Statistical Process Control 6th Edition John S Oakland - Solutions

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In Section 2.5.2 we noted that one of the reasons that water quality microbiological standards may use the sample median rather than the sample geometric mean is that the sample geometric mean is always a biased estimator of the true geometric mean. Can you think of another reason?
Show that the sample geometric mean can be calculated as the antilog of the mean of the sample logarithms. Apply this to the MPN data given on Table 2.1. What are the implications if one of the data values is zero?
Show that the area under a normal distribution between the mean plus or minus one standard deviation is 0.6826 and that the area under that distribution between the mean plus or minus two standard deviations is 0.9544. Show that these results hold for any normal distribution.
What is the total area under the "sampling distributions" (unit normal, t, x2 and F), and why is this?
Why is precision of measurements different from precision of an estimate?
In the estuary deposition example in Section 2.1, what would be the impact on the posterior probability had the tribunal taken an impartial stance regarding the merits of the two competing hypotheses, before hearing further evidence?.6 For three events A, B, and C, where A is sampled from one
Continuing the estuarine deposition example in Section 2.1, let's consider that the urbanization pressure is not expected for another 20 years, and that climate scientists advise that there is a 70% chance that there will be a climate shift in that period such as to modify the probabilities to
What is the difference between independent events and mutually exclusive events?
What can you say about the relative values of the probabilities Pr(A|B) and Pr(A and В)?
What is the distinction between the probabilities Pr(A B) and Pr(A and B)?Give an example.
6 As quality director of a large aircraft manufacturing organization, you are considering the launch of a six-sigma-based continuous improvement programme in the company. Explain in detail the key stages of how you will ensure the financial success of the six-sigma projects that will be part of the
5 What is Design of Experiments (DoE)? What are the basic steps in DoE and how do they link together to support six-sigma approaches?
4 You have been appointed operations director of a manufacturing and service company which has a poor reputation for quality. There have been several attempts to improve this during the previous 10 years, including quality circles, ISO9000-based quality systems, SPC, TQM and the Excellence Model.
3 Detail the steps of the six-sigma DMAIC methodology (Define, Measure, Analyse, Improve, Control) and indicate the tools and techniques which might be appropriate at each stage.
2 Using process capability indices, such as Cp and Cpk (see Chapter 10)explain the different performance levels of 1 to 6 sigma increasing by integers.
1 Explain the statistical principles behind six-sigma process quality and why it is associated with 3.4 ppm defect rate. Show the effect of increasing sigma capability on ‘defects per million opportunities’and how this relates to increased profits.
5 Reducing the variation of key processes should be a major objective of any improvement activity. Outline a three-step approach to assigning nominal target values and tolerances for variables (product or process parameters) and explain how this will help to achieve this objective.
4 What are the major headings of Taguchi’s approach to reducing costs and improving quality in manufacturing? Under each of these headings, give a brief summary of Taguchi’s thinking. Explain how this approach could be applied in a service environment.
3 Discuss in detail the ‘never-ending improvement cycle’ and link this to the activities of a team facilitator.
2 What is the role of teamwork in process improvement? How can the simple techniques of problem identification and solving help teams to improve processes?
1 Explain how a documented management system can help to reduce process variation. Give reasons why the system and SPC techniques should be introduced together for maximum beneficial effect.
6 (a) Explain the term ‘hunting’ and show how this arises when processes are adjusted on the basis of individual results or data points.(b) What are the most frequently found assignable or special causes of process change?
5 Sketch the cusum charts for mean which you would expect to plot from the process changes listed in question 4.
4 Describe, with the aid of sketch diagrams, the patterns you would expect to see on control charts for mean for processes which exhibit the following types of out of control:(a) sustained shift in process mean;(b) drift/trend in process mean;(c) frequent, irregular shift in process mean.Assume no
3 Discuss the ‘effects of single factors’ and ‘group factors’ in planning process investigations.
2 Explain how you would develop a process improvement study paying particular attention to the planning of data collection.
