Manufacturing Technology (ME461) Lecture22

8/12/2019 Manufacturing Technology (ME461) Lecture22

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Review of previous lecture

Failure mode effect analysis Seven tools of QC1. Histogram

2. Check sheet3. Pareto chart

4. Cause and effect diagram5. Scatter daigram

6. Defect concentration diagram7. Control chart


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Control ChartA typical control chart is a graphical display of a quality characteristic measuredon a sample versus the sample number. There are 3 essential elements of acontrol chart:

1. Center line representing the average value of the quality characteristiccorresponding to the in control state.

2. Upper control limit (UCL) represented by the upper horizontal line of the

chart.3. Lower control limit (LCL) represented by the line below the central line.

The selection of the upper and the lower points also depend on the notionthat all the sample points should fall between them if the process is in

control. Points lying outside these limits signal the presence of assignable causes. The process should then be investigated to eliminate assignable causes.


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Variable Control Chart If the quality characteristic can be measured and expressed as a continuous variable, then itcan be conveniently characterized by measures of the central tendency and variability.

Variable control charts can explain the process data in terms of both location (in terms ofaverage) and spread (in terms of piece to piece variability). For this reason the control chartsfor variables are always developed and analyzed in pairs.

The X chart is widely used for controlling central tendency. Charts based on either thesample range (R chart) or the sample standard deviation (S chart) are used to control the

process variability.

The range chart is relatively efficient for smaller subgroup sample sizes, especially below 8.

The S chart is used with larger sample sizes.


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Characteristics of Data( )

The notations are for the average and the standard deviation for a sample of data.

We think as a typical value of the Xs in a sample, or as a point around which thenumbers tend to cluster.

The standard deviation s is a typical deviation of an observation x from the average

It is a deviation descriptive of variation within the sample.

From a well organized frequency distribution as we have already seen above we can saythe following:

1. Between


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Standard deviation

This formulae simplifiescalculations in afrequency table.


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Mean and Variance in a FrequencyTable


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Calculation of Mean and Variance using the frequency method


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Checklist necessary for X and R charts It is helpful to visualize the decisions and calculations that must be made and theactions that need to be taken for plotting a X and a R chart. They are the following:

1. Decisions preparatory to the control charts Some possible objectives of the charts. Choice of variables. Decisions on the basis of subgroups. Decisions on size and frequency of subgroups. Setting up the forms for recording the data.

Determining the method of measurement.2. Starting the Control Charts Making and recording measurements and recording other relevant data. Calculating the average X and range R of each subgroup. Plotting the X and R charts.3. Determining the trial control limits

Decision on required number of subgroups before control limits are calculated. Calculation of trial control limits. Plotting the central lines and limits on the charts.4. Drawing preliminary conclusions from the charts Indication of control or lack of control. Interpretation of processes in control. Relationships between processes out of control and specification limits.


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Decision on the basis of sub-grouping

The key idea in Shewhart method is the division of observations into whatShewhart called rational subgroups .The subgroups should be selected in a way that makes each subgroup ashomogeneous as possible and that gives the maximum opportunity for variationfrom one subgroup to another. As applied to control charts on production, this means that it is of vital importancenot to lose track of the order of production. Particularly, if the purpose of the control chart is to keep detecting shifts in theprocess average, one subgroup should consist of items produced as nearly as

possible at one time; the next subgroup should consist of items all produced at asingle time later; and so forth.

Decision on the size and frequency of subgroups

Shewhart suggested 4 as the ideal sub group size. In industrial uses 5 seems tobe a better alternative because of ease of calculations.The essential idea of the control chart is to select subgroups in a way that givesminimum opportunity for variation within a subgroup. It is therefore desirable thatthe size be as small as possible.Subgroups of two or three may often be used to good advantage, particularlywhere the cost of measurements is so high as to veto the use of largersubgroups.

Larger subgroups of 10 or 20 are sometimes appropriate if it is desired to makethe control chart insensitive to small changes.


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Setting up the forms for recording the data

Layout of data should be as per convenience of calculation and analysis.The forms should have a recording space for item of measurement, unit of

measurement, and operator remarks about tool change, operator change, machinechange etc.


