Statistical_Process_Control

A process is a series of steps or sequence of business activities conducted to achieve customer satisfaction. Customer satisfaction would be achieved by providing customers with what they need, when they need it and in the way that they need it. An input and an output are always associated with a process. There are many variables that are involved at each stage of the process between he input and the output. The variables consist of the quality of activities involved, how the activities are organized, cost, people resources, accuracy and speed (Cook, 1996). Process improvement is a method of identifying and analyzing how a set of business activities is organized and managed within an organization. This paper will complete the statistical process control for preparing dinner, analyze the control limits and the effect of any seasonal factors, as well as discuss the confidence intervals. Statistical Process Control Statistical process control (SPC) uses statistical techniques to measure and analyze the variation in processes to ensure the process operates at maximum potential to produce a consistent product. The goals of SPC are to maximize profits by improving production quality, improving productivity, streamlining processes, reducing waste, and improving customer service. Each day I must decide what my family will eat for dinner. According to Chase et al, SPC involves testing a random sample of output from a process to determine whether the process is producing in a pre-selected range (2006). After creating a flowchart to outline each step of the dinner making process, I collected data for 20 days on how long it took me to prepare dinner during the weeknights. I used the time study method to measure the sample data. A standard approach to controlling processes is variables sampling and attribute sampling. Attribute sampling determines whether something is good or bad, fits or doesn’t fit. However, for these purposes, variables sampling will be used. In variable sampling, control charts are used to determine the acceptability or rejection of a process based on actual measurements (Chase et al, 2006). The X-bar and R charts applications are used to determine whether a process is accepted or rejected. Control Limits A control limit is the horizontal line used to identify the upper and lower limits for judging the significance of variations in plotted data (business dictionary, 2010). If the process goes beyond a control limit, then the process is considered to be out of control. It is standard practice to set control limits for variables three standard deviations below the mean and three standard deviations above the mean. The X-chart is a plot of the means of the samples and the R-chart is a plot of the range within each sample (Chase et al, 2006). The descriptive statistics and quality control process chart features in Excel Metastat, were used to develop the X and R-charts (see Attachment A) and to determine the upper and lower control limits. The upper control limit is 48.91 minutes and the lower control limit is -10.50 minutes. This means that 99.7 percent of the sample means are expected to fall within these ranges. Upon a review of the charts, all of the data points fall within the upper control and lower control limits, therefore the process is in control. Seasonal Factors A seasonal factor is the amount of correction needed in a time series to adjust for the season of the year (Chase et al, 2006). A simple calculation based on past seasonal data can be used to show how seasonal indexes are determined. Using the existing data, each week will be used as a different season. The average number of minutes used to prepare dinner for the entire year is 19.21 minutes. On average, for week one (Spring), it took 29.92 minutes to prepare dinner. For week two (Summer), it took an average of 13.83 minutes to prepare dinner, week 3 (Fall) took 23.63 minutes and week 4 (Winter) took 9.15 minutes. The seasonal factor is the ratio of the minutes taken to prepare dinner divided by the average for all weeks (seasons). For our purposes, the yearly amount divided equally for all seasons is 19.21 ÷ 4 = 4.81 minutes. The seasonal factors are: Past minutes Avg minutes for each season (19.21/4) Seasonal Factor Week 1 (Spring) 29.92 4.81 6.22 Week 2 (Summer) 13.83 4.81 2.88 Week 3 (Fall) 23.63 4.81 4.91 Week 4 (Winter) 9.05 4.81 1.88 Using these factors, if we expected demand for next year to be increased to 24.21 minutes, we would forecast the demand to be as follows: Expected Demand for Next Year Avg minutes for each season (24.21/4) Seasonal Factor Next Year's Seasonal Forecast Week 1 (Spring) 6.05 6.22 37.65 Week 2 (Summer) 6.05 2.88 17.40 Week 3 (Fall) 6.05 4.91 29.73 Week 4 (Winter) 6.05 1.88 11.39 Confidence Intervals Confidence intervals are used to indicate the reliability of an estimate. The confidence interval tells how likely the interval will contain the parameter. The wider the confidence level, the more certain that the sample data would fall within the specified range. Confidence intervals are affected by sample sizes, percentage, and population size. The confidence interval represents the range of values around the sample mean that include the true mean. The confidence intervals with a 99% confidence level were calculated as follows: Monday Tuesday Wednesday Thursday Friday confidence interval 99.% lower -69.0131 -28.7803 -61.9071 -74.5175 -26.6782 confidence interval 99.% upper 103.3331 46.2503 100.3921 123.4875 79.4832 Therefore, 99% of the time, the time to prepare dinner would fall between the upper and lower intervals for each respective day. Conclusion All processes can be monitored and brought under control by gathering and using data. Statistical process control is a useful tool to measure and analyze the variation of a process. The benefits of SPC are a consistent product that would create maximum customer satisfaction and ultimately maximum profits for the organization. Attachment A Descriptive statistics Monday Tuesday Wednesday Thursday Friday count 4 4 4 4 4 mean 17.1600 8.7350 19.2425 24.4850 26.4025 sample variance 870.6661 165.0153 772.1135 1,149.2123 330.3560 sample standard deviation 29.5071 12.8458 27.7869 33.9000 18.1757 minimum 2.3 2 2 3.02 9.02 maximum 61.42 28 60.26 75.07 51.33 range 59.12 26 58.26 72.05 42.31 Quality Control Process Charts Sample size 5 Number of samples 4 Mean Range Upper Control Limit, UCL 48.9133 108.8446 Center 19.2050 51.4875 Lower Control Limit, LCL -10.5033 0.0000 References Business Dictionary (2010). Retrieved from www.businessdictionary.com. Chase, R. B., Jacobs, F. R., & Aquilano, N. J. (2006). Operations management for competitive advantage (11th ed). New York: McGraw Hill/Irwin Cook, Sarah (1996). Process Improvement: A Handbook for managers. Retrieved from http:// books.google.com.