1 You are the Operations Manager in a medium-sized manufacturing company which is experiencing quality problems. The Managing Director has asked to see you and you have heard that he is not a happy man; you expect a difficult meeting. Write notes in preparation for your meeting to cover: which
8 A company which operates with a 4-week accounting period is experi- encing difficulties in keeping up with the preparation and issue of sales invoices during the last week of the accounting period. Data collected over two accounting periods are as follows: Accounting Period 4 Number of sales
7 A mortgage company finds that some 18 per cent of application forms received from customers cannot be processed immediately, owing to the absence of some of the information. A sample of 500 incomplete application forms reveals the following data: Information missing Applicant's Age Daytime
6 The manufacturer of domestic electrical appliances has been examining causes of warranty claims. Ten have been identified and the annual cost of warranty work resulting from these is as follows:306 Statistical Process Control Cause Annual cost of warranty work (£)A 1090 B 2130 C 30690 D 620 E
5 The principal causes of accidents, their percentage of occurrence, and the estimated resulting loss of production per annum in the UK is given in the table below:Accident cause Percentage of all Estimated loss of production accidents (£million/annum)Machinery 16 190 Transport 8 30 Falls from
4 A company manufactures a range of domestic electrical appliances.Particular concern is being expressed about the warranty claims on one particular product. The customer service department provides the following data relating the claims to the unit/component part of the product which caused the
3 Discuss in detail the applications of Pareto analysis and cause and effect analysis as aids in solving operations management problems.Give at least two illustrations.You are responsible for a biscuit production plant, and are concerned about the output from the lines which make chocolate
2 You have inherited, unexpectedly, a small engineering business which is both profitable and enjoys a full order book. You wish to be personally involved in this activity where the only area of immediate concern is the high levels of scrap and rework – costing together a sum equivalent to about
1 You are the Production Manager of a small engineering company and have just received the following memo:MEMORANDUM To: Production Manager From: Sales Manager Subject: Order Number 2937/AZ Joe Brown worked hard to get this order for us to manufacture 10,000 widgets for PQR Ltd. He now tells me
6 In Discussion question No. 10 in Chapter 6, the specification was given as 540 5 mm, comment further on the capability of the panel making process using process capability indices to support your arguments.
5 Show the difference, if any, between Machine I and Machine II in Discussion question No. 9 in Chapter 6, by the calculation of appropriate process capability indices.
4 Calculate Cp and Cpk process capability indices for the data given in Discussion question No. 8 in Chapter 6 and write a report to the Development Chemist.
3 From the results of your analysis of the data in Discussion question No. 6, Chapter 6, show quantitatively whether the process is capable of meeting the specification given.
2 Using the data given in Discussion question No. 5 in Chapter 6, calculate the appropriate process capability indices and comment on the results.
1 (a) Using process capability studies, processes may be classified as being in statistical control and capable. Explain the basis and meaning of this classification.(b) Define the process capability indices Cp and Cpk and describe how they may be used to monitor the capability of a process, its
10 A cusum scheme is to be installed to monitor gas consumption in a chemical plant where a heat treatment is an integral part of the process. The engineers know from intensive studies that when the system is operating as it was designed the average amount of gas required in a period of 8 hours
9 The data given below are taken from a process of acceptable mean value μ0 8.0 and unacceptable mean value μ1 7.5 and known standard deviation of 0.45.Sample number x –Sample number x –1 8.04 11 8.11 2 7.84 12 7.80 3 8.46 13 7.86 4 7.73 14 7.23 5 8.44 15 7.33 6 7.50 16 7.30 7 8.28 17
8 Small plastic bottles are made from preforms supplied by Britanic Polymers. It is possible that the variability in the bottles is due in part to the variation in the preforms. Thirty preforms are sampled from the extruder at Britanic Polymers, one preform every 5 minutes for two and a half hours.