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Starting the Control chartsMaking and recording the measurements and recording other relevant data:

The actual work of the control charts start with the first measurements.

Any method of measurement will have its own inherent variability; it is important that this isnot increased by mistakes in reading measurement instruments or errors in recording data.

Calculating the average and range for each subgroup:


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Possible relationships of a process in control to upperand lower specification limits

Case I: The spread of the process 6 isappreciably less than the differencebetween the specification limits.Case II: The spread is approximatelyequal to the difference between thespecification limits.Case III: The spread of the process isappreciably greater than the differencebetween the specification limits.

C I Wh th 6 i i bl l th diff b t ifi ti


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Case I: When the process 6 is appreciably less than difference between specificationlimits

Frequency curves A,B,C, D and E indicate variouspositions in which the process can be centered.With any of the position A, B and C practically allthe products manufactured will meet thespecifications as long as the process stays in control.In general when conditions A, B and C come itrepresents the ideal manufacturing situation. Whenthe control chart shows that one of this controlchart exists, many different possible actions may beconsidered depending on the relative economy.

For example it may be considered economically advisable to permit X to go out of control if it does not gotoo far, i.e., the distributions may be allowed to move between positions B and C. This may avoid the costof frequent machine setup and of delays due to hunting of assignable causes of variation that will not be

responsible for unsatisfactory product.Or where acceptance has been based on 100% inspection, it may be economical to substitute acceptancebased on control charts.Or where there is an economic advantage to be gained by tightening the specification limits, such actionmay be considered.With the process in the position D some points will fall above the upper specification limit. Similarly withthe process in position E some products will fall below the lower limit. In either case the obvious action isto bring the centering of the process towards that of A.

Case II: When the process 6 is equal to the difference between


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Case II: When the process 6 is equal to the difference betweenspecification limits In this situation only the process

exactly centered between thespecification limits, as in positionA, will practically produceeverything conforming to thespecifications.If the distribution shifts awaythis exact centering as in B or C, itis apparent that some of theproducts will fall outside thespecification limits.

Here the obvious action is to take all steps possible to maintain the centering ofthe process. This usually calls for continuous use of the control charts for X and R

with subgroups at frequent intervals and immediate attention to points out ofcontrol.If fundamental changes can be made that reduce dispersion that eases thepressure.Consideration should also be given to changing of the tolerances.


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Possible relationships of a process in control to a single specification

I: Low value of distribution ( ) isappreciably above LSL.II: Low value of distribution is at LSL.III: Low value of the distribution isappreciably below LSL.

P ibl l i hi f i l i l


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Possible relationships of a process in control to a singlespecification

The first situation is one in which there is a margin of safety.The second is a one in which the specification is just barely met as long as the processstays in control. The third is one in which some non conforming products are produced unless there is afundamental change in the process spread or increase in process average.All three distributions A,B and C have the same lower value. However, distribution B with agreater dispersion must have a greater process average than A for the low points to be atthe same level. Similarly distribution C should have a greater process average than B. It isevident that the greater the distribution the higher the average must be for the entiredistribution to fall above the lower specification limit. The relationship between average and cost is vital in many instances. For example in thefilling of containers a reduction in dispersion may reduce cost by reducing the averageoverfill.

On the other hand, the less the dispersion, the more important it is that the process

average does not go out of control. This is illustrated by comparing distributions A and C inCase III. In Case III both process averages have shifted an equal amount below theirposition. However, the proportion of bad product, as indicated by the area of thedistribution below the specification limit, is much greater in A than in C.


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Use on control charts by a purchaser to help suppliers improvetheir processes.

Facts of the case:

A manufacturer of electronic devices had trouble with the cracking of a certain small cross shapedceramic insulator used in the device.The cracking generally took place after the manufacturing operations were nearly completed and didso in a way that made it impossible to salvage the unit.Hence the costs resulting from each cracked insulators during manufacturing operations suggestedthat others might be likely to crack under service conditions.

