fraction   defective chart for these data.

Sample number                       number of defective

switches

1                                                   8

2                                                   1

3                                                   3

4                                                   0

5                                                   2

6                                                   4

7                                                   0

8                                                   1

9                                                  10

10                                                   6

11                                                   6

12                                                   0

 

12. Explain the oc curve of a control chart in detail.

 

 

13. Explain the theory behind the construction of control limits for  and S charts.
14. Explain the double sampling plan in detail.
15. Draw box-whisker plots for the following data on two variables and compare.

Sample no:    1      2      3      4       5       6      7      8       9     10      11     12

x₁       :    6     10     7      8       9      12    16     7       9     15       8       6

x₂       :   15    11     5     13     13     10     9      4      12    13      16     11

 

16. Explain the CUSUM chart in detail.
17. Explain the methods of measuring process capability in detail.
18. A p-chart is used with UCl=.19,CL=.1,LCL=.01 to control a process
    • If 3-σ limits are used , find n .
    • Obtain the α-risk.
    • Obtain the β-risk if p has shifted to p=.2

 

PART-C

Answer any 2 questions:                                                      2 x 20=40

 

19.a) A paper mill uses a control chart to monitor the defects in finished rolls of a

paper. Use these data to set up chart for defects per roll of paper. Does the

process  appear to be in control?

 

Day                  Number of Rolls                Total number of defects

1                                18                                         12

2                                18                                         14

3                                24                                         20

4                                22                                         18

5                                22                                         15

6                                22                                         12

7                                20                                         11

8                                20                                         15

9                                20                                         12

10                               20                                         10

 

1. b) Explain the need for

i)Pareto diagram

ii)Cause and effect diagram

iii)Defect concentration diagram in statistical process control .

 

20. a)The data shown below represents from nominal diameter value for holes drilled

in aerospace  manufacturing.

Sample no                       x1               x2              x3                x4              x5

1                            -30               50             -20               10              30

2                               0                50            -60              -20              30

3                            -50               10              20               30               20

4                            -10              -10              30              -20              50

5                              20              -40              50               20             10

6                               0                  0               40             -40             20

7                               0                  0               20             -20             10

8                              70               -30             30              -10              0

9                               0                  0               20              -20            10

10                             10                 20             30               10             50

Set up  & R charts. Is the process  in control?

 

 

b)A normally distributed quality characteristic is controlled through use of an

and R  charts.

 

 

char                                                      R-chart

UCL=626                                              UCL=18.795

CL=620                                                 CL=8.236

LCL=614                                              LCL=0

 

1. i) If specifications are 610±15 what percentage of defective items is produced?
2. ii) What is the probability of detecting a shift in the process mean to be 610 on

the first sample? (σ remains constant).

iii) What is the probability of type I error?

1. iv) If S chart were to be used for the R chart what would be the approximate

parameters of the S chart?           (4x 2.5)

21. a) Draw EWMA control chart for the following data on the sample mean with λ = .2 ,σ = 2.

 

Sample number                                   x

• 45
• 55
• 37
• 64
• 95
• 08
• 5
• 87
• 25
• 46
• 39
• 69

b)Also obtain the tabular CUSUM values with Δ=.5σ ,α=.005

 

22. a) Draw the oc curve for a single sampling plan with n=100,c=2,N=1000

 

1. b) Obtain the single sampling plan for which

P= .01, α = .05, P= .06, β= .10

 

1. c) Obtain the expressions for AOQ and ATI. (10+10)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 30

SIXTH SEMESTER – APRIL 2008

ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date : 23/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

 

PART – A

Answer ALL the questions:                                                                          (10 x 2 = 20)

 

1. Mention the reasons for Quality improvement in a new business strategy.
2. What is TQM philosophy?
3. What is the Box plot?
4. Explain the Stem and Leaf plot.
5. Define Statistical Process control.
6. What benefits are expected out of the use of control charts?
7. What is a CUSUM chart?
8. Define process capability analysis and mention its purpose.
9. Mention disadvantages of Acceptance sampling.
10. What is item – by – item sequential sampling plan?

 

 

PART – B

Answer any FIVE  questions.                                                                      (5 x 8 = 40)

 

1. Explain how variation is described through the frequency distribution and histogram.
2. Explain the link between Quality improvement and productivity.
3. How will you prepare the control charts for fraction defectives?
4. Distinguish between CUSUM chart and Shewhart chart.
5. Discuss the process capability analysis using a control chart.
6. How can the Shewhart control charts be interpreted to draw meaningful conclusions?
7. What is acceptance sampling? Mention the situations it is most likely to be useful.
8. Describe the operating procedure of double sampling plan.

