Using Minitab to construct Control ChartPart 2

Example:The given table presents the inside diameter measurements of forged automobile engine piston rings. Each sample or subgroup consists of five piston rings. We will use these data to illustrate the construction and operation of and s charts.

SN 1 2 3 4 51 74.030 74.002 74.019 73.992 74.0082 73.995 73.992 74.001 74.011 74.0043 73.988 74.024 74.021 74.005 74.0024 74.002 73.996 73.993 74.015 74.0095 73.992 74.007 74.015 73.989 74.0146 74.009 73.994 73.997 73.985 73.9937 73.995 74.006 73.994 74.000 74.0058 73.985 74.003 73.993 74.015 73.9889 74.008 73.995 74.009 74.005 74.00410 73.998 74.000 73.990 74.007 73.99511 73.994 73.998 73.994 73.995 73.99012 74.004 74.000 74.007 74.000 73.99613 73.983 74.002 73.998 73.997 74.01214 74.006 73.967 73.994 74.000 73.98415 74.012 74.014 73.998 73.999 74.00716 74.000 73.984 74.005 73.998 73.99617 73.994 74.012 73.986 74.005 74.00718 74.006 74.010 74.018 74.003 74.00019 73.984 74.002 74.003 74.005 73.99720 74.000 74.010 74.013 74.020 74.00321 73.982 74.001 74.015 74.005 73.99622 74.004 73.999 73.990 74.006 74.00923 74.010 73.989 73.990 74.009 74.01424 74.015 74.008 73.993 74.000 74.01025 73.982 73.984 73.995 74.017 74.013

Attribute Control ChartAttribute control charts are the charts that plot nonconformities (defects) or nonconforming units (defectives). A nonconformity refers to a quality characteristic and a nonconforming unit refers to the overall product. A unit may have many nonconformities, but the unit itself is either conforming or nonconforming. For example, a scratch on a metal panel is a nonconformity. If several scratches exist, the entire panel may be considered nonconforming.

In fact, control charts for attributes are used to measure quality characteristics that are counted rather than measured. Attributes are discrete in nature and entail simple yes-or-no decisions. For example, this could be the number of nonfunctioning lightbulbs, the proportion of broken eggs in a carton, the number of rotten apples, the number of scratches on a tile, or the number of complaints issued.

Types of control charts for attributesTwo of the most common types of control charts for attributes are p-charts and c-charts.

P-charts are used to measure the proportion of items in a sample that are defective. Examples are the proportion of broken cookies in a batch and the proportion of cars produced with a misaligned fender. P-charts are appropriate when both the number of defectives measured and the size of the total sample can be counted. A proportion can then be computed and used as the statistic of measurement.

C-charts count the actual number of defects. For example, we can count the number of complaints from customers in a month, the number of bacteria on a petri dish, or the number of barnacles on the bottom of a boat. However, we cannot compute the proportion of complaints from customers, the proportion of bacteria on a petri dish, or the proportion of barnacles on the bottom of a boat.

The primary difference between using a p-chart and a c-chart is as follows. A p-chart is used when both the total sample size and the number of defects can be computed. A c-chart is used when we can compute only the number of defects but cannot compute the proportion that is defective.

P-charts are used to measure the proportion that is defective in a sample. The computation of the center line as well as the upper and lower control limits is similar to the computation for the other kinds of control charts. The center line is computed as the average proportion defective in the population, . This is obtained by taking a number of samples of observations at random and computing the average value of p across all samples. To construct the upper and lower control limits for a p-chart, we use the following formulas:

where z standard normal variable the sample proportion defectivethe standard deviation of the average proportion defective

The sample standard deviation is computed as follows:

where n is the sample size.

Example:A production manager at a tire manufacturing plant has inspected the number of defective tires in twenty random samples with twenty observations each. Following are the number of defective tires found in each sample:

Construct a three-sigma control chart (z = 3) with this information

No. defects1 32 23 14 25 16 37 38 29 110 211 312 213 214 115 116 217 418 319 120 1

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The center line of the chart is

In this example the lower control limit is negative, which sometimes occurs because the computation is an approximation of the binomial distribution. When this occurs, the LCL is rounded up to zero because we cannot have a negative control limit.

The np Control Chart. It is also possible to base a control chart on the number nonconforming rather than the fraction nonconforming. This is often called an number nonconforming(np) control chart. The parameters of this chart are as follows.