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A statistical-heuristic approach to estimating mold costs.

A Statistical/Heuristic Approach to Estimating Mold Costs

Most mold vendors can estimate mold costs analytically, because they know their own labor rates, machine rates, schedules, and workloads. Mold buyers also estimate costs, but they often do not have access o the detailed information necessary for analysis.

IBM has developed technology to provide mold buyers with such information by creating a knowledge base of guidelines derived from corporate purchasing history. This expert system predicts costs based on similarities to past situations.

The system is now in place at 22 IBM locations worldwide. It is as accurate as previous methods and allows a person with no tooling experience to estimate the cost of a mold in about 10 minutes. The techniques used to develop the system can be duplicated by any organization with a statistically significant (>50) number of yearly mold purchases.


From December 1986 to October 1987, the Plastics Technology Center at IBM Lexington undertook a project to develop an expert system that would estimate the cost of a plastic injection mold. To shorten the learning curve for new plastics manufacturing engineers, a decision was made to begin systematically capturing the knowledge of plastics engineers through the use of expert systems technology. Because mold cost estimating appeared to be a smaller domain than such areas as mold or part design or process technology, it was pursued first.

Traditionally, two methods are used for estimating mold cost. The first method is an analytical approach, in which a mold is outlined piece by piece on paper, and cost estimates for each piece are made. Cost estimates are based on the amount of time to grind, bore, drill, mill, and in general, work the metal into the desired shape. The total number of hours is calculated and multiplied by labor rate to get a cost estimate. This estimating method is the one most favored by mold vendors.

There are, however, three problems that mold purchasers encounter when using this method:

1. It is time-consuming, and not many people have the skills to design a mold from scratch.

2. Often, estimates are needed for preliminary project evaluations long before a vendor is selected. This means that the estimator must guess at labor rates, lead time, methods of construction, and other pertinent information for making reliable estimates.

3. The customer's cost includes vendor profit, which cannot be predicted by this method. In many cases, quotes from reliable vendors can differ by more than 100%. These differences can often be attributed to low bidding when the vendor needs work or is trying to get "a foot in the door," and high bidding when the vendor has a backlog.

The second method attempts to estimate the customer's cost through a complex combination of past experience, mold design, economic conditions, and familiarity with the vendor. The estimator tends to evaluate these factors subconsciously, relying on a "feel" for the present mold buying situation. This is sometimes known as "tacit knowledge."

Most mold-cost estimators in the industry are manufacturing engineers with a background in toolmaking. In many cases, their knowledge has been acquired through experience rather than advanced education. Even though this implicit knowledge is difficult to describe and sounds arbitrary, it has validity because of their extensive experience.

A common method of acquiring knowledge for expert systems is that of interviewing experts. But the existence of tacit knowledge--which can be difficult to articulate--militates against the use of the expert interview as a means of knowledge acquisition, so other techniques must be used. The statistical survey technique outlined in this article is a viable knowledge-gathering technique. It works best when.

1. The output of the expert system is a numerical estimate, rather than a recommendation of action, e.g., cost estimates, work force requirements, and job length estimates.

2. There is an adequate supply of data from past events to provide a statistical evaluation.

3. The estimating process is complex enough that experts have difficulty describing their methods through traditional interviews.

4. The incidents within the domain by which a novice gains experience occur infrequently.

A Typical Interview

Even though estimators may have difficulty describing their methods, interviews are still necessary for developing a working model of the experts' cognitive processes. In this case, the experts interviewed were willing to cooperate, but they had difficulty in expressing the though processes involved in cost estimating. Questions designed to elicit details were often answered with "I donht know; I just do it!" or "It depends on a lot of things." So a more specific approach was developed. Experts were given a sample part print from which to estimate the mold cost. A typical response, often requiring only a cursory glance at the print, was: "Making a widget? glance at the print, was: "Making a widget? Looks like a pretty big one, too. Probably going to cost around $30,000 for the mold. Wait, this hole on each end will push it up to around $40,000."

Although the experts had difficulty explaining how they arrived at cost figures, there was indirect evidence, from their words and actions (as indicated above), that a two-step cognitive process was involved. In the first step of estimating base cost, the expert compares the general pattern nsize, geometry, part type, etc.) of the part with a rough average cost based on past experiences. In the second step, the cost is modified as exceptions to the general pattern are discussed. It is this two-step approach that we have attempted to model--using data to generate a statistically derived base estimate--subsequently modified (if necessary) by the heuristic guidelines of the expert system.

Survey Technique

To gather the necessary historical data, we developed a survey that was made available to all plastics manufacturing engineers. It is important to note that the survey was not limited to experts, but open to any manufacturing engineer involved in purchasing molds.

We estimated that it would be necessary to obtain data on 75 to 100 molds purchased within the last two years in order to provide a statistically significant sample. This created two opposing risk factors during survey development:

1. The survey might be so detailed that few engineers would take the time to return it.

2. The survey might be so simple that no statistical cost relationships could be identified.

To offset the risk factors, the best approach was to request a copy of a part drawing for each mold purchased. This provided the engineer with a relatively easy way to submit a large amount of data. For those aspects of mold building that could not be accounted for on the part drawing, we developed a simple one-page survey with multiple choice and fill-in-the-blank questions. By requesting that a part print accompany each survey, we were able to streamline the questionnaire to nine essential tooling-related questions.

Step One--Base Model


The initial survey results yielded a database of 85 molds from a variety of geographic locations. As specified in the survey request, all molds had been purchased within the past two years. From the combination of survey form and accompanying part print, we identified 38 parameters-per-mod for analysis. We placed the data in a matrix and used a step-wise regression technique to fit an exponential curve to the data. The resulting equation was a very simple one, indicating that cost was a function of only six of the parameters:

1. Number of dimensions on the print (used as an index of complexity);

2. Number of different surface finishes required;

3. Length of part:

4. Depth of part;

5. Tightest tolerance;

6. Number of cavities.

Note that all but one of the above parameters can be obtained from the part print. The one that cannot nnumber of cavities) can be derived from user input to the expert system, based on part size and production requirements. Therefore, the only knowledge the user needs in oder to arrive at a base cost estimate is blueprint reading and production volume estimation.

Testing the base equation against the original data showed a high enough correlation coefficient to warrant continuation of the project. Preliminary tests against external data have shown the model to predict costs at least as accurately as present methods.

Step Two--The Revised


Had this been a traditional analysis of data, we'd have made an effort to develop a curve that would have fit all of the data points. But the synergistic effect of the addition of the expert system allowed us to treat the extreme points as exceptions. This gave us an equation that was extremely reliable for most of the data, and heuristic guidelines to accommodate the remainder. The following examples illustrate the rationale behind the decision to eliminate some data in the statistical model:

* Typically, cost decreases with part size, but there comes a point when the fine detail required to make a tiny part increases the cost. While most molded parts were of "reasonable" size, two parts in the survey measured 1 to 2 millimeters per side. The cost of these molds was 5.5 times what the equation predicted.

* All molds but one were made from steel. The remaining mold was made of aluminum and cost one third as much as predicted.

* All molds in the database had four cavities or fewer, with most having only one. Because of the exponential nature of the equation, the test results using a 64-cavity mold indicated a cost of $34 million, considerably higher than the actual cost. (If the 64-cavity mold had been added to the database, the result would have been detrimental to the overall usefulness of the model. Thus the need for rules to handle exceptions.)

As we analyzed the exceptions, it became a simple matter (as shown above) to write guidelines to accommodate them. In fact many of the exceptions can be handled with little or no additional user input. For instance, since cavity level is already being calculated for the base cost estimate, the expert system can also check for extremely high cavity levels and modify cost accordingly. Length and depth are also needed for the base cost, so guidelines that trigger a small part-cost modification can be written. Aluminum molds are used for short-run prototyping, and low volume products. Since production volume is needed for cavity calculations, it can also be used to determine the appropriate mold material. This leads to an added bonus of the database: the ability to configure the mold.

Mold Configuration

Although still under development, this portion of the expert system shows promise in making reasonable assumptions about the mold configuration. For any given mold, there are numerous ways to get the plastic into the cavity and get the part out the mold. There are also various kinds of steel that are used for different applications. Given a large enough data sample, a mold configuration for a given part can be deduced from past history, and the presence or absence of a characteristic can be used to estimate the incremental cost associated with that feature. This will allow part designers to identify the areas of the part design that most affect the mold cost. The system will provide inexperienced tooling engineers with a workable configuration, yet allow more experienced engineers who might disagree to change details for a revised cost estimatE.


In cost estimating, because the result is a hard number rather than a recommendation or suggestion, there is a tendency on the part of the user to expect greater accuracy from a computer program than from a human. To counter this expectation, we tested the system for what we labeled "absolute" accuracy and "relative" accuracy. Absolute accuracy is simply how well the system's estimate compares with the actual cost of the mold. Relative accuracy compares the system's estimated cost to the cost estimated by previous methods.

The nature of cost estimating is such that estimates can be off by varying amounts. To compensate, we measured accuracies in terms of means and standard deviations, and also in terms of both percent deviation and absolute dollars. Estimating a $300,000 mold at $250,000 is an error of only 17%, but $50,000 is a large amount of money to be short. Conversely, an estimate of a $5000 mold at $10,000 is only $5000 off the actual price, but 100% is an unacceptable error level.

Feedback from users since the initial release of the system indicates an average of 85% to 90% accuracy in predicting mold costs.


The use of a survey for knowledge acquisition and the combination of statistical and heuristic techniques for model building provide better results in some circumstances than the more traditional expert interview. Some of the advantages of this approach are:

* Experts who use "tacit knowledge" in solving problems are often using a subconscious base of historical information to arrive at the most common, or "average," solution. This behavior can be effectively modeled using statistical analysis of historical data.

* The survey allows wider participation in development, rather than limiting it to a few experts. This leads to increased interest by the user community. Personality conflicts are minimized, and the complex issue of cooperation by the knowledge source is reduced to a simple choice of whether or not to fill out the survey.

* Opportunities for mold cost estimating do not occur often enough for most people to gain the experience needed to become an expert. By acquiring survey data from across the corporation, the expert system "sees" many more cases than any one human estimator. This consolidation provides a means by which patterns are discovered and allows the corporate experience to be codified.

* The difference between opinion and fact can often become nebulous in expert interview. In a survey, the knowledge is based on verifiable data and is interpreted mathematically rather than linguistically, arising almost spontaneously from the data.

* Often, "community" tacit knowledge, of which none of the experts is aware, can be discovered. For instance, this study indicated a very high correlation between the number of dimensions on a part print and the cost of the mold to make the part. As far as research showed, no one had previously used this relationship in cost estimating or was even aware that it existed.

* The synergistic effects of the combination statistical/heuristic system are reduced program size, shortened development time, and increased reliability. It would have taken many hours of interviews and hundreds of rules to develop the base cost using only the expert system. In fact, a base cost would probably have not been used at all, but rather a set of rules for each discrete mold configuration. On the other hand, the use of rules allowed us to take the majority of molds that were relatively homogeneous and develop a mathematical cost model, while treating the remainder on a case-by-case basis.

* This technique has the interesting property of restructuring the model to maintain its reliability by mirroring its users. At one extreme, a large number of returned surveys from a variety of users (the most desirable situation) would provide a general tool for use in any environment. At the other extreme, a small number of returned surveys from one or two locations would not be generally applicable, but (assuming the survey participants are the most likely users) would be a customized tool for those participants.

Future system enhancements. The knowledge base will be updated periodically by maintaining an ongoing two-year database of current mold statistics, providing both recalculation of the base equation and guidelines for rule changes. This periodic update will allow us to indirectly account for general cost differences due to changing trends in economic conditions, vendor workloads, mold building technology, design techniques, and product mixes. To analyze and evaluate independently the effect each trend has on mold cost would be practically impossible.

This expert system will eventually be integrated into a package containing a collection of cost and design aids. We would like to interface the package with 3-D design software so that assessments of complex geometries can be made directly, rather than use the present indirect method of counting dimensions on a part print. The overall strategy in developing the package is to reduce development time of new products, and to provide an automated form of the early manufacturing involvement (EMI) concept during the product design phase.
COPYRIGHT 1989 Society of Plastics Engineers, Inc.
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Author:Pearce, Dennis
Publication:Plastics Engineering
Date:Jun 1, 1989
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