LOYOLA  COLLEGE (AUTONOMOUS), CHENNAI-600 034.

M.Sc. DEGREE  EXAMINATION  – STATISTICS

FourTh SEMESTER  – APRIL 2003

ST  4801/ S  1016   indusTrial STATISTICS

16.04.2003

1.00 – 4.00                                                                                             Max: 100 Marks

PART – A                                       (10 ´ 2 = 20 Marks)

Answer ALL the questions.

 

1. Discuss the logic and statistical basis underlying the general use of 3s limits on control charts.
2. Mention the theoretical basis of p-chart and setup its control limits.
3. How is lack of control of a process determined using control chart techniques?
4. What is process capability ratio (PCR)?
5. Briefly explain the process -capability analysis.
6. What is Average run length (ARL)?
7. Explain an attribute single sampling plan.
8. What purpose does an OC curve serve?
9. Define AOQ and give an expression for AOQ for a single sampling plan.
10. Explain six-sigma quality.

 

PART – B                                          (5 ´ 8 = 40 Marks)

Answer any FIVE questions.

 

11. Define the terms : i) rational subgroups  ii) Specification limits

iii) natural tolerances iv) chance and assignable causes.

12. For the following case, state:
13. Which control charts(s) would be appropriate to use for ongoing

statistical process control;

1. Why you suggest the chart(s) given in a); ?
2. What assumptions are you making in suggesting the charts given in a)?

 

Case: A factory manufactures power sockets for use in the refining oil.  These

sockets look like those use by automobile mechanics, except that they are much

larger than and the surface in covered with block oxide instead of stainless steel

to indicate that they are specially designed for power tools.   The hexagonal

inside of  the socket is  prepared by an electrolytic method, and the resulting

diameter of the hexagon is very critical.

Rather than measure every possible diagonal in the socket, one diagonal is

selected at random. from each socket and recorded.  A sample of five

consecutively  produced sockets is taken each day, and the measures are made.

The process will be to collect data for a month, which consists of 22 observations,

and  develop trial  control limits.

 

 

 

 

 

 

 

 

 

 

 

13. A control chart indicates that the current process fraction non-conforming is

0.02. If 50 items are inspected each day, what is the probability of detecting a

shift  in the fraction  non-conforming to 0.04 on the first day after the shift?

By the end of the third day following the shift?

14. Write a detailed note on the moving average control chart.
15. Consider a modified control chart with center line at m= 0 and s =1.0. If n = 5, the tolerable fraction non-conforming is s = 0.00135 and the control limits

are at 3, sketch the OC curve for the chart.

16. Viscosity measurements on polymer are made every 10 minutes by an on-line viscometer. Eighteen observation are shown below.  The target viscosity for this process is m_o = 3200.

 

3169	3173	3162	3154	3139	3145	3160	3172	3175
3205	3203	3209	3208	3211	3214	3215	3209	3203

 

Construct a tabular cusum for this process using standardized values

of h = 8.01  and k = 0.25.

17. For the sampling plan N =120, n₁= n₂ =13, c₁ = 0 and c₂ =1, obtain Pa, ASN

(full inspection), AOQ (defective found replaced) and ATI when the submitted

lot has the fraction non-conforming at p = 0.18

18. What are acceptance and rejection lines of a sequential sampling plan for attributes? How are the OC and ASN values obtained for this plan?

 

PART – C                                       (2 ´ 20 = 40 Marks)

Answer any TWO questions.

 

19. a) Distinguish between c and u charts. Explain the situations where c and u

charts are applicable and how are the limits obtained for these charts.

1. b) Explain the procedure of obtaining the OC curve for a p-chart

with an illustration.                                                                                (10+10)

20. a) What are modified control charts? Explain the method of obtaining control

limits for modified control charts.

1. b) Write a detailed note on control charts based  on extreme values.          (12+8)

 

21. a) What purpose does a cumulative sum chart serve?
22. b) Outline the procedure of constructing V-                                      (5+15)

 

22. a) Explain with an illustration the methods of obtaining the probability of

acceptance   for a triple sampling plan.

1. What are continuous sampling plans and mention a few situations where these

plans are applied.                                                                                   (10 +10)

 

 

Go To Main page

 

 

 

 

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AC 46

FOURTH SEMESTER – APRIL 2006

                                                     ST 4801 – INDUSTRIAL STATISTICS

 

 

Date & Time : 25-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

Answer all the questions.                                                                                  10 ´ 2 = 20

1. Discuss the logic and statistical basis underling the general use of 3 – sigma limits on control charts.
2. Mention the theoretical basis of p – chart and set up its control limits.
3. How is lack of control of a process determined using control chart techniques?
4. What is process capability ratio (PCR)?
5. Write down the control limits of a coefficient of variation chart.
6. What is an average run length (ARL)?
7. Explain an attribute single sampling plan.
8. Define AOQ for a single sampling plan.
9. Discuss the concepts of chance and assignable causes of variability.
10. Write a short note on multivariate control chart.

 

PART – B

Answer any five questions.                                                                     5 ´ 8 = 40

 

11. Explain the method of constructing control limits for X-bar and R charts when the sample sizes are different for various subgroups.
12. A control chart indicates that the current process fraction non-conforming is 0.02. If 50 samples are inspected each day, what is the probability of detecting a shift in the fraction non-conforming to 0.04 on the first day after shift? By the end of the third day following the shift?
13. Write a detail note on the moving average control chart.
14. Consider a modified control chart with CL at m = 0 and s =1. If n = 5, the tolerable fraction non-conforming d = 0.00135 and the control limits are at 3, sketch the OC curve of the chart.
15. Design a cumulative sum control chart to detect a shift of D = 0.75 that has L(0) = 400. Is it possible to find a cumulative sum control chart for detecting this shift that has L(0.75) £ 12? What is L(0) for this chart?
16. For the double sampling plan N = 120, n₁ = n₂ = 13, c₁ =0 and c₂ = 1, obtain P_a, ASN, AOQ and ATI when the submitted lot has the fraction non – conforming at p = 0.18.
17. What are acceptances and rejection lines of a sequential sampling plan for attributes? How are the OC and ASN values obtained for this plan?
18. What are modified control charts? Explain the method of obtaining control limits.

 

PART – C

Answer any two questions.                                                                   2 ´ 20 = 40

 

19. a). Distinguish between c and u charts. Explain the situations where c and u charts are

applicable and how are the limits obtained for these charts.

b). Explain the procedure of obtaining the OC curve for a p – chart with an

illustration.

(10 + 10)

20. a). Define the terms i). Rational subgroups ii). Specification limits

iii). Natural tolerance limits iv). Probability limits.

b). Explain the relevance of non-parametric method in quality control procedures with

an illustration.                                                                                              (10 + 10)

21. a). What purpose does a cumulative sum chart serve?

b). Outline the procedure of constructing a V-mask.                                         (5 + 15)

22. a). What are continuous sampling plans and mention a few situation where these

plans are applied

b). Explain with an illustration the method of obtaining the probability of acceptance

for a triple sampling plan.                                                                            (10 + 10)

 

 

Go To Main page

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AC 48

FOURTH SEMESTER – APRIL 2007

ST 4801 – INDUSTRIAL STATISTICS

 

 

 

Date & Time: 18/04/2007 / 9:00 – 12:00          Dept. No.                                                          Max. : 100 Marks

 

 

SECTION A  

Answer all the questions                                                                             10 x 2 = 20

 

1. Define rational subgroup concept.
2. What are chance and assignable causes of variation?
3. What information is provided by the OC curve of a control chart?
4. Write down the expression for process capability ratio (PCR) when only the lower specification is known.
5. Why is the np chart not appropriate with variable sample size?
6. What is an Average Run Length (ARL)?
7. Explain an attribute single sampling plan.
8. Give an expression for AOQ for a single sampling plan.
9. What is a control chart?
10. Write a short note an multivariate quality control chart

 

SECTION B  

Answer any five questions                                                              5 x 8= 40

 

11. 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 is 1 – b. Find the following:

a). The probability that the out of control condition will be detected on the second sample following the shift.

b). The expected number of subgroups analyzed before the shift is detected.

12. A control chart for the fraction non-conforming is to be established using a CL of p = 0.10. What sample size is required if we wish to detect a shift in the process fraction non-conforming to 0.20 with probability 0.50?
13. Explain the method of constructing control limits for and R charts when the sample sizes are constant.
14. In designing a fraction non-conforming chart with CL at p =0.20 and 3-sigma control limits, what is the simple size required to yield a positive LCL? What is the value of n necessary to give a probability of .50 of detecting a shift in the process to 0.26?
15. Estimate process capability using  and R charts for the power supply voltage data. If specifications are at 350 ± 5 V, calculate PCR, PCR_k and PCR_km. Interpret these capability ratios.

Sample

1. 1 2          3          4          5          6          7          8          9          10

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

x₂:        9          4          8          9          10        11        10        5          7          16

x₃:        10        6          10        6          7          10        8          10        8          10

x₄:        15        11        5          13        13        10        9          4          12        13

16. Find a single sampling plan for which p₁ = 0.05, a = 0.05 p₂ = 0.15 and b = 0.10.
17. What is chain sampling and skip-lot sampling plans?
18. Write short notes on V-mask procedure.

SECTION C  

Answer any TWO questions                                                                      2 x 20= 40

 

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

1. b) Explain process capability analysis with an illustration.        ( 12+8 )

20  a) What are acceptance and rejection lines of a sequential sampling plan for

attributes?. How are the OC and ASN values obtained for this plan

b). A control chart for non-conformities per unit uses 0.95 and 0.05 probability limits.

The center line is at u = 2.4.Determine the control limits if the sample size n =15

(10+10)

21  a) Write a detailed note on the moving average control chart.

1. b) What are modified control charts?. Explain the method of obtaining control limits

for modified control charts.                                                                              (8+12)

22 a) Explain with an illustration the method of obtaining the probability of acceptance

for a double sampling plan.

1. b) What are continuous sampling plans and mention a few situations where these plans

are applied.                                                                                                         (12+8)

 

 

 

Go To Main Page