Taguchi Loss Function PDF

27-07-2024 Taguchi Loss function Dr K. Sri Yogi Dr K Sri Yogi SIBMHYD Genichi Taguchi (Japanese) is an engineer and Statistician Dr K Sri Yogi SIBMHYD ...

27-07-2024 Taguchi Loss function Dr K. Sri Yogi Dr K Sri Yogi SIBMHYD Genichi Taguchi (Japanese) is an engineer and Statistician Dr K Sri Yogi SIBMHYD  27-07-2024  Taguchi Method is a statistical method developed largely by GENICHI TAGUCHI to improve quality of manufactured goods.  The philosophy of off-line quality control. Designing of “robust” products and processes  Innovations in the design of experiments. Dr K Sri Yogi SIBMHYD Taguchi Loss Function : Definition  Taguchi loss function, used to measure financial loss to society resulting from poor quality;  Taguchi defines Quality as “the loss imparted by the product to society from the time the product is shipped.”  LOSS = Cost to operate, Failure to function, maintenance and repair cost, customer satisfaction poor design.  Product to be produced “being within specification” Dr K Sri Yogi SIBMHYD  27-07-2024 Five Important points of Taguchi  Continual quality improvements and cost reduction  The total loss that is generated by a product to the society should be taken as the measure of quality of the product  Pre production experimental procedure from varying factor at a time vary.  Customer loss due to poor quality-square of the deviation of the performance characteristics from its target (nominal value).  Achieving conformance to specifications---achieving the target and minimize the variability by analyzing the non linear effects of factors. Dr K Sri Yogi SIBMHYD Taguchi’s Quadratic Quality Loss Function  Quality Loss Occurs when a product’s deviates from target or nominal value.  Deviation Grows, then Loss increases.  Taguchi’s U - shaped loss Function Curve. Dr K Sri Yogi SIBMHYD  27-07-2024 Formula to find Taguchi’s Loss Fn Taguchi uses Quadratic Equation to determine loss Curve L (y) = k (y-m)² Where L = cost incurred as quality deviates from the target y = performance characteristics m = target value k = cost coefficient (i.e; quality loss coefficient) Dr K Sri Yogi SIBMHYD The quality loss function takes three forms Nominal-the-best (NTB) - the nominal value is best because it is the one that satisfies the customer’s need. The characteristic value away on either side of the target is undesirable, such as air pressure in vehicle tires or location of gauges on the instrument panel. Smaller-the-better (STB) – a smaller value is better and higher values are undesirable, such as vehicle emissions or fuel consumption (dollar per distance). Dr K Sri Yogi SIBMHYD  27-07-2024 Larger-the-better (LTB) – a larger value is better and smaller values are undesirable, such as gas mileage (distance per gallon). Dr K Sri Yogi SIBMHYD Dr K Sri Yogi SIBMHYD  27-07-2024 Quadratic Quality Loss Function And Signal-to- Noise Ratio Robust design is achieved by applying a three-step decision making process: 1. Define the objective; 2. Define the feasible options; and 3. Select the feasible option that best meets the objective. Dr K Sri Yogi SIBMHYD  Best criterion to measure robust design is the signal-to-noise (S/N) ratio.  Maximum robustness means minimum quality loss and maximum customer satisfaction.  The S/N ratio recognizes and measures deviation from the nominal value and integrates the information into one metric (Taguchi et al., 1999).  It is very important to define the measure of the quality loss and then incorporate the same into the design. Dr K Sri Yogi SIBMHYD  27-07-2024  Several performance characteristics exist and it is important to distinguish between these when evaluating quality.  Therefore, a different S/N ratio is needed for each performance characteristic.  The nominal value is the best performance characteristic value for a given parameter.  NTB should be used whenever possible because this allows the two-step optimization.  The S/N ratio measures deviation from the nominal value allowing for subsequent adjustment. Dr K Sri Yogi SIBMHYD Response and Signal Ratio Dr K Sri Yogi SIBMHYD  27-07-2024 A large S/N ratio means lower standard deviation.  In the case of dynamic signals, e.g., steering wheel or brake pedal application, a series of dynamic S/N ratios exist. A signal factor is a control factor chosen that can modify output response in a linearly proportional way. Dr K Sri Yogi SIBMHYD  For example, for a steering wheel, the turn angle of the steering wheel is the signal factor that adjusts the radius of curvature for vehicle motion as the output response.  Similarly for a brake system, the brake pedal pressure is the signal factor which regulates the braking distance as the output response. Dr K Sri Yogi SIBMHYD  27-07-2024 The objective for achieving a robust design is to have the highest S/N ratio (i.e., the smallest standard deviation or variation). Dr K Sri Yogi SIBMHYD The mean-squared deviation (MSD) for LTB is given in Equation The quality loss for LTB Dr K Sri Yogi SIBMHYD  27-07-2024 Taguchi’s Loss Function Customer Tolerance Loss Manufacturer Tolerance Target Performance Characteristic Dr K Sri Yogi SIBMHYD Loss Due to Off-Target Performance Dr K Sri Yogi SIBMHYD  27-07-2024  Taguchi’s loss function for the NTB and STB takes the form as in  For the LTB, however, the quality loss function takes the form as in Equation Dr K Sri Yogi SIBMHYD The term Δ0 is taken to the numerator instead of the denominator which introduces an inconsistency among the NTB, STB, and LTB methods. Therefore, Δ0 needs to be taken to the denominator instead of the numerator in order to bring back the consistency among all three cases. Dr K Sri Yogi SIBMHYD  27-07-2024 Dr K Sri Yogi SIBMHYD Dr K Sri Yogi SIBMHYD  27-07-2024 Dr K Sri Yogi SIBMHYD Soft Drinks Case Dr K Sri Yogi SIBMHYD  27-07-2024 Dr K Sri Yogi SIBMHYD Loss Function (L) for parameters of four Soft drinks Dr K Sri Yogi SIBMHYD  27-07-2024 Projected loss function costs for three different cases Dr K Sri Yogi SIBMHYD