درباره انتخاب بهینه جایگزین های فرآیند در اجرای شش سیگما

Six Sigma is at the top of the agenda for many companies that try to reduce cost and improve productivity. Many of the top manufacturing companies implement thousands of Six Sigma projects every year and this implementation demands a significant investment of capital that requires a careful analysis to make sure that the benefits obtained are much higher than the actual investment. This cost benefit analysis is crucial, especially for companies whose products have a small profit margin. In this paper, two optimization models that will assist management to choose process improvement opportunities are presented. These models consider a multi-stage, asynchronous manufacturing process with the opportunity to improve quality (scrap and rework rates) at each of the stages. The first model is to maximizing the sigma quality level of a process under cost constraint while the selection of Six Sigma alternatives to maximize process returns is considered by the second model. Process quality improvement usually results in costs associated with the purchase of new technology, modification of existing equipment, training employees, hiring new employees and investment in information technology infrastructure. The proposed models recognize that a company competes for funds and that benefits can result in either improved revenue or reduction in costs. An example illustrates the application of the optimization models developed and results show that in some scenarios implementing Six Sigma may not be financially beneficial.

Six Sigma, a trademark of Motorola, was introduced more than 20 years back as a method to reduce manufacturing defects. The concept behind this method was developed by William Smith to deal with the high failure rate experienced by the systems produced. Smith proposed Six Sigma as a tool to improve the reliability and the quality of products and thus, focused it at reducing defects by improving manufacturing processes. Initially developed as an operational strategy, Six Sigma has evolved into a competitive corporate strategy used extensively throughout the corporate world. Even traditional companies that adhere to conventional management frameworks have started embracing Six Sigma as a method of substance with the potential to increase market share and profitability (Harry, 1998). The benefits of implementing Six Sigma programs have been extensively reported in the literature (Hendricks and Kelbaugh, 1998; Hahn et al., 1999; Lanyon, 2003; Robinson, 2005) and range from the simple reduction in the number of manufacturing defects to the improvement of the market share and the competitive advantage of a company. In this sense, Anon (2003) conducted a study of 13 high profile corporate houses in the US from a wide variety of industries and reported that Six Sigma programs returned more than double the investment. However, as discussed by Deleryd (1999), with the increasing number of organizations using process capability studies, warnings have been launched that imprudent use of numerical measures of capability, might lead the user to make erroneous decisions. In this respect, recently there have been many cases reported in the literature where Six Sigma has failed to deliver the desired results. Zimmerman and Weiss (2005), quote a survey conducted by Aviation Week magazine among major aerospace companies, which reported that less than 50% of the companies expressed satisfaction with results from Six Sigma projects, nearly 20% were somewhat satisfied and around 30% were dissatisfied. Even at these levels of satisfaction, Six Sigma has been accounted to do better than many other process improvement techniques. Zimmerman and Weiss (2005) also point that 60% of the companies in the survey selected opportunities for improvement on an ad-hoc basis and only 31% relied on portfolio approach. It is interesting to note that companies that used a portfolio approach gained better results. As illustrated in Table 1, Six Sigma is the process management tool that has yielded the greatest results (Dusharme, 2006). Moreover, the fact that in this table Six Sigma is ranked much higher than other process improvement techniques, illustrates the effect of concurrently implementing various process improvement techniques given that most of these techniques constitute the Six Sigma toolbox. This fact is important because none of the remaining quality improvement initiatives have much application outside manufacturing industry.Although Six Sigma was originally conceived to reduce waste due to process deficiencies in manufacturing, it is now used by almost all industries including service industries such as health care management (Krupar, 2003; Antony, 2004; Antony and Fergusson, 2004; Moorman, 2005; Frings and Grant, 2005). That is, Six Sigma has the flexibility to be used as an operational strategy to reduce the number of defects or as a business strategy to improve business processes and evolve new business models. Many proponents of Six Sigma stress that the power of Six Sigma lies in the fact that it can be used as a business strategy to improve market share and profitability. Table 2 provides some of the different areas where Six Sigma has been applied to improve manufacturing and business processes. Table 3 provides an updated list of the benefits of Six Sigma as reported in Kwak and Anbari (2006).In general, Six Sigma can be considered as an extension of other quality improvement initiatives such as Deming's statistical quality control and Total Quality Management (TQM). Furthermore, the main objective of Six Sigma, like most of other management strategies on quality initiatives, is focused around meeting the customer requirements. Anbari (2002) and Kwak and Anbari (2006) summarize Six Sigma as a strategy, which includes TQM, strong customer focus, additional data analysis tools, financial results and project management, to satisfy costumer needs. Six Sigma uses the following five major phases to achieve process improvement: Define, Measure, Analyze, Improve and Control (DMAIC). The DMAIC cycle has a lot of similarities with Deming's “Plan-Do-Check-Act” cycle (Bertels, 2003). However, Six Sigma provides a well-defined target for quality that the process defect rate should not exceed 3.4 defects per million opportunities. This focused target, along with a well-defined DMAIC procedure, has probably resulted in higher success rate for Six Sigma as compared to TQM. Another important difference between Six Sigma and TQM is that Six Sigma is mostly a business results oriented model compared to a return on investment orientation of TQM (Bertels, 2003). For manufacturing companies the direct benefit of Six Sigma, results from the reduction in the number of defects due to improved manufacturing processes. For these companies, Six Sigma or Sigma quality level is a measure of the process defect rate and thus, can be used to measure the quality of the manufacturing process (i.e. a high Sigma level indicates that the process results in a lower defect rate whereas, a low Sigma level illustrates a higher defect rate). Moreover, Sigma quality level also helps to set a realistic target for improvement of process quality during the DMAIC cycle (i.e. it can be used as a benchmarking tool). Reducing process variations is the core objective of Six Sigma projects, since process variations result in higher quality loss. In this respect, Taguchi and Clausing (1990) reported a classic example on the impact of process variations using the case of Ford versus Mazda. Ford, which owned 25% of Mazda, had asked the Japanese company to build transmissions for the cars that it sold in the United States. The transmissions were built to identical specifications and Ford was adopting zero defects as its standard. However, after the cars had been in the market it was observed that Ford's transmission system was generating far higher warranty costs as compared to the transmission systems built by the Mazda. The reasons was traced to the fact the Ford's transmissions had much higher process variability compared to the transmissions built by Mazda. Sony Corporation reported a similar case for their televisions manufactured at Tokyo and San Diego. The televisions manufactured at Tokyo had less variability on the color density compared to the televisions manufactured at San Diego. As a result the customer satisfaction levels for televisions manufactures at Tokyo was much higher than the televisions manufactures at San Diego. It is well understood that the marginal benefit of any Six Sigma project decreases as the sigma quality level increases. It is also well understood that the process yield increases (at a decreasing rate) as the sigma quality level increases. Fig. 1 shows the relationship between sigma quality level and decrease in number of defects as a function of process yield. In economical terms, this figure illustrates that because of the decreasing returns to scale in process yield as sigma quality increases, at some point it may not be economically beneficial to increase sigma quality level, especially if the process change requires high investment. For example, consider improving a process from a 3 sigma level to a 4 sigma level. This improvement reduces the number of defects per million opportunities (DPMO) from 66,811 to 6210. From a Taguchi quality loss perspective (Taguchi, 1986), at 3 sigma level the Taguchi quality loss is higher compared to the Taguchi quality loss at 4 sigma level. Similarly improving sigma level from a 5 sigma level to a 6 sigma level reduces the DPMO from 233 to 3.4. Note however, that in most cases more effort will be required to improve a process from 5 to 6 sigma level as compared to improving a process from 3 to 4 sigma level. The improvement of sigma level obviously requires reduction in the process variability, i.e., the process sigma itself.Any improvement in Sigma level is likely to reduce the Cost of Poor Quality (CoPQ). CoPQ is a result of manufacturing defects and, a function of rework cost, excessive use of material, warranty related costs and unnecessary use of resources. Under the assumption that CoPQ is linearly related to the number of defects produced by the process, the marginal benefit of increasing sigma levels (i.e. process improvement) decreases. Models such as Taguchi's quality loss function (Taguchi, 1986; Chou and Chen, 2001; Ganeshan et al., 2001) are used to estimate the loss due to poor quality. Taguchi claims that the loss due to variability follows a quadratic function (Taguchi, 1986; Taguchi and Clausing, 1990). However, in our model, we assume that the loss is a linear function which depends on the number of rework and scrap generated by a process. The most appropriate model for evaluating loss due to poor quality would require analysis of relevant data on case-by-case basis. Process improvement may involve replacing the existing process with a new improvement alternative. In this respect, Gowen and Tallon (2005) point out that Six Sigma programs must take into consideration the level of technological intensity of the organization to determine the impact of implementing Six Sigma. The replacement or upgrade of an existing process with a new process alternative can be costly. Moreover, if the resulting process does not improve the sigma level significantly, the investment made may not translate into significant returns. Like any other process improvement technique, Six Sigma would also fail to deliver if the management fails to understand the cost of implementing Six Sigma and its effectiveness. This paper presents two mathematical models that will assist management in choosing among different process improvement alternatives. These models acknowledge that the implementation cost for a successful Six Sigma initiative can be considerable and failure to select an optimal alternative may further translate into loss of expected returns. The solution to the proposed models represent the first attempt to optimally select Sigma process alternatives that maximize the process sigma levels while taking into account the cost associated with such alternatives. Any change in a process requires investment in the form of procurement cost of new processes and, in costs related to operation and maintenance. The selection of alternatives for process improvement has been traditionally modeled as a multi-criteria decision-making problem. Parkan and Wu (2000) have demonstrated use of operational competitiveness rating analysis, analytic hierarchy process, and data envelopment analysis for process selection using a case study by treating production quality as one of the criteria. A mixed integer programming approach was used by Stuart et al. (1999) to select process under environmental constraints such as material consumption, energy consumption and waste rate. Bowman and Schmee (2004) used Monte Carlo simulation to demonstrate sensitivity of process capability to each parameter of the input variables and proposed a method to improve process performance. Although the basis of Six Sigma is process improvement, few research studies have been carried out on the actual alternative selection itself. Thus, this research is an attempt to fill such a gap by providing a quantitative model for selection of process in a Six Sigma implementation project that would result in maximum benefit The rest of the paper is organized as follows: Section 2 introduces a mathematical relationship between a process Sigma level and its yield. This relationship is subsequently used as a surrogate metric to develop a mathematical programming model to optimize the process sigma level, under a cost constraint. Section 3 presents a mathematical programming model to maximize profit based on the optimal selection of improvement alternatives. In Section 4, an example is used to illustrate and compare the models presented. Finally, conclusions and future research are presented in Section 5.

This paper underscores the need to perform both economic and non-economic analyses to evaluate the value of selecting competing quality improve- ment alternatives. Far too often corporations, based upon other companies or industries experience, rush into implementing quality improvements to their existing processes without quantifying the economic consequences. Experience has shown that the initial, perceived euphoria of implementing a Six Sigma initiative, e.g., can bear little resemblance to its resulting economic consequences. Six Sigma con- tinues to be a predominate target to try and obtain a competitive advantage. However, not all companies are successful in implementing many of these quality improvement strategies. Although many companies attribute their success to following a quality improvement program such as TQM and Six Sigma, there are a significant number of companies that fail to gain any measurable benefit after implementing these quality strategies. Given that quality improvements are far reaching and potentially costly, this paper introduced and developed two economic-based mathematical mod- els to assist managers in making the decision on what, if any, quality improvement alternatives to implement. The objective of this paper is to develop mathematical models that can be used to select the process improvement techniques in an optimal way. Two mathematical programming models have been developed in the paper, one finds an optimal sigma quality level using yield as a surrogate revenue measure and another model maximizes the profit from a Six Sigma project by selecting the best processes for Six Sigma implementation. An illustrative example is used to show how the mathematical models developed in the paper can be used in practice. Additional research is required to develop models that fully capture the economic advantages of Six Sigma, most notably increasedmarket share, apart from reduction in wastage cost. Once the relationship between benefit due to improved quality of a manufacturing process and a higher sigma level is established, one can modify the optimization models presented in this paper.