In an effort to improve the situation, all incoming insulators of this type were given 100% inspection.This 100% inspection failed to decrease the percentage defective units.A simple testing was then constructed to measure the actual strength in flexure by testing insulatorsto destruction. From each incoming lot of insulators 25 were tested. As the insulators came from 2suppliers, control charts (X and R) from both suppliers were separately maintained. The tests showedthat both suppliers had approximately the same % defectives but the explanations for defectives weredefectives.Supplier A had higher average strength but complete lack of anything resembling statistical control.Supplier B on the other hand had excellent statistical control but at a level such that an appreciablepart of frequency distribution was below the required minimum strength.This diagnosis of the situation was brought to the attention of both suppliers and they wereencouraged to exchange information about production methods. Finally product control could beachieved.

Milli l i i f i l


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Milling a slot in an aircraft terminalblock.

Decisions preparatory to the control chart:

High percentages of rejections for many of the parts made in the machine shop of anaircraft company indicated the need for examination of the reasons for trouble.As most of the rejections were for failure to meet dimensional tolerances, it was decidedto try to find the causes of trouble by the use of X and R charts.These charts which off-course required the measurements of dimensions, were to beused only for those dimensions that were causing numerous rejections.Among the many dimensions, the ones selected for control charts were those havinghigh costs of spoilage and rework and those on which rejections were responsible fordelays in assembly operations.This example deals with one such critical dimension, the width of a slot on the duralumin

forging used as a terminal block at the end of the rear tail or an airplane.The final matching of the slot width was a milling operation. The width of the slot wasspecified as 0.8750 .

The design engineers had specified this dimension with an unilateral tolerance becauseof the fit requirements of the terminal block; it was essential that the slot width be at

least .8750 in and desirable that it is very close to this value.

Milli g l ti d


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Milling example continued Due to the small no. of availableinspection personnel it was decidedthat for each chart the sample would

be inspected would be approximately5% of the total production of the partsin question.It was decided that all measurementswould be made at the place ofproduction and it was decided that a

part be measured every 20 partsproduced. The subgroup size was thusfixed as 5. The figure on left shows allobservations. The method to inspection to securedata for each of the charts was tomeasure two portions of the slot widthusing a micrometer screw gauge andaverage these measurements.

Milli l i d


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Milling example continuedStarting the control charts:

The actual measurements of the first 16 subgroups are shown in the table. These numbers of subgroupscorrespond to a production order for 1600 of these terminal blocks.At the time of the 12 th subgroup, before the completion of this production order and before the calculation of thecentral line or control limits, the quality control inspector noticed that the machine operator was occasionallychecking performance on a terminal block that had just come off the machine and was still hot.After the 12 th subgroup the operator was asked to do measurements after some time of cooling is allowed.

Determining the trial control limits:

Calculations of the trial control limits wasmade after the first 16 subgroups whichcompleted the production order. As shown inthe figure on the right these were done byfinding out the A 2 and D 4 factors for asubgroup size 5.

Drawing preliminary conclusions from thegraphs:

Subgroup 1 is above the upper control limiton the R chart.Subgroup 10 is below the lower control limit

on the X chart. Moreover the last 10- of the 6points fall below the central line.


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Milling Example ContinuedIt is obvious that the measurements madeare not the result of a constant system ofchance causes. If subgroup 1 is eliminated fromconsideration, R for the remaining 15subgroups is 536/ 15 = 36. This gives us a revised upper control limit

D4 (R) = 2.11 (36) = 76.

Subgroup 5 falls exactly on the upper

control limit in the X chart. Hence a secondrevision of R with subgroup 5 eliminatedseems reasonable. Therefore R = 460/14 =33. .

An estimate may be made of from the Rvalues. With a d 2 value of 2.362corresponding to the subgroup size 5 we geta = R/ d 2 = 0.0014 in.

The value of the natural tolerance or spreadof the process is therefore 6 = 6 (.0014) =.0084 in.

This spread may be compared with

tolerance spread: U-L = .0050in

It is evident from the process that the natural tolerance of thespread is substantially greater than the specified tolerance.Therefore, unless the process dispersion is reduced the processwill keep producing non conforming components.

Manufacturing Technology (ME461) Lecture22

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Transcript of Manufacturing Technology (ME461) Lecture22