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16Received December 1991Revised May 1992

M odelling F ai lure M odes a n d

Effects AnalysisWarren Gilchrist

Sheffield Hallam University, UK

IntroductionThe world of quality control and improvement has , like so many others in thepast, developed by inspiration and expediency, driven by practical need.

There comes a time, however, when some of the ad hoc techniques need to beput on a more rigorous theoretical base; otherwise they lack the precisionfrom which new developments can take place. In particular, they need to bespecified in term s of a clear model, so tha t their natu re and properties can beclearly understood. One technique which would appear to be in need of sucha development is failure modes and effects analysis (FMEA).

The objective of this article is to propose a model for FMEA. In thefollowing sections we look at the nature of FMEA, examine the internalproblems and contradictions of the methods used, propose a more rigorousmodel and examine its properties, look at some further extensions of themodel and, finally, draw some conclusions.

Brief Review of FMEThe standard definitions and structure of FMEA are often taken to be thosepublished by the Ford Motor Com pany[l,2].

The general structure of the fault process analysed by FMEA is shown inFigure 1.

FMEA is a systematic method of seeking out potential causes of failurebefore they become a reality. It is intended to be applied during thedevelopment stages of a product or service, when it is being defined anddesigned and when the production/delivery is being planned. It is also

beginning to be used in the design of systems. It is a tool designed for use byteams. Historically it was in use by NASA as early as 1963 but becamebetter known when implemented by the Ford car manufacturers in about1977. The Ford Instruction Manual[l,2] appears to be the best-knowndocument on the subject, but see also Feigenbaum[3] and Juran[4]. Noteth at FMEA is sometimes referred to as FMECA (failure modes and effectscriticality analysis)[5].

Faults a re produced in reality in production, bu t are created potentially a tthe design and planning stage of a product. FMEA provides a systematicway of identifying faults and assessing the risks associated with failures andfaults. The problems are identified and the effectiveness of remedial actionassessed. There is a standard form almost universally used to carry through

International Journal of Quality &Reliability Management,Vol. 10 No 5,19 93, pp 16-23© MCB University Press,0265-671X

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the analysis, which is carried out by a team of people with direct knowledgeof the products and processes concerned. The elements in the process are:

• The identification and listing of modes of failure and the consequentfaults.

• Assessing the chances that these faults occur.• Assessing the chances that the faults are then detected.• Assessing the severity of the consequences of the faults.• Calculating a measure of risk.• The ranking of the faults on the basis of the risk.• Action on the high-risk problems.• Checking the effectiveness of the action, using a revised measure of

risk.The two sets of chances and the severity are measured and themeasurements combined to create a measure of risk, so that highly criticalfaults may be prioritized above less critical faults. The measure of risk, therisk priority num ber (RPN), also gives a way of measuring the reduction inrisk produced by the counter-measures taken in the critical cases. The threemeasures of chance and severity make use of ten-point scales with 10denoting a high chance of a fault being produced, a high chance of it reachingthe customer, undetected by the producer, and a high severity in its effect.Table I shows a typical basis for these scales. The numbers given on thesescales are called scores or ranks. We denote the chance of failure score bySf , the chance of undetection score by Sd and the severity of the effect ofthe failure on the customer by S. The RPN is then given by:

RPN = S fS dS.

Table II illustrates the layout of an FMEA and the calculation of the RPN.The various faults are ranked on the basis of their RPN. A successful attackon the fault will reduce the RPN.

Crit ique of FMEThe approach and concept of FMEA has proved to be highly successful. Theuse of a standard form and a way of prioritizing failure modes and theireffects is central to the method. It is not the intention of this article to criticizethese general features of FMEA. The criticism is of the way in which theRPN is derived. The ad hoc way FMEA has developed has led to a measure

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a) The chance of a fault occurring

Criteria

Remote chance of failureLow failure rate

Moderate failure rate

High failure rate

Very high failure rate

Score123456789

10

b) The chance of a fault reaching the customer

Chan ce of not d etecting fault

Remote

Low

Moderate

High

Very high

c) The severity of a fault

Severity

Customer will probably not noticeSlight annoyanceCustomer dissatisfactionHigh degree of dissatisfaction

Safety/regulatory consequences

Score

1

23

456

78

910

Possible failure

occurrence rat es

01/20,0001/10,0001/20001/10001/2001/1001/201/101/2

Probability of anindividual defect

reaching the customer

Per cent

0 - 5

6 - 1 51 6 - 2 5

2 6 - 353 6 - 454 6 - 55

5 6 - 656 6 - 75

7 6 - 858 6 - 1 0 0

Score

12,3

4,5,67,8

9,10able I.

FMEA Scores (Ranks)

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which does not satisfy the usual requirements of measurement. To see this,consider the elements of the RPN , outlined below.

The Chance That a Fault OccursThe standard assessment of the chance of a fault occurring uses a scoringsystem with scores, Sf,, going from 1 to 10, as in Table II. These aretraditionally called Ranks, though they are not ranks according to the correctuse of the word. The score 1 represents a remote probability of occurrence, 10a very high failure rate of around 0.5 and above. The suggested relationbetween the score and the probability expressed as 1/200 or 1/2,000 is highlynon-linear, with 3 to 4 going from 1/10,000 to 1/2,000 (a change of 0.0004and 7 to 8 going from 1/100 to 1/20 (a change of 0.04).

The Chance of Failure of DetectionThe assessment of the chance of not detecting a fault, once it has occurred, isalso based on a 1 to 10 scoring system, Sd, going from 1 to remote to 10 forvery high. However, in suggesting an equivalent probability scale a linearrelation is now chosen, as in Table I. A consequence of choosing differentscales is that there seem to be no sensible rules of algebra to apply to thesenumbers. The RPN multiplies them. Thus, if the fault score is 3 and thedetection score is 4, we get a 12. If the fault score is 4 and the detection scoreis 3, we also ge t 12 bu t in the first case the probability of a customer getting afaulty part is around 0.00003, while in th e second it is about 0 00010 Yet the

RPN should measure the chance of a customer receiving a faulty part.According to the rules of probability we can halve the risk of a customergetting such a part by either halving the chance of it being produced orhalving the chance of it not being detected. This simple requirement is notmodelled by the scoring systems recommended for use in FMEA.

The SeverityThe third element in the R PN is the severity of the effect on the customers ofthe fault reaching them, S . A gain, a scoring system is used with a 1 for thesituation where a customer will not even notice the fault to a 10, where there

are regulatory or safety consequences. (For severity of 9 or 10 Fordrecommend special action, irrespective of the probabilities.) This is a notunreasonable scoring system but the comparison of scores is not really

Process

Process A

Potentialfailuremode

Failuremode A

FailuremodeB

Potentialeffect offailure

Effect A

Effect B

Potentialcause offailure

Cause ACause BCause C

Cause DCause E

Sf

8105

98

Sd

5104

74

S

444

88

RPN

16014080

504256Table II.

Illustrative FMEALayout

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probability. So why not express the chance of a fault and the chance tha t itescapes detection by probabilities P f and pd?Assuming tha t these are

independent, then the probability that the customer receives a faulty par t is,by the multiplication law of probability, pf x pd . The values of theseprobabilities can be estimated by the use of standard production andcustomer records and the results of sampling inspection. The cost of thecustomer receiving this faulty part may be harder to estimate. However, thewhole philosophy of modern quality think ing is that we need to make a veryserious attempt to understand and estimate these costs. We may finish upwith very rough estimates, based on our own internal costs of scrap, rework,warran ty, etc., all of which the customer ultimately has to pay. Even so, thiswill be better than the totally unclear scoring system. Suppose that the costper fault is C and suppose tha t n items are produced per batch or per year,then the average (termed expected by theory) cost on the customers is

EC = Cnpfpd,

where EC stands for expected cost and npf pd is the expected number of faultsreaching the customers. This measure of the cost of faults avoids all thepitfalls of the RPN and it has the great benefit of forcing people to thinkabout quality costs. If we find the EC value for a particular fault over a yearis £50,000, not only does it help us to pu t it in a priority ranking, bu t also itgets our attention as something into which we have to be prepared to putresources in order to get it right.

It is accepted that estimating probabilities with any great accuracy is adifficult task. Figure 2 gives a layout in which the probabilities usedcorrespond to either 1 or 5 parts per 10, 100, 1,000, 10,000 etc. The faultsillustrated are the dents, splits and blemishes which occur in glassmanufacture. Provided th at the expected costs are not similar, this does wellas a provider of ball-park figures, which are all th at are usually needed. Thechoice of wha t probabilities to use in such a layout will depend on the knownbehaviour of the products considered and is best decided by the team as partof the FMEA exercise.

Extending the ModelHaving obtained the model, it can be readily extended to cover furthersophistications:

(1) Suppose that the fault has an underlying cause which occurs withprobability p. Experience suggests that in some areas an underlyingfault, say with a m achine, does not always produce 100 per cent faultyproducts. So we assume that, when present, the cause has the effect ofproducing the fault with probability pe. In this case

P f= PP e.Thus EC = Cnppepd.

(2) Suppose tha t there are several possible costs to the customer. He m ay

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ault occurrence

Failuremode

Probability1/105/1001/1005/1,0001/1 0005/10,0001/10 0005/100,0001/100 000

5/1,000,0001/1 000 000

1. Dent

Undetection probabilitiesFailuremode

Probability10/108/106/103/101/10

5/1001/1005/1,0001/1 0001/10 000

ostsFailuremode1. Dent2. Split3. Blemish

1. Dent

Cost peritem £

30100

10

1/1 000 = 1 fault per 1,000 items= Probability fault) = 0.001

2. Split 3. Blemish

1/10 = out of ten faulty parts one not detected

2. Split

Production/month100,000

50,000100,000

3. Blemish

ProbabilitiesOccurrence Unde tection Expected cost

0.01 0.1 3,0000.0005 0.05 1250.001 0.005 5

Figu re 1.FMEA ProbabilitySheet

spot the fault (probability ps)and return it under warran ty (cost W).He may not spot it pm), have an accident and sue the company (costA). We can construct simple models for this type of situation. Here Cwould become a n expected cost:

C = p sW + pmA.

There is also a probability, 1 — ps — pm, that the firm gets away withit. These calculations can get difficult, b ut it is worth remembering tha tthey are the stock-in-trade of the actuarial profession. A quoted

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insurance price will give an estimate of such expected costs (after somerounding down).

(3) As indicated above, the way in which the RPN is built up implies th atRPNs from different faults cannot be sensibly added. The expectedcosts, like any costs, can be added. The table of expected costs producedby FMEA can therefore be used not only for ranking but also as thebasis for a proper Pareto analysis of the Cumulative Expected Costs.This additive feature can be combined with the type of underlyingcause model of (1) to look at its overall expected cost. For example,suppose the underlying cause, occurring with probability p, canproduce three types of failure, A, B and C, with probabilities pa pb andpc respectively and with fault non-detection probabilities of r a r b and r crespectively. The total expected cost for this underlying fault will be

P par aCa + P br bCb + p c r c C c ) ,

where C a, Cb and C c are the costs for A, B and C respectively. Again itis apparent that, once a clear underlying model is available, it can formthe basis for further developments.

Conclus ionsFMEA is a major tool for quality improvement. It seeks to prevent faults inproducts and processes at the design stage. It harnesses the insight and

imagination of those m ost concerned with product and service quality and itprovides a structured approach to analysis. If it is to be developed and usedmore widely, it must use a valid model and measurement method to assessthe risks, used for prioritization. This article has sought to show the lack ofvalidity in the currently used RPN and to propose a more rigorous, yetpractical, alternative.

References1. Ford Motor Company, Instruction Manu al Process FMEA, 1988.2. Ford Motor Company, Instruction Man ual Design FMEA, 1988.3. Feigenbaum, A.V., Total Quality Control 3rd edition revised, McGraw-Hill, New

York, NY, 1991.4. Juran, J.M., Quality Control Handbook McGraw-Hill, New York, NY, 1989.5. Lancaster, J., Searstone, K. and Gilchrist, W.G., A Workbook on FMEA, Centre for

Quality, Sheffield City Polytechnic, 1992.