6: II 7: III
4.1 Introduction
Statistical Quality Control (SQC) consists of methods to improve the quality of process outputs. Statistical Process Control (SPC) is a subset of Statistical Quality Control (SQC). The objective for SPC is to specifically understand, monitor, and improve processes to better meet customer needs.
InChapter 2and 3, the MIL-STD documents for acceptance sampling were described. In 1996, the U.S. Department of Defense realized that there was an evolving industrial product quality philosophy that could provide defense contractors with better opportunities and incentives for improving product quality and establishing a cooperative relationship with the Government. To this end MIL-STD-1916 was published. It states that process controls and statistical control methods are the preferable means of preventing noncon- formances; controlling quality; and generating information for improvement.
Additionally, it emphasizes that sampling inspection by itself is an inefficient industrial practice for demonstrating conformance to the requirements of a contract.
Later civilian standards have provided more detailed guidelines, and should be followed by all suppliers whether they supply the Government or private companies. ASQ/ANSI/ISO 7870-2:2013 establishes a guide for the use and understanding of the Shewhart control chart approach for statistical control of a process. ISO 22514-1:2014—Part 1: provides general principles and concepts regarding statistical methods in process management using capability and per- formance studies. ASQ/ANSI/ISO 7870-4:2011 provides statistical procedures for setting up cumulative sum (cusum) schemes for process and quality control using variables (measured) and attribute data. It describes general-purpose methods of decision-making using cumulative sum (cusum) techniques for monitoring and control. ASQ/ANSI/ISO 7870-6:2016 Control charts—Part 6: EWMA control charts: Describes the use of EWMA Control Charts in Pro- cess Monitoring. These documents can be accessed athttps://asq.org/quality- press/, and all the methods will be described in detail in this chapter and chapter 6.
The output of all processes, whether they are manufacturing processes or processes that provide a service of some kind, are subject to variability. Vari- ability makes it more difficult for processes to generate outputs that fall within 73
desirable specification limits. Shewhart[86] designated the two causes for vari- ability in process outputs to be common causes and special or assignable causes. Common causes of variability are due to the inherent nature of the process. They can’t be eliminated or reduced without changing the actual process. Assignable causes for variability, on the other hand, are unusual dis- ruptions to normal operation. They should be identified and removed in order to reduce variability and make the process more capable of meeting the spec- ifications.
Control charts are statistical tools. Their use is the most effective way to distinguish between common and assignable cause for variability when mon- itoring process output in real time. Although control charts alone cannot re- duce process variability, they can help to prevent over-reaction to common causes for variability (which may make things worse), and help to prevent ignoring assignable cause signals. When the presence of an assignable cause for variability is recognized, knowledge of the process can lead to adjustments to remove this cause and reduce the variability in process output.
To illustrate how control charts distinguish between common and assignable causes, consider the simple example described by Joiner[48]. Eleven year old Patrick Nolan needed a science project. After talking with his father, a statistician, he decided to collect some data on something he cared about;
his school bus. He recorded the time the school bus arrived to pick him up each morning, and made notes about anything he considered to be unusual that morning. After about 5 weeks, he made the chart shown inFigure 4.1 that summarized the information he collected.
FIGURE 4.1: Patrick’s Chart (Source B.L. Joiner Fourth Generation Man- agement, McGraw Hill, NY, ISBN0-07032715-7)
FIGURE 4.2: Control Chart of Patrick’s Data
A control chart of the number of minutes past 8:00AM that the bus arrived is shown inFigure 4.2. In this figure, the upper control limit (UCL) is three standard deviations above the mean, and the lower control limit (LCL) is three standard deviations below the mean. The two points in red are above the upper control limit, and they correspond to the day when Patrick noted that the school bus door opener was broken, and the day when there was a new driver on the bus. The control chart shows that these two delayed pickup times were due to special or assignable causes (which were noted as unusual by Patrick). The other points on the chart are within the control limits and appear to be due to common causes. Common causes like normal variation in amount of traffic, normal variation in the time the bus driver started on the route, normal variation in passenger boarding time at previous stops, and slight variations in weather conditions are always present and prevent the pickup times from being exactly the same each day.
There are different types of control charts, and two different situations where they are used (Phase I, and Phase II (see Chakraborti[20])). Most text- books describe the use of Shewhart control charts in what would be described as Phase II process monitoring. They also describe how the control limits are calculated by hand using tables of constants. The constants used for calculat- ing the limits can be found in the vignette SixSigma::ShewhartConstants in the R package SixSigma. There are also functions ss.cc.getd2(), ss.cc.getd3(), and ss.cc.getc4() in the SixSigma package for retriev- ing these and other control chart constants. Examples of their use are shown by Cano et. al.[18]. In addition, tables of the constants for computing control chart limits, and procedure for using them to calculate the limits by hand are
shown in Section 6.2.3.1 of the online NIST Engineering Statistics Handbook (https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm)[1].
Sometimes Shewhart control charts are maintained manually in Phase II real time monitoring by process operators who have the knowledge to make adjustments when needed. However, we will describe other types of control charts that are more effective than Shewhart control charts for Phase II mon- itoring inChapter 6. In the next two sections of this chapter, we will describe the use of Shewhart control charts in Phase I.