Question

What role do variability and statistical methods play in controlling quality?

Answer 1

Introduction

The quality of products and services is an important factor in most businesses today. Regardless of whether the consumer is an individual, a corporation, a military defense program, or a retail store, when the consumer is making purchase decisions, he or she is likely to consider quality of equal importance to cost and on-time delivery. Consequently, quality improvement has become a major concern to many corporations.

A well-operated, documented management system provides the necessary foundation for the successful application of SQC. Note, however, that SQC is not just a collection of techniques.It is a strategy for reducing variability, the root cause of many quality problems. SQC refersnto the use of statistical methods to improve and enhance quality and through it customer satisfaction. However, this task is seldom trivial because real world processes are affected by numerous uncontrolled factors. For instance, within every factory, conditions fluctuate with time. Variations occur in the incoming materials, in machine conditions, in the environment and in operator performance. A steel plant, for example, may purchase good quality ore from a mine, but the physical and chemical characteristics of ore coming from different locations in the mine may vary. Thus, everything isn't always "in control."

Another prospect in which statistical methods can help to improve product quality is the design of products and processes. It is now well-understood that over 2/3rd of all product malfunctions may be traced to their design. Indeed, the characteristics or quality of a product depend greatly on the choice of materials, settings of various parameters in the design of the product and the production process settings. In order to locate an optimal setting of the various parameters which gives the best product, we may consider using models governing the outcome and the various parameters, if such models can be established by theory or throughe xperimental work.

Input factors - >    Process - >    Output responses

x1, x2, x3, …    y = f(x)    y1, y2, y3,

There are various definitions of quality. The classical definition is that quality means fitness for use. For example, you or I may purchase automobiles that we expect to be free of manufacturing defects and that should provide reliable and economical transportation, a retailer buys finished goods with the expectation that they are properly packaged and arranged for easy storage and display, or a manufacturer buys raw material and expects to process it with no rework or scrap. In other words, all consumers expect that the products and services they buy will meet their requirements. Those requirements define fitness for use. Quality or fitness for use is determined through the interaction of quality of design and quality of conformance. By quality of design we mean the different grades or levels of performance, reliability, serviceability, and function that are the result of deliberate engineering and management decisions. By quality of conformance, we mean the systematic reduction of variability and elimination of defects until every unit produced is identical and defect-free. Because both of these activities involve reducing variability in the key parameters that define fitness for use, a more modern definition of quality is focused on reduction of unnecessary variability in these parameters.

Statistical methods play a vital role in quality improvement.Some applications are outlined below

: 1. In product design and development, statistical methods, including designed experiments, can be used to compare different materials, components, or ingredients, and to help determine both system and component tolerances. This application can significantly lower development costs, reduce overall development time, and decrease time to market.

2. Statistical methods can be used to determine the capability of a manufacturing process. Statistical process control can be used to systematically improve the capability of a process by reducing variability.

3. Experimental design methods can be used to characterize and optimize processes. This can lead to higher yields and lower manufacturing costs.

4. Statistical methods can be used to characterize the performance of measurement systems, which can lead to more informed decisions about product disposition.

5. Life testing provides reliability and other performance data about the product. This can lead to new and improved designs and products that have longer useful lives and lower operating and maintenance costs.

Methods of Statistical Quality Control

The field of statistical quality control can be broadly defined as those statistical and engineering methods that are used in measuring, monitoring, controlling, and improving quality. Statistical quality control is a relatively new field, dating back to the 1920s. Dr. Walter A. Shewhart of the Bell Telephone Laboratories was one of the early pioneers of the field. In 1924 he wrote a memorandum showing a modern control chart, one of the basic tools of statistical process control. Dr. W. Edwards Deming and Dr. Joseph M. Juran were instrumental in spreading statistical quality-control methods in the last 50 years. Much of the interest in statistical quality control and improvement focuses on statistical process monitoring and control and experimental design. Many companies have extensive programs to implement these methods in their manufacturing, engineering, and other business organizations. Online statistical process control is a powerful tool for achieving process stability and improving capability through the reduction of variability.

It is customary to think of statistical process control (SPC) as a set of problem- solving tools that may be applied to any process.

The major tools of SPC are:

1. Histogram

2. Pareto chart

3. Cause-and-effect diagram

4. Defect-concentration diagram

5. Control charts

6. Scatter diagram

7. Check sheet

Some prefer to include the experimental design methods as part of the SPC toolkit. We did not do so, because we think of SPC as an online approach to quality improvement using techniques founded on passive observation of the process, while design of experiments is an active approach in which deliberate changes are made to the process variables. As such, designed experiments are often referred to as offline quality control. Although the complete set of tools are important to the implementation of SPC, in this chapter we focus on only control charts.

Natural variability is a quality control related concept. All manufacturing or service exhibit a certain amount of “natural” variability. (Such variability is also known as chance or random variation.) This natural variability is the cumulative effect of several minor factors. The extent of natural variability inherent in a process differs from process to process, and changes over time. For instance, older machines will generally exhibit a higher degree of natural variability than newer machines, partly because of worn parts and partly because newer machines may incorporate design improvements that reduce the variability of their output.

Ideally, only random variation (or natural variability) should be present in a process, because it represents the acceptable amount of variation. Improving the system itself can reduce natural variability. A process that is operating with only natural variability is said to be “in a state of statistical control.”

Assessing Variability for Quality Improvement

We often see an average (a.k.a. the mean) used to summarize a population or a process. For example, a pizza restaurant might state that their mean delivery time is 20 minutes. Deceptively, this seems like a very intuitive measure.

While the mean is important, people often react to the variability even more. Variability is a measure of how spread out the data are from the mean. How many times have you watched a weather report where the forecaster shows extreme heat and fires in one region and flooding in another? Wouldn’t it be nice to average those together? People feel pain at the extremes more than the average.

This is true of customers as well. Purchasers of a product or service expect a certain experience based on previous purchases. Customers value consistency and predictability in order to feel confident that their money is well spent. In short, customers want low variability and they will notice a deviation from their expectations.

How To Measure Variability and See Its Effects

The standard deviation is the most common measure of variability. It is the average absolute distance of each data point from the mean. If you measure a sample of pizza delivery times and they are all very similar, you have a smaller standard deviation. If the values are more different, you have a larger standard deviation.

Let’s compare 2 pizza delivery restaurants, both of which claim to have an average delivery time of 20 minutes. How could you decide which one to order from? Look at their variability.

Let’s assume that both places have an average delivery time of 20 minutes but one has a standard deviation of 5 minutes while the other has a standard deviation of 10 minutes. We'll also assume that the delivery times are normally distributed. Additionally, you consider waiting 30 or more minutes to be unacceptable. How big of a deal is the difference in variability? Use Minitab’s Probability Distribution Plots to find out!
  

The graphs above show the distribution of delivery times. The shaded area represents the proportion of delivery times that exceed 30 minutes. The high variability restaurant has a wider distribution curve and nearly 16% of its deliveries exceed 30 minutes. The low variability restaurant has a narrower curve and only about 2% of its deliveries exceed 30 minutes. I know which place I’d order from if I were hungry!

This example illustrates how the mean provides incomplete information, because we have two identical means but two very different results. Higher variability reduces the purchaser’s certainty regarding the product or service that they will receive.

Assess Variability Using Minitab

As you can see, assessing the variability in your process analysis is extremely important for quality improvement. Minitab Statistical Software has many tools to help you assess the variability that you have and help you find ways to reduce it.

Hypothesis Tests

Hypothesis testing uses your sample data to draw conclusions about one or more populations.

1 Variance
Determine how the variance of one population compares to a target value. For example, you measure the strength of steel in a sample and want to determine whether the variability of the plant’s production is less than a critical threshold.

2 Variances
Determine how 2 population variances compare to each other. For example, you measure the strength of steel in samples from 2 plants and want to determine which plant produces steel that has a more consistent strength.

Test for Equal Variances
Determine whether the variances of 2 or more populations are all equal. This test will tell you if steel from multiple plants are equally consistent or not.

Analyze Variability in Design of Experiments (DOE)

A designed experiment is a series of runs, or tests, in which you purposefully make changes to input variables simultaneously and observe the responses.

Analyze Variability is an analysis in Minitab’s Design of Experiments (DOE) toolkit that identifies factor settings that produce less variable results in 2-level factorial designs with repeat or replicate measurements. For example, say you are studying different manufacturing settings and want to determine how they affect steel quality. Analyze Variability will help you determine how to produce steel with more consistent strength.