Statistical process control
What is Statistical Process Control? It is a tool (discovered by Dr. Walter Shewart in 1920) for making analytical decisions. It is employed in checking whether a process is going on in the correct way or not. All processes have got inconsistency in form of variations an thus it needs to be determined if it is natural or if correction is needed. This is what entails quality control. In Statistical Process Control, process control charts are what determine if the process at hand is in control or not (Chase e.tal 2006).
Process Control charts are used during the period of the process to indicate any variations in the measurements. They should not be confused with process capability charts which are used to indicate a summary of the reports. Control charts determine the process capability and assist in identifying unique factors that hinder peak performance. Control charts monitor a process by comparing variances against two limits namely upper limit and lower limit. This is done to check if the variation falls within the normal or expected range. If the variance falls in the expected level, then the process is considered in control and any variance in the measurement is regarded as normal and an attribute of the process. On the other hand the process is out of control if the variance doesn’t fall within the limits (Chase e.tal 2006).
The most important part of Statistical Process Control is the calculation and determination of the control limits. This are got from the statistical data collected. There are two control limits; the lower control unit and the upper control limit. Both are normally set at 3-sigma by default as it is the popular limit in use. The purpose of these limits is to determine the occurrence of the observed data that indicate a stable and continuous process. Factors such as choice of equipment and the operations accuracy and precision obtained from the design can lead to inconsistency and fluctuation from the limits (Chase e.tal 2006).
In calculating the limits, the average x-bar and s values are taken as the center line. This together with the each sample’s average value is used to plot the control chart. Calculation of the upper and lower limits for the x and s charts is done first with the s chart. The s chart takes precedence because it’s used to determine whether or not the process is in control statistically according to the variance. In addition it shows if the process is not in control. The x chart is immediately constructed once the process is determined to be under control in relation to variance. The central limit theorem forms the basis for the formulas that are used in determining the limits (Steel e.tal 1980). The calculation of the upper and lower limits is shown below from the given data.
Day of the week
Seasonal factors are due to a particular time of the year when certain activity occur which can directly or indirectly affect the data collected. Seasonal factors are usually short term behavior in the data and are not always observed unless it is that time of the year (Foster 2004). For instance if it was that time of the year when there is snow storms or heavy rain the roads will become wet and slippery and therefore the time taken to drive will increase since one has to reduce the speed of the vehicle in order to avoid accident. On Fridays it takes a longer time to drive maybe because of a seasonal event that takes place on Fridays of that week that causes the traffic to increase. This may be due to the fact that people want to reach work on time so as to finish their work and later catch the latest movies showing each Friday.
In every statistical process performance data there is an measurable approximation of error. This is known as uncertainty. Elimination of uncertainty can be done through calculation of confidence interval. What does a confidence interval do? It serves to indicate an approximate range of values close to the mean which illustrates the nature of the measurement. In calculation of the confidence interval three factors are put into consideration. These include the standard error, the mean and the z value. The formula for determining the mean is shown below.
The assurance degree determines the confidence interval size. Comparing a 99% confidence interval to a 95% confidence interval, the former is narrow compared to the latter. Thus 95% represents a larger interval. The data points influence the calculation of confidence interval in that a wide range results from fewer points. This makes it hard to get the exact interval. On the other hand the more the data points the easier it is to narrow down the range hence making the data more beneficial (Foster 2004).
In conclusion it is true that process control is very important in making crucial decisions about a process that is continuous. It is of utter importance in the manufacturing process to check and control the quality of end products within the manufacturing process. The upper and lower limits determine whether the process is in control or out of control for corrective measures to be taken. Seasonal factors that occur once or twice within a year usually affect the data collection only when they coincide. The confidence interval of data is determined by the number of data points collected in that the more the data points the narrow the range and thus the usefulness of the data.
Chase, R. B., Jacobs, F. R., & Aquilano, N. J. (2006).Operations management for competitive advantage (11th ed.). New York: McGraw Hill/Irwin.
Steel, R. G. D. and J. H. Torrie (1980), Principles and Procedures of Statistics. New York: McGraw-Hill.
Foster, S. Thomas (2004). Managing Quality: An Integrative Approach, 2nd Edition. Upper Saddle River, NJ: Prentice-Hall