DECIDING OPTIMAL SPECIFICATION LIMITS AND PROCESS ADJUSTMENTS UNDER QUALITY LOSS FUNCTION AND PROCESS CAPABILITY INDICES

In traditional screw manufacturing, if buyers want to have high quality products, they have to pay the appreciate quality costs to their manufacturers. To satisfy the quality requirements of buyers with minimum loss of quality costs, this study proposes a modified totally expected quality loss model using Taguchi’s quality loss function and process capability indices for normal and non-normal distributions. The three-parameter Weibull distribution is used to estimate a skewed process. These models determine the optimal adjusted process mean, adjusted process standard deviation and specification limits based on the minimum costs and process capability requirements of buyers. This study also considers the design of optimal adjusted process parameters and specification limits using two examples: the hexagon head cap screw, and oil seal

Measuring process capability for bivariate non-normal process using the bivariate burr distribution

As is well known, process capability analysis for more than one quality variables is a complicated and sometimes contentious area with several quality measures vying for recognition. When these variables exhibit non-normal characteristics, the situation becomes even more complex. The aim of this paper is to measure Process Capability Indices (PCIs) for bivariate non-normal process using the bivariate Burr distribution. The univariate Burr distribution has been shown to improve the accuracy of estimates of PCIs for univariate non-normal distributions (see for example, [7] and [16]). Here, we will estimate the PCIs of bivariate non-normal distributions using the bivariate Burr distribution. The process of obtaining these PCIs will be accomplished in a series of steps involving estimating the unknown parameters of the process using maximum likelihood estimation coupled with simulated annealing. Finally, the Proportion of Non-Conformance (PNC) obtained using this method will be compared with those obtained from variables distributed under the bivariate Beta, Weibull, Gamma and Weibull-Gamma distributions

Assessment of Process Capability Using Weibull Analysis

For a production process, meeting the customer's specification is important. Thus process capability should assist the company to overview their manufacturing processes. In order to maintain the satisfaction of the customer, production has to achieve a normal distribution for their production output, where the production itself has to be in between the limit that the customer set. With this pattern, process capability can be find using normal process capability indices. These normal process capability indices however cannot be applied to non-normal distribution production data. Thus, in a normal approach assessing a non-normal distribution production data is to convert the distribution to be a normal distribution using specific variables as stated by Peter J. Sherman. With this method, process capability indices for normal distribution now can be use for the non-normal distribution of production data. Besides using the method of transforming the non-normal distribution, a new process capability index Spmk is established, this process capability index can straight away finding the process capability for non-normal distribution without having to convert it first. This study will use Weibull distribution to find a process capability on one set of production data. Process capability able to identifY whether the manufacturing process is at the top of the games or some improvement can be done to improve the production rate. After knowing the process capability, further step can be taking for example applying Six Sigma into the manufacturing processes. Six sigma help company to improve the quality of process output by eliminate the causes of production error or defects and minimizing the variable in manufacturing process to deliver near-perfect products to the customer. Finding a process capability is essential for the company to maximize profit by increasing the process capability. Without careful measurement of process capability, company will end up losing more money unwittingly

Evaluation of Modified Non-Normal Process Capability Index and Its Bootstrap Confidence Intervals

Process capability index (PCI) is used to quantify the process performance and is becoming an attracted area of research. A variability measure plays an important role in PCI. The interquartile range (IQR) or the median absolute deviation (MAD) is commonly used for a variability measure in estimating PCI when a process follows a non-normal distribution In this paper, the efficacy of the IQR and MAD-based PCIs was evaluated under low, moderate, and high asymmetric behavior of the Weibull distribution using different sample sizes through three different bootstrap confidence intervals. The result reveals that MAD performs better than IQR, because the former produced less bias and mean square error. Also, the percentile bootstrap confidence interval is recommended for use, because it has less average width and high coverage probability.11Ysciescopu

Sintered silver finite element modelling and reliability based design optimisation in power electronic module

This paper discusses the design for reliability of a sintered silver structure in a power electronic module based on the computational approach that composed of high fidelity analysis, reduced order modelling, numerical risk analysis, and optimisation. The methodology was demonstrated on sintered silver interconnect sandwiched between silicon carbide chip and copper substrate in a power electronic module. In particular, sintered silver reliability due to thermal fatigue material degradation is one of the main concerns. Thermo-mechanical behaviour of the power module sintered silver joint structure is simulated by finite element analysis for cyclic temperature loading profile in order to capture the strain distribution. The discussion was on methods for approximate reduced order modelling based on interpolation techniques using Kriging and radial basis functions. The reduced order modelling approach uses prediction data for the thermo-mechanical behaviour. The fatigue lifetime of the sintered silver interconnect and the warpage of the interconnect layer was particular interest in this study. The reduced order models were used for the analysis of the effect of design uncertainties on the reliability of the sintered silver layer. To assess the effect of uncertain design data, a method for estimating the variation of reliability related metrics namely Latin Hypercube sampling was utilised. The product capability indices are evaluated from the distributions fitted to the histogram resulting from Latin Hypercube sampling technique. A reliability based design optimisation was demonstrated using Particle Swarm Optimisation algorithm for constraint optimisation task consists of optimising two different characteristic performance metrics such as the thermo-mechanical plastic strain accumulation per cycle on the sintered layer and the thermally induced warpage

Capability Indices for Non-Normal Distribution using Gini’s Mean Difference as Measure of Variability

This paper investigates the efficiency of Gini's mean difference (GMD) as a measure of variability in two commonly used process capability indices (PCIs), i.e., Cp and Cpk. A comparison has been carried out to evaluate the performance of GMD-based PCIs and Pearn and Chen quantile-based PCIs under low, moderate, and high asymmetry using Weibull distribution. The simulation results, under low and moderate asymmetric condition, indicate that GMD-based PCIs are more close to target values than quantile approach. Beside point estimation, nonparametric bootstrap confidence intervals, such as standard, percentile, and bias corrected percentile with their coverage probabilities also have been calculated. Using quantile approach, bias corrected percentile (BCPB) method is more effective for both Cp and Cpk, where as in case of GMD, both BCPB and percentile bootstrap method can be used to estimate the confidence interval of Cp and Cpk, respectively.1133Ysciescopu

A Theoretical Foundation for the Development of Process Capability Indices and Process Parameters Optimization under Truncated and Censoring Schemes

Process capability indices (PCIs) provide a measure of the output of an in-control process that conforms to a set of specification limits. These measures, which assume that process output is approximately normally distributed, are intended for measuring process capability for manufacturing systems. After implementing inspections, however, non-conforming products are typically scrapped when units fail to meet the specification limits; hence, after inspections, the actual resulting distribution of shipped products that customers perceive is truncated. In this research, a set of customer-perceived PCIs is developed focused on the truncated normal distribution, as an extension of traditional manufacturer-based indices. Comparative studies and numerical examples reveal considerable differences among the traditional PCIs and the proposed PCIs. The comparison results suggest using the proposed PCIs for capability analyses when non-conforming products are scrapped prior to shipping to customers. The confidence interval approximations for the proposed PCIs are also developed. A simulation technique is implemented to compare the proposed PCIs with its traditional counterparts across multiple performance scenarios. The robust parameter design (RPD), as a systematic method for determining the optimum operating conditions that achieve the quality improvement goals, is also studied within the realm of censored data. Data censoring occurs in time-oriented observations when some data is unmeasurable outside a predetermined study period. The underlying conceptual basis of the current RPD studies is the random sampling from a normal distribution, assuming that all the data points are uncensored. However, censoring schemes are widely implemented in lifetime testing, survival analysis, and reliability studies. As such, this study develops the detailed guidelines for a new RPD method with the consideration of type I-right censoring concepts. The response functions are developed using nonparametric methods, including the Kaplan-Meier estimator, Greenwood\u27s formula, and the Cox proportional hazards regression method. Various response-surface-based robust parameter design optimization models are proposed and are demonstrated through a numerical example. Further, the process capability index for type I-right censored data using the nonparametric methods is also developed for assessing the performance of a product based on its lifetime

Process Capability Calculations with Nonnormal Data in the Medical Device Manufacturing Industry

U.S. Food and Drug Administration (FDA) recalls of medical devices are at historically high levels despite efforts by manufacturers to meet stringent agency requirements to ensure quality and patient safety. A factor in the release of potentially dangerous devices might be the interpretations of nonnormal test data by statistically unsophisticated engineers. The purpose of this study was to test the hypothesis that testing by lot provides a better indicator of true process behavior than process capability indices (PCIs) calculated from the mixed lots that often occur in a typical production situation. The foundations of this research were in the prior work of Bertalanffy, Kane, Shewhart, and Taylor. The research questions examined whether lot traceability allows the decomposition of the combination distribution to allow more accurate calculations of PCIs used to monitor medical device production. The study was semiexperimental, using simulated data. While the simulated data were random, the study was a quasiexperimental design because of the control of the simulated data through parameter selection. The results of this study indicate that decomposition does not increase the accuracy of the PCI. The conclusion is that a systems approach using the PCI, additional statistical tools, and expert knowledge could yield more accurate results than could decomposition alone. More accurate results could ensure the production of safer medical devices by correctly identifying noncapable processes (i.e., processes that may not produce required results), while also preventing needless waste of resources and delays in potentially life-savings technology, reaching patients in cases where processes evaluate as noncapable when they are actually capable