7 Middshire Water Company discharges effluent, from a sewage treatment works, into the River Midd. Each day a sample of discharge is taken and analysed to determine the ammonia content. Results from the daily samples, over a 40-day period, are given in the table.Ammonia content Day Ammonia (ppm)
5 Shewhart charts are to be used to maintain control on dissolved iron content of a dyestuff formulation in parts per million (ppm). After 25 subgroups of 5 measurements have been obtained,i-25 =390 and R = 84, where I mean of ith subgroup; R = range of ith subgroup; Design appropriate cusum charts
4 The table below gives the average width (mm) for each of 20 samples of five panels. Also given is the range (mm) of each sample.Sample number Mean Range Sample number Mean Range 1 550.8 4.2 11 553.1 3.8 2 552.7 4.2 12 551.7 3.1 3 553.9 6.7 13 561.2 3.5 4 555.8 4.7 14 554.2 3.4 5 553.8 3.2 15
3 The following record shows the number of defective items found in a sample of 100 taken twice per day.Sample number Number of Sample Number of defectives number defectives 1 4 21 2 2 2 22 1 3 4 23 0 4 3 24 3 5 2 25 2 6 6 26 0 7 3 27 1 8 1 28 3 9 1 29 0 10 5 30 3 11 4 31 0 12 4 32 2 13 1 33 1 14 2
2 In the table below are given the results from the inspection of filing cabinets for scratches and small indentations.Cabinet No. 1 2 3 4 5 6 7 8 Number of defects 1 0 3 6 3 3 4 5 Cabinet No. 9 10 11 12 13 14 15 16 Number of defects 10 8 4 3 7 5 3 1 Cabinet No. 17 18 19 20 21 22 23 24 25 Number of
1 (a) Explain the principles of Shewhart control charts for sample mean and sample range, and cumulative sum control charts for sample mean and sample range. Compare the performance of these charts.(b) A chocolate manufacturer takes a sample of six boxes at the end of each hour in order to verify
8 Acontrol chart for a new kind of plastic is to be initiated. Twenty-five samples of 100 plastic sheets from the assembly line were inspected for flaws during a pilot run. The results are given below. Set up an appropriate control chart.Sample No. 1 2 3 4 5 6 7 8 Number of flaws/sheet 2 3 0 2 4 2
7 Given in the table below are the results from the inspection of filing cabinets for scratches and small indentations.Cabinet No. 1 2 3 4 5 6 7 8 Number of defects 1 0 3 6 3 3 4 5 Cabinet No. 9 10 11 12 13 14 15 16 Number of defects 10 8 4 3 7 5 3 1 Cabinet No. 17 18 19 20 21 22 23 24 25 Number of
6 Twenty samples of 50 polyurethane foam products are selected. The sample results are:Sample No. 1 2 3 4 5 6 7 8 9 10 Number defective 2 3 1 4 0 1 2 2 3 2 Sample No. 11 12 13 14 15 16 17 18 19 20 Number defective 2 2 3 4 5 1 0 0 1 2 Design an appropriate control chart.Plot these values on the
5 The following record shows the number of defective items found in a sample of 100 taken twice per day.Sample number Number of Sample number Number of defectives defectives 1 4 11 4 2 2 12 4 3 4 13 1 4 3 14 2 5 2 15 1 6 6 16 4 7 3 17 1 8 1 18 0 9 1 19 3 10 5 20 4 Sample number Number of defectives
4 Afactory finds that on average 20 per cent of the bolts produced by a machine are defective. Determine the probability that out of 4 bolts chosen at random:(a) 1, (b) 0, (c) at most 2 bolts will be defective.
3 Write down the formulae for the probability of obtaining r defectives in a sample of size n drawn from a population proportion p defective based on:(i) the binomial distribution;(ii) the Poisson distribution.
2 Explain the difference between an:np-chart, p-chart, c-chart.
1 (a) Process control charts may be classified under two broad headings,‘variables’ and ‘attributes’. Compare these two categories and indicate when each one is most appropriate.(b) In the context of quality control explain what is meant by a number of defectives (np-) chart.
8 (a) Discuss the use of control charts for range and standard deviation, explaining their differences and merits.(b) Using process capability studies, processes may be classified as being in statistical control and capable. Explain the basis and meaning of this classification. Suggest conditions
7 The National Rivers Authority (NRA) also monitor the discharge of effluent into the River Midd. The NRA can prosecute the Water company if ‘the ammonia content exceeds 30 ppm for more than 5 per cent of the time’.The current policy of Middshire Water Company is to achieve a mean ammonia
6 Middshire Water Company discharges effluent, from a sewage treatment works, into the River Midd. Each day a sample of discharge is taken and analysed to determine the ammonia content. Results from the daily samples, over a 40 day period, are given below:Ammonia content Day Ammonia (ppm)
5 The weekly demand of a product (in tonnes) is given below. Use appropriate techniques to analyse the data, assuming that informa- tion is provided at the end of each week.Week Demand (Tn) Week Demand (Tn)1 7 25 8 2 5 26 7.5 3 8.5 27 7 4 7 28 6.5 5 8.5 29 10.5 6 8 30 9.5 7 8.5 31 8 8 10.5 32 10 9
4 The catalyst for a fluid-bed reactor is prepared in single batches and used one at a time without blending. Tetrahydrofuran (THF) is used as a catalyst precursor solvent. During the impregnation (SIMP) step the liquid precursor is precipitated into the pores of the solid silica support. The solid
3 In a batch manufacturing process the viscosity of the compound increases during the reaction cycle and determines the end-point of the reaction. Samples of the compound are taken throughout the whole period of the reaction and sent to the laboratory for viscosity assessment.The laboratory tests
2 The data in the table opposite shows the levels of contaminant in a chemical product:(a) Plot a histogram.(b) Plot an individuals or run chart.(c) Plot moving mean and moving range charts for grouped sample size n 4.Interpret the results of these plots.Sample Result (ppm) Sample Result (ppm)1
1 Comment on the statement, ‘a moving mean chart and a conventional mean chart would be used with different types of processes’.
10 The following table gives the average width in millimetres for each of 20 samples of five panels used in the manufacture of a domestic appliance. The range of each sample is also given.Sample Mean Range Sample Mean Range number number 1 550.8 4.2 11 553.1 3.8 2 552.7 4.2 12 551.7 3.1 3 553.8 6.7
9 Conventional control charts are to be used on a process manufacturing small components with a specified length of 60 1.5 mm. Two identical machines are involved in making the components and process capability studies carried out on them reveal the following data:Sample size, n 5 Sample number
8 The following data were obtained when measurements of the zinc concentration (measured as percentage of zinc sulphate on sodium sulphate) were made in a viscose rayon spin-bath. The mean and range values of 20 samples of size 5 are given in the table.Sample Zn conc. Range Sample Zn conc. Range(%)
7 You are a trader in foreign currencies. The spot exchange rates of all currencies are available to you at all times. The following data for one currency were collected at intervals of 1 minute for a total period of 100 minutes, five consecutive results are shown as one sample.Sample Spot exchange
6 You are a Sales Representative of International Chemicals. Your Manager has received the following letter of complaint from Perplexed Plastics, now one of your largest customers.To: Sales Manager, International Chemicals From: Senior Buyer, Perplexed Plastics Subject: MFR Values of Polymax We
5 Plot the following data on mean and range charts and interpret the results. The sample size is 4 and the specification is 60.0 2.0.Sample Mean Range Sample Mean Range number number 1 60.0 5 26 59.6 3 2 60.0 3 27 60.0 4 3 61.8 4 28 61.2 3 4 59.2 3 29 60.8 5 5 60.4 4 30 60.8 5 6 59.6 4 31 60.6 4
4 You are responsible for a small plant which manufacturers and packs jollytots, a children’s sweet. The average contents of each packet should be 35 sugar-coated balls of candy which melt in your mouth.Every half-hour a random sample of five packets is taken and the contents counted. These
3 The following are measures of the impurity, iron, in a fine chemical which is to be used in pharmaceutical products. The data is given in parts per million (ppm).Sample X1 X2 X3 X4 X5 1 15 11 8 15 6 2 14 16 11 14 7 3 13 6 9 5 10 4 15 15 9 15 7 5 9 12 9 8 8 6 11 14 11 12 5 7 13 12 9 6 10 8 10 15
2 A machine is operated so as to produce ball bearings having a mean diameter of 0.55 cm and with a standard deviation of 0.01 cm. To determine whether the machine is in proper working order a sample of six ball bearings is taken every half-hour and the mean diameter of the six is computed.(a)
1 (a) Explain the principles of Shewhart control charts for sample mean and sample range.(b) State the Central Limit Theorem and explain its importance in SPC.
5 To: International Chemicals Supplier From: Senior Buyer, Perplexed Plastics Ltd SUBJECT: MFR Values of Polyglyptalene As promised, I have now completed the examination of our delivery records and have verified that the values we discussed were not in fact in chronological order. They were simply
4 State the Central Limit Theorem and explain how it is used in SPC.
3. Abottle filling machine is being used to fill 150 ml bottles of a shampoo.The actual bottles will hold 156 ml. The machine has been set to discharge an average of 152 ml. It is known that the actual amounts discharged follow a normal distribution with a standard deviation of 2 ml.(a) What
2 Describe the characteristics of the normal distribution and construct an example to show how these may be used in answering questions which arise from discussions of specification limits for a product.
1 Calculate the mean and standard deviation of the melt flow rate data below (g/10 minutes):3.2 3.3 3.2 3.3 3.2 3.5 3.0 3.4 3.3 3.7 3.0 3.4 3.5 3.4 3.3 3.2 3.1 3.0 3.4 3.1 3.3 3.5 3.4 3.3 3.2 3.2 3.1 3.5 3.2 3.3 3.2 3.6 3.4 2.7 3.5 3.0 3.3 3.3 2.4 3.1 3.6 3.6 3.5 3.4 3.1 3.2 3.3 3.1 3.4 2.9 3.6 3.6
5 How could the overall variability of a process be determined? What does the term ‘capability’ mean in this context?
4 ‘In the examination of process data, a distinction should be made between accuracy and precision.’ Explain fully the meaning of this statement, illustrating with simple everyday examples, and suggesting which techniques may be helpful.
3 (a) What is meant by the inherent variability of a process?(b) Distinguish between common (or random) and special (or assignable) causes of variation, and explain how the presence of special causes may be detected by simple techniques.
2 (a) Explain why mangers tend to look at individual values – perhaps monthly results, rather than obtain an overall picture of data.(b) Which simple techniques would you recommend to managers for improving their understanding of process and the variation in them?
1 Design a classroom ‘experience’, with the aid of computers if necessary, for a team of senior managers who do not appear to understand the concepts of variation. Explain how this will help them understand the need for better decision-making processes.
5 To establish a manufacturing specification for tablet weight, a sequence of 200 tablets was taken from the production stream and the weight of each tablet was measured. The frequency distribution is shown below.State and explain the conclusions you would draw from this distribution, assuming the
4 The table below shows the recorded thicknesses of steel plates nominally 0.3cm 0.01 cm. Plot a frequency histogram of the plate thicknesses, and comment on the result.Plate thicknesses (cm).2968 .2921 .2943 .3000 .2935 .3019 .2991 .2969 .2946 .2965 .2917 .3008 .3036 .3004 .2967 .2955 .2959
3 Describe, with examples, the methods which are available for presenting information by means of charts, graphs, diagrams, etc.
2 Operators on an assembly line are having difficulties when mounting electronic components onto a printed circuit board. The difficulties include: undersized holes in the board, absence of holes in the board, oversized wires on components, component wires snapping on bending, components longer
1 Outline the principles behind a systematic approach to process improvement with respect to the initial collection and presentation of data.
4. What are the steps in a critical examination of a process for improvement?Flowchart these into a systematic approach.
3 Describe in detail the technique of flowcharting to give a ‘dynamic model’ of a process. Explain all the symbols and how they are used together to create a picture of events.
2 Construct a ‘static model’ or map of a process of your choice, which you know well. Make sure you identify the customer(s) and outputs, suppliers and inputs, how you listen to the ‘voice of the customer’and hear the ‘voice of the process’.
1 Outline the initial steps you would take first to understand and then to improve a process in which you work.
8 What are the basic tools of SPC and their main application areas?
7 Explain a system for SPC which concentrates attention on prevention of problems rather than their detection.
6 Using a simple model of a process, explain the main features of a process approach to quality management and improvement.
5 You are a management consultant and have been asked to assist a manufacturing company in which 15 per cent of the work force are final product inspectors. Currently, 20 per cent of the firm’s output has to be reworked or scrapped.Write a report to the Managing Director of the company
4 MEMORANDUM To: Quality Manager From: Managing Director SUBJECT: Quality Costs Below are the newly prepared quality costs for the last two quarters:Last quarter First quarter last year this year Scrap and Rework £156,000 £312,000 Customer returns/warranty £262,000 £102,000 Total £418,000

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Statistical Process Control 6th Edition John S Oakland - Solutions

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