Q 553. Suppose we have a scenario where data is being gathered for both defects and defectives in a specific process. In addition, the defects are categorized into minor, major, and critical, which are the three types of defects that various organizations typically recognize. In this situation, which type of control