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Quality economics/ Basics of probability concepts

Quality economics

Quality economics

• Montgomery (1985) indicates that there are several reasons why the cost of quality should be explicitly considered in an organization:

1) An increase in the cost of quality because of increases in technology use.

2) Increasing sophistication of end users in their consideration of lifecycle costs.

3) Internally, an increase of the use of quality cost data to make quality management-related decisions.

What are quality related costs?• There is no universal consensus upon just what

constitutes quality costs.• Traditionally, costs of quality (COQ) have been

considered as the cost of running a quality assurance system (complete or in development), with perhaps the inclusion of other costs, such as scrap and warranty costs.

• Quality costs are incurred in the design, implementation, maintenance and improvement of a quality system.

• Cost of quality (COQ) crosses inter- and intradepartmental boundaries, much as the process for developing and producing the product or services does in that organization.

What are quality related costs?

• No department or group is isolated and therefore is not immune to the constraints and opportunities of managing quality costs.

• Cost of quality is not confined to the internal environment of the organization, as the activities of, say, suppliers, etc., can affect the outcome of costs related to quality.

Classification of quality costs BS 4778-part 2 (British standard institution

standards) classifies quality costs into the following:

1. Quality related costs: the expenditure incurred in defect prevention and appraisal activities plus the losses due to internal and external failure.

2. Prevention costs: the cost of any action taken to investigate, prevent or reduce defects and failures. Prevention costs can include the cost of planning, setting up and maintaining the quality concern system. They also include process design, product and service design and employee training schemes.

Classification of quality costs3) Appraisal costs: the cost of assessing the quality

achieved. Appraisal costs can include the cost of inspecting, testing, etc. carried out during and on completion of manufacture of product or service.

4) Failure costs-internal: the costs arising within the manufacturing processes of the organization of the failure to achieve specified quality. This can include the cost of scrap, rework and re-inspection.

5) Failure costs-external: the costs arising from outside the manufacturing organization of the failure to achieve quality specified. The term can include the costs of claims against warranty, replacement and consequential losses of customs and goodwill.

Importance of quality costs to the quality oriented organization

• According to Dale and Plunkett(1991) the quality related costs commonly range from 5%-20% of company annual sales turnover.

• Generally 95% of the total quality related costs are expended on appraisal and failure elements.

• Failure costs must be regarded as avoidable and a reduction in such costs in usually attributable to such activities as eliminating causes of non conformance, which may lead to a reduction in appraisal costs. There is therefore a demonstrated need to balance future failure costs with appraisal costs.

• Managerial requirements suggests that what can be measured, can be managed.

Importance of quality costs to the quality oriented organization

• Robertson states that for the average UK organization the analysis of quality related costs are 65% failure costs, 30% appraisal costs and 5% prevention costs, and further indicates that 4-20 % costs are attributed to quality related costs of total sales turnover.

• Garvin (1983) compares Japanese air-conditioning manufacturers with their American counterparts, focusing on warranty claims. Garvin indicates that Japanese company warranty claims are 0.6% of sales turnover, the best an American company could report 1.8% with the worst being 5.2%.

Quality costs – why measure them?

• Measuring quality costs will provide a means to quantify in management terms the effect that quality related activities have on organizational performance.

• It should influence employees and their attitudes towards the quality system, TQM and related continuous quality improvement schemes and practices.

• Measurement of quality costs will focus attention upon such areas as appraisal, prevention and failure and therefore provide opportunities for cost reductions.

Quality costs – why measure them?

• Performance across a wide range of quality related activities may need to be measured and this will provide a basis for internal cost comparisons between departments, processes, services and products.

• The measurement of quality costs can be clearly seen as a major step towards quality control, quality improvement and TQM.

Cost of quality versus cost of non quality

• The cost of quality can be divided into three main aspects:

1. Failure costs2. Appraisal costs3. Prevention costs from these only prevention can be regarded as a cost

of quality, whereas the other two are in essence the cost of non-quality- inspection and rework of errors; rather than the principle of working to attain zero defects.

Cost of quality versus cost of non quality• Finding shows that costs of non-quality in the service

industry may be very high.• The intangible nature of the service products means

that the mistakes, which can never be undone, will have to be regarded as a cost factor.

• Client, who have been dissatisfied may not only never return, but may even influence other people into not using the defective services that the organization provide.

• What losses are incurred because of this process are very difficult to substantiate, many organizations have turned a blind eye to these losses.

Cost of quality versus cost of non quality

• However if they are truly committed to TQM, it will be recognized that one aspect able to reduce this cost of non quality is to ensure that the incidences are reduced to an absolute minimum.

• This can be accomplished through proper training of staff in the communications skills required to be able to asses clients, need better and to bring customer satisfaction to the optimum- whether internal and external customers.

