Fuzzy membership function in determining statistical process control position

Statistical process control (SPC) is a technical tool that is used to control and to improve almost any kind of process. However, because of cost consideration, management need to decide which part should apply SPC. In this paper, we propose the use of probability and fuzzy membership function to determine SPC position. Conditional probability is used to analyze process failure and process repair. Then, using Markov matrix, we calculate the probability of out-of-control process (PO). Nevertheless, in a production line that consists of many parts, the probability values are not adequate to be used as a reference to determine SPC position since these values would cause ambiguity. To illustrate this ambiguity, consider the following crisp definition of the out-of-control condition: If the probability of out-of-control process (PO) is 0.25 (or 25%), with a tolerance of 0.05, then the process is considered "high", otherwise it is considered "low". Now, suppose the value of PO is 0.23 (or 23%), with the same value of tolerance, could we definitely say it as "low"? Therefore, to overcome this problem we apply fuzzy membership function (MF) that uses linguistic terms and degree of memberships to analyze PO instead of the probability values.