 

PART – C

Answer any TWO   questions.                                                                      (2 x 20 = 40)

1. a) State the specific functional responsibilities of total Quality Management.

1. b) A TV voltage stabilizer manufacturer checks the quality of 50 units of his product nonconforming units are as follows.

 

Days:	1	2	3	4	5	6	7	8	9
Fraction defectives:	0.10	0.20	0.06	0.04	0.16	0.02	0.08	0.06	0.02

 

Days:	10	11	12	13	14	15
Fraction defectives:	0.16	0.12	0.14	0.08	0.10	0.06

Construct 3 – sigma trial Control limits for fraction defectives and comment on it.

(12+8)

 

 

 

 

1. a) How do you set the Control limits for R-charts in Statistical quality control?

1. b) Sixteen boxes of electric switches each containing 20 switches were randomly selected from a lot of switch boxes and inspected for the number of defects per box. The numbers of defects per box were as follows:

 

Box Numebr:	1	2	3	4	5	6	7	8	9	10
No. of defects:	12	15	9	14	18	26	8	6	11	12

 

Box Number:	11	12	13	14	15	16
No. of defects:	16	13	19	18	14	21

 

Calculate 3-sigma limits for c-chart and draw conclusion.                             (12+8)

 

1. a) Describe the operational aspects of CUSUM charts and the role of v-mask.

1. b) How can sequential sampling plan be implemented graphically under SPRT? (12+8)

1. a) Explain the Operating procedure of Single Sampling plan and obtain its OC curve.

1. b) What are continuous sampling plans and mention a few situations where these plans are applied. (12+8)

 

 

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       LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

YB 30

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2009

ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date & Time: 23/04/2009 / 9:00 – 12:00   Dept. No.                                                  Max. : 100 Marks

 

 

PART A

 

Answer ALL the questions:                                                                           (10 x 2 = 20)

 

1. Define Total Quality Management.
2. Mention the basic concepts in quality improvement.
3. How will you model the process quality?
4. Define quantile plot.
5. Distinguish between control charts for attributes and control charts for variables.
6. What are the advantages of control charts?
7. Define the purpose of process capability analysis.
8. What are slant control charts?
9. Mention an application where continuous sampling plan can be used.
10. Explain multiple sampling plan for attributes.

 

PART B

 

Answer any FIVE questions:                                                                         (5 x 8 = 40)

 

1. Examine the need for quality control techniques in production.

 

1. Explain the chance and assignable causes of variation in the quality of manufactured product.

 

1. The sample given below represents the number of defectives found in batches of a production line. Construct a stem and leaf display with stem labels 1,2,3,4,5,6,7,8,9 and leaves ordered.

258	639	739	839	579	679	588	688	654	673
838	412	638	619	369	759	859	679	779	628
728	659	471	571	671	534	693	738	106	206
465	608	708	808	908	998	639	739	489	674
556	656	329	567	509	523	428	528	628	495

 

1. What is a control chart? Explain the basic principles underlying the control charts.

 

1. A machine produces spark plugs to tolerance limits of 25 thousandths of an inch ± 2 thousandth of an inch. Plugs outside this range would give erratic running of the engine. It is decided to set up control charts for the machine. Records reveal that the average range for sample of 5 items is 1 and the mean of the means is 25.1. Setup the mean and range charts.

(d₂ = 2.326, D₃ = 0, D₄ = 2.11)

 

1. Explain the basic principles underlying the slant control charts.

 

1. Explain the terms: (i) Producer’s and consumer’s risks

(ii) AQL and LTPD

 

1. Discuss the relative merits and demerits of single and double sampling plans.

 

PART C

Answer any TWO questions:                                                                                     (2 x 20 = 40)

 

1. a) Explain the need and utility of Total Quality Management.                                  (10)

 

1. b) Batches of 100 components were taken at fixed interval of time from a production line and tested. The following figures are the number of components found to be non-conforming in each of the batches:

4

3

2

0

7

5

2

4

1

3

4

6

Calculate the mean proportion rejected. Draw a quality control chart for samples of 200 such that the inner limit is equal to the mean plus one standard error and the outer limit is equal to mean plus two standard error.                                                                        (10)

 

1. a) Explain histogram and frequency distribution as methods of describing quality variation.

(10)

 

1. b) Draw a suitable control chart for the following data pertaining to the number of coloured threads considered as defects in 15 pieces of cloth in a certain synthetic fibre and state your conclusions:

7	12	3	20	21	5	4	3	10	8
0	9	6	7	20					(10)

 

1. a) Explain the underlying principle and working of CUSUM chart                           (10)

 

1. b) Explain in detail the item by item sequential sampling plan (10)

 

1. a) What is meant by acceptance sampling procedures? What are its advantages?     (10)

 

1. b) Describe single sampling plan. Obtain the OC and AOQ curves for this plan. (10)

 

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2011

ST 6605/ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date : 09-04-2011              Dept. No.                                                    Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION   A (10 x 2 = 20 Marks )

Answer ALL the questions

1. What do you mean by the term “ cost of quality” ?
2. List the characteristics of TQM derived from its definitions.
3. When do you use Histogram ?
4. What do you mean by frequency distribution ?
5. Mention the purpose of the p-chart.
6. When are C- charts used ?
7. What are control charts ?
8. The following are the and R values of  4 sub-groups of readings:

= 10.2 , 12.1, 10.8 and 10.9

R  =  1.1 ,  1.3  , 0.9 and 0.8

A₂= 0.73 ; D₃ = 0 ; D₄ = 2.28  ; d₂ = 2.059

Find the control limits for   chart.

9. What does average total inspection mean?
10. Define Consumer’s Risk and Producer’s Risk.

 

SECTION B  ( 5 x 8 = 40 Marks )

Answer any FIVE questions

11. Explain “Cost of Prevention”.
12. State the benefits of TQM
13. Explain the Box Plot technique.
14. Explain the logic behind the usage of 3 sigma control limits.
15. What are the advantages of variable control charts over attribute control charts?
16. Distinguish between CUSUM chart and Shewhart  control chart.
17. What do you mean by Acceptance sampling ? Mention the situations it is most likely to be useful
18. Explain the OC curve for a single sampling plan.

SECTION   C ( 2 x 20 = 40 Marks )

Answer any TWO questions

1. a) State the requirements for successful implementation of TQM

 

1. b) The following are weekly yield data from a semiconductor fabrication facility.  Construct a

Stem and Leaf-plot  by selecting the stem values 5, 6,7,8 and 9.

 

Week :  1     2      3      4      5     6      7     8   9    10   11   12   13   14     15    16    17    18    19   20

Yield   : 58   63   69   72    51   79   83   86   85   78   87   83   64   73     81    68    72    65    91   88

Week:  21     22    23   24   25    26  27   28   29   30   31   32    33    34   35   36    37   38     39    40

Yield   : 64    68    67   60   59    63   64  52   70   92   75   76    81    74   82    76   75    62    63    92

 

 

20. a) What are p and np charts? How they are constructed?
21. b) Discuss in detail the criteria for lack of control with respect to  -chart.

 

21. a) Describe the operational aspects of CUSUM charts and the role of V-mask.
22. b)  A certain product has been statistically controlled at a process average of 46 and a standard

deviation of 1.00. The product is presently being sold to two customers who have different

specification requirements.  Customer A has established a specification of 48 4.0 for the

product, and customer B has specification of 46  4.0. Use normal distribution and find what

percentage of items go outside the specification limits of (i) Customer A, (ii) Customer B.

 

22. a) Mention the advantages and disadvantages of Acceptance Sampling.
23. b) Explain Double Sampling Plan in detail.

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2012

ST 6605/ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date : 20-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

Answer All the questions:                                                                                    (10×2=20marks)

 

1. What is quality?
2. Write the need of Total Quality Management.
3. Write the purpose of Histogram.
4. Explain Q-Q Plot.
5. What is statistical process control?
6. Define ‘C’ chart.
7. Explain process capability analysis.
8. Explain the concept of subgroups.
9. What is Acceptance Sampling?
10. Explain consumer’s risk and producer’s risk.

 

PART – B

 

Answer any FIVE questions:                                                                                (5×8=40marks)

 

11. Describe Quality improvement in the modern business environment.
12. Explain the concept of 3-sigma limits. When do you say the process is out of control?
13. Describe the Box plot technique.
14. Describe process-capability analysis using a Histogram.
15. Explain the construction ofand R charts.
16. Write the advantages of acceptance sampling.
17. What are the basic principles of CUSUM control chart?
18. Explain the technique of single sampling plan for attributes.

 

PART C

Answer any TWO questions:                                                                              (2X20=40marks)

 

19. (a) State the requirements for successful implementation of TQM.

(b) Discuss the relation between quality improvement and productivity.

20. (a) Draw the stem and leaf plot for the following data:

13,15,16,22,24,28,35,32,37,26,41,85,66,45,46,49,44,50,54,58,57,59,61,62,65,93,78,74,72,77,81,82,95,34,38,39,53,55,47,64,

(b) Explain Frequency distributions and its applications.

 

21. (a)Explain the construction of any two control charts for attributes.

(b) Write the applications of u chart and np chart.

22. (a) Explain the construction of CUSUM control chart.

(b) Explain double sampling plan in detail.

 

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