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Semester II Examinations 2008/ 2009
Exam Code(s) 1DQ1, 4BI
Exam(s) Higher Diploma in Quality Assurance BE Degree Industrial Engineering & Information Systems
Module Code(s) IE879, IE Module(s) Statistical Quality Control II Quality Engineering
External Examiner Prof J Antony Internal Examiners Dr D O'Sullivan Prof J Sheil
Instructions: Answer Q1,^ and^ any^ two^ from Q2, Q3, Q4, Q5, Q
Duration: 2 Hours
No. of Pages: 3 plus cover Department: Industrial Engineering Course Coordinator: Prof J Sheil
Attachment(s): Control Chart Factors
Requirements : Cambridge Elementary Statistical Tables Graph Paper Mathematical ('log') Tables
Q1. [compulsory: 40(10x4 ) marks ]
(i) How are conventional Shewhart Control Charts constructed and interpreted? (ii) State the principal statistical/distributional assumptions underlying the design and interpretation of each of the following control charts: R-charts , np-charts , c-charts.
(iii) Lower Control Limits are sometimes omitted from control charts. List any three control chart types that are subject to this practice, and state why the practice is followed.
(iv) What practical considerations dictate the use of demerit rating/control systems. Suggest a possible demerits system for quantifying vendor performance. (v) A c-chart with UCL at c = 8 and LCL at c = 1 is used in conjunction with a process which, when in-control , produces(on average) 2 defects per observation unit. What is the false alarm rate?
(vi) If Cpu = 1.7 and Cpl = 0.9, find Cpk and Cp and interpret their values.
(vii) In completing a Gauge Capability Study you have found/estimated σrepeatability and σreproducibility as 1.02 and 0.19 respectively. Comment on the relative sizes of these two components of measurement error and estimate σgage.
(viii) The diagram below shows three components linked to form a simple assembly. Specifications on individual component lengths are also shown. Calculate conventional and statistical tolerance limits on the overall length of the assembly, stating any assumptions underlying your analysis.
1±0.002 1.5±0.002 2±0.
(ix) Consider a single (n, c) attributes sampling plan where n = 50 and c =2. At what level of lot quality (θ) will this plan reject lots 90% of the time?
(x) In what way(s) do Dodge-Romig AOQL sampling plans differ from LTPD plans?
Q2. (30 marks) (a) Write very briefly on each of the following: (i) Differentiate between probability limits and 3-sigma limits for control charts. (ii) What does it mean if a process is in a state of statistical control? [4 marks] (b) A process producing gaskets is to be controlled by using an np-chart. Samples of 150 gaskets have been examined each day for the past 25 days. The daily numbers of nonconforming gaskets found in the samples were as follows:
4, 3, 5, 3, 6, 3, 2, 3, 1, 6, 5, 3, 2, 4, 7, 1, 2, 3, 4, 3, 2, 5, 3, 4, 6.
Establish a control chart to control future production. [20 marks]
Suggest a smallest subgroup size which might be used in this case, if a non-zero lower control limit is required. [6 marks]
Q5. (30 marks) Write a technical essay on Process Capability Analysis. Your essay should explain what the term means and should list reasons for conducting such analyses. You could also consider the tools/techniques/measures used in conducting and reporting capability studies, how to interpret these, etc. A minimum of 12 specific points, pieces of information is envisaged and your presentation must take the form of an essay - a cryptic listing of points will attract minimal credit.
Q6. (30 marks)
(a) Consider a single (n, c) attributes sampling plan which is being used for acceptance sampling of a stream of lots of size N. Let θ represents the lot fraction nonconforming. The probability P(θ), that a lot is passed, can be approximated by c
P(θ) ≅ Σ (n θ)r.e-^ n^ θ/r!
r=
Explain/show how this expression for P(θ) is arrived at? [5 marks]
If rejected lots are 'screened'/rectified, show that the average number of items inspected per lot is I(θ) = Ν − (Ν−n).P(θ). [3 marks] Ηence, determine the average number of items rectified per lot when a: (i) (50, 0) plan is used in conjunction with lots of 1000 items, generated by a process which yields an average of 99% good units; [4 marks] (ii) (80, 1) plan is used where the lot size is 2000 and the process average is 2% nonconforming [4 marks]
For both (i) and (ii) above, determine long-run average values for the lot proportion defective, after completion of the sampling/rectification activity. [4 marks]
(b) What is meant by the ASN of a double sampling plan? [ 2 mark ]
For the double sampling plan with n 1 = n 2 = 50, c 1 = 1 and c 2 = 4, find P(θ) and the ASN when θ = 0.1. [8 marks]
