Dr Taguchi Tolerances and Specification

In order to establish what the western concept of Quality with regard to Specification and Tolerance is and to create a foil for comparison to Dr. Taguchi and his Quality philosophy we should first examine the work of Philip Crosby. Philip Crosby was an American veteran of World War Two and the Korean War. in 1952 he started his working life on the assembly line at Crosley Corporation, Crosby then progressed to a Quality and Reliability Engineering position at the Bendix Corporation in 1955.

After two years he left to become a senior quality engineer for The Martins Company in Florida.

At the Bendix Corporation and the Martins company Crosby was working on pioneering ballistic missile design and manufacturing programs. The process was incredibly complex and expensive with thousands of individual components required to complete the build. Defect detection at inspection or worse assembly or worse again during testing proved to be extremely costly in terms of time and money. This spurred Crosby to conceive his “”Zero Defects”” and “”Right First Time”” Quality mantras. Crosby build the Zero Defects system on Four Absolutes of Quality Management:

1. Quality is conformance to requirements.
2. Quality prevention is preferable to quality inspection.
3. Zero defects is the quality performance standard.
4. Quality is measured in monetary terms – the price of non-conformance.

Crosby coupled these 4 absolutes of Quality management with 14 steps towards Quality improvement. In essence the 14 steps are largely aimed at making Quality a core value in an organisation by engaging people at every level in an organisation through management committing to quality, providing education, regular Quality meetings and continuous recognition of positive quality behaviours and achievements. Crosby was essentially proposing measurements and methods designed to reduce costs incurred through non conformance a goal he certainly shared with Dr. Taguchi.

Crosby’s Zero Defects methodology utilised what is commonly now termed a “”Goalposts”” view of conformance relative to Specification and tolerances. Limits if thought of in Sporting terms could be viewed as Goal posts. In sports such as football when a ball passes between the posts a goal is scored if the ball passes outside the posts it is a miss.

A Process Variable will have a desired target value. Acceptable process limits must be determined and specified resulting in an Upper Specified Limit (USL) and a Lower Specified Limit (LSL). Once the measured variable falls between the process limits it is considered good. How close to the Limits or far from the desired measurement is not considered once the measurement is within tolerance. There is only “”Within Tolerance Specifications”” or “”Outside Tolerance Specifications”” when assessing the quality of a measurement. However should consideration be given to how close the measurement is to the desired target measurement?

Consider a machined steel pin in a machine assembly where precision and reliability is critical. The pin diameter is specified as 19.90mm +/- 0.10mm. This gives a 0.2mm tolerance for the pin with a USL of 20.00mm and LSL of 19.80mm. Taking the goalposts view of this once the pin is machined to any value within these tolerances it is good.

Therefore a pin machined to 19.81mm or 19.99mm is expected to perform as well as a pin machined to 19.90mm. However a pin machined to 19.79mm will be binned. Now consider the dimensions of the machined hole the pin will be placed the hole is specified as 20.00mm +0.10/-0 The tolerances of the hole are one sided the target value of 20.00mm and the LSL are matched. The USL is 20.10mm giving a tolerance of 0.1mm.

If a pin machined to 19.81mm is paired with a hole machined to 20.09mm there is a 0.28 difference in size between the pin and the hole. Both measurements fall between the goalposts. Within the confines of the Western concept of Tolerance and Specifications performance of the hole and shaft will be as good as a hole machined to 20.01mm and a pin machined to 19.92mm. The difference in size between the hole and the pin known as the allowance is permitted to be between 0.0mm and 0.30mm. Is a 0.0mm allowance or transition fit as good as a 0.30mm allowance?

As the difference in size increases there may be a risk of additional wear caused by the extra play between the parts. There could also be a risk of additional particle generation or vibration that may inhibit part performance or lead to a requirement for early part failure, maintenance requirements or a negative impact on the machines process performance.

Dr. Genichi Taguchi, a Japanese engineer identified the fact that the further a measurement deviated from the target value and the closer it was to the Lower or Upper Specification Limit the more likely it was that cost would be incurred due to non-optimum performance.

Dr. Taguchi was born in Japan in 1912 after serving in the Japanese Navy during World War 2, Dr Taguchi took an interest in statistics and after joining Electrical Communication Laboratory in 1950 began his work developing what went on to become known as robust engineering.

Dr. Taguchi posited that any deviation from the target value would incur a loss that could be quantified as a monetary value. The larger the deviation from the target value, the greater the loss that will be incurred. This loss will be incurred both by the customer due to lack of reliability of the product and to the manufacturer in costs incurred remedying the fails and loss of reputation and repeat business.

Dr. Taguchi theorised that this relationship could be demonstrated as a quadratic function.The Quadratic function can be plotted as a Quadratic slope where the Vertex of the slope occurs at the target value. The area under the slope quantifies the rate of loss as the measurement deviates from the target. Fig.1 below illlustrates the contrast in assessment of quality of variation of measurements within in Specified limits and likely costs of deviation for target.

The graph plotting Dr. Taguchi’s loss function demonstrates that units measured at dimension A are likely to perform better than units measured with dimension B. As the measured dimensions’ deviation from the target increases as does the the predicted loss cost.

The traditional Western concept of quality and conformance with regard to Tolerance and specification could be summarised that a measurement inside Specified Tolerance limits is good. Loss due to manufacturing defects can be eliminated by eliminating out of spec measurements.

Taguchi modelled that the potential for loss begins once measurements begin to deviate from process target value. This cost can be quantified. In order to reduce the potential for loss it is not good enough to simply be within tolerance the process must be as close to the target value as possible. Reduce deviation from target and reduce variation within Specified Limits to reduce loss.

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