Hidden costs of quality• Where errors in manufacturing produce waste, scrap or rework,

then the hidden cost of quality or rather non quality can be seen as:

1. The extra material needed to be supplied to accommodate this extra wastage.

2. The extra manpower costs of labour and perhaps overtime.3. The opportunity cost of working on a part the second time round

or, in the case of a scrapped item, on a completely new part.4. Possible delays in the ultimate shipment of the order.5. Increase risk of machine breakdown.6. Increase machine maintenance and repair costs.7. Reduced production capacity resulting from the need to

overproduce in order to manufacture a given quantity of production items.

Lifecycle costs• Juran and Gryna (1993) discuss the impact of the

lifecycle costs theory.• All products/markets/services have lifecycles.• Fashion for example is a cycle.• According to Juran and Gryna’s application is that the

cost of the product/service should not just be limited to the cost at purchase. It should also include the cost of maintenance and the running cost of the product.

• Designing a product that lowers the overall lifecycle cost may mean that the initial cost may be higher than originally anticipated, but the consumer would benefit in the long run.

Lifecycle costs

• An example is that of laser printer.; advertised by Kyocera Electronics that the cost of their laser printer – over a three year period- was not the cheapest to purchase, but the cheapest to run over that time in costs/page printed.

The management of quality costs• Survey conducted by Roche and Duncalfe and Dale

suggested that only about one-third of the companies studied acutely collected quality cost data and that these findings indicated that less than 40% of companies collect and analyze quality costs data in systematic manner.

• The costs most measured were suggested to be those for cost of scrap, rework and warranty claims.

• Although the importance of not placing complete reliance upon the data from quality costing as a means of improving quality and of reducing costs, quality cost data should be used as some basis for the quantification of quality related activities, but not solely to be used as a weapon by top management to cut costs.

The management of quality costs• Throwing vital resources into appraisal rather than

prevention is not good practice, as many organizations have found to their folly.

• It is just that point that has made Japanese manufacturers more effective than their American and European counterparts during the 60’s and 70’s.

• American and Europeans funded appraisal rather than prevention; they were essentially targeting the symptom rather than the Japanese approach of targeting the core problem and developing an effective solution to it.

Basic probability concepts

Statistical tools in quality

• Statistics is the collection, organization, analysis, interpretation, and presentation of data. The body of knowledge of statistical methods is an essential tool of the modern approach to quality. Without it drawing conclusions about data becomes lucky at best and disastrous in some cases.

Concept of variation• The concept of variation states that no two items will

be perfectly identical. Variation is a fact of nature and a fact of industrial life. For example even identical twins vary slightly in height and weight at birth.

• The cans of tomato soup vary slightly from can to can; the time required to assign a seat at an airline check-in counter varies from passenger to passenger. To disregard the existence of variation (or to rationalize falsely that it is small) can lead to incorrect decisions on major problems. Statistics helps to analyze data properly and draw conclusions, taking into account the existence variation.

Concept of variation

• Data summarization can take several forms: tabular, graphical, and numerical. Sometimes one form will provide a useful, complete summarization. In other cases, two or even three forms are needed for complete clarity.

Tabular summarization of data: Frequency distribution

• A frequency distribution is a tabulation of data arranged according to size. The raw data of the electrical resistance of 100 coils are given in the table.

3.37 3.34 3.38 3.32 3.33 3.28 3.34 3.31 3.33 3.34

3.29 3.36 3.30 3.31 3.33 3.24 3.34 3.36 3.39 3.34

3.35 3.36 3.30 3.32 3.33 3.25 3.35 3.34 3.32 3.38

3.32 3.37 3.34 3.38 3.36 3.27 3.36 3.31 3.33 3.30

3.35 3.33 3.38 3.37 3.44 3.22 3.36 3.32 3.29 3.35

3.38 3.39 3.34 3.32 3.30 3.29 3.36 3.40 3.32 3.33

3.29 3.41 3.27 3.36 3.41 3.37 3.36 3.37 3.33 3.36

3.31 3.33 3.35 3.34 3.34 3.34 3.31 3.36 3.37 3.35

3.40 3.35 3.37 3.35 3.32 3.36 3.38 3.35 3.31 3.334

3.35 3.36 3.39 3.31 3.31 3.30 3.35 3.33 3.35 3.31

Tabular summarization of data: Frequency distribution

Resistance Frequency Cumulative frequency

3.415-3.445 1 1

3.385-3.415 8 9

3.355-3.385 27 36

3.325-3.355 36 72

3.295-3.325 23 95

3.265-3.295 5 100

total 100

Graphical summarization of data: the histogram• A histogram is a vertical bar chart of a frequency

distribution. Figure shows the histogram for the electrical resistance data.

• Note that as in the frequency distribution, the histogram highlights the center and amount of variation in the sample of data. The simplicity of construction and interpretation of the histogram makes it an effective tool in the elementary analysis of data.

• Graphical methods are essential to effective data analysis and clear presentation of results.

• The vividness of a picture when compared to the cold logic of numbers has practical benefits, e.g. identifying subtle relationships and presenting results in clear form. Experience dictates that the first step in data analysis is: Plot the data.

Histogram

3.325-3.355

Quantitative methods of summarizing data: Numerical indices

• Data can also be summarized by computing 1) a measure of central tendency to indicate where most of the data are centered and 2) the measure of dispersion to indicate the amount of scatter in the data, often these two measures provide an adequate summary.

• The key measure of the central tendency is the arithmetic mean, or average. The definition of the average is X= ∑ x

n


• Another measure of central tendency is the median- the median value when the data are arranged according to size. The median is useful for reducing the effects of extreme values.

• Two measures of dispersion are commonly calculated. When the amount of data is small (ten or fewer observation). The range is useful. The range is the difference between the maximum value and the minimum value in the data. As the range is based on only two values, it is not as useful when the number of observation is large.


• In general the standard deviation is the most useful measure of dispersion. Like the mean, definition of the standard deviation is a formula:

s= √ ∑ (x- x)2n-1

• A problem that sometimes arises in the summarization of data is that one or more extreme values are far from the rest of the data. A simple but not necessarily correct solution is available. Drop such values. The reasoning is that a measurement error or some other unknown factor makes the values unrepresentative.

Probability distribution: General • A distinction is made between a sample and a population.

A sample is a limited number of items taken from a larger source. While a population is a large source of items from which the sample is taken.

• Measurements are made on the items. Many problems are solved by taking the measurement results from a sample and based on these results, making predictions about the defined population containing the sample.

• It is usually assumed that the sample is a random one i.e. each possible sample of n items has an equal chance of being selected (or the items are selected systematically from material that is itself random due to mixing during process)

Probability distribution: General

• A probability distribution function is a mathematical formula that relates the values of the characteristic with their probability of occurrence in the population.

• The collection of these probabilities is called a probability distribution. Some distribution and their functions are summarized as:

Probability distribution: General• Normal distribution: applicable when there is a

concentration of observations about the average and it is equally likely that observations will occur above and below the average. Variations in observations is usually the result of many small causes.

• Exponential distribution: applicable when it is likely that more observations will occur below the average than above.

• Weibull distribution: applicable in describing a wide variety of patterns in variation, including departures from the normal and exponential.


• Poisson distribution: same as binomial but particularly applicable when there are many opportunities for occurrence of an event, but a low probability less than 0.10 on each trial.

• Binomial distribution: applicable in defining the probability of r occurrences in n trials of an event which has a constant probability of occurrence on each independent trial.


• Distribution are two types:1. Continuous (for variable data): when the

characteristics being measured can take on any value ( subject to the fineness of the measuring process); its probability distribution is called a continuous probability distribution. For example , the probability distribution for the resistance data is an example of a continuous probability distribution because the resistance could have any value, limited only by the fineness of the measuring instrument.


• Discrete (for attribute data): when the characteristics being measured can take on only certain specific values (e.g. integers 0, 1, 2, 3, 4, 5 etc.), its probability distribution is called a discrete probability distribution. The common discrete distributions are the Poisson and binomial.

Basic theorems of probability

• Probability is expressed as a number which lies between 1.0 ( certainly that an event will occur) and 0.0 (impossibility of occurrence).

• A convenient definition of probability is one based on a frequency interpretation: if an event A can occur in s cases out of a total of n possible and equally probable cases, the probability that the event will occur is

P (A)= s = number of successful cases n total number of possible cases

Basic theorems of probability

• Example: a lot consists of 100 parts. A single part is selected at random, and thus each of the 100 parts has an equal chance of being selected. Suppose that a lot contains a total of 8 defective. Then the probability of drawing a single part that is defective is then 8/100 or 0.08.

Basic theorems of probability• The following theorems are useful in solving

problems:Theorem1: If P(A) is the probability that an event A will occur, then the probability that A will not occur is 1-P(A)Theorem2:If A and B are two events, then the probability that either A or B will occur is

P(A or B)= P(A) + P(B) – P(A and B)In case A and B are mutually exclusive then the

P(A or B)= P(A) + P(B)

Basic theorems of probability• Theorem3: if A and B are two events then the

probability that events A and B occur together is:P(A and B)= P(A) x P(B|A)

Where P(B|A) means probability that B will occur assuming A has already occurred.

A special case in this theorem occurs when the two events are independent, i.e. when the occurrence of one event has no influence on the probability of the other event. If A and B are independent, then the probability of both A and B occurring is

P(A and B)= P(A) x P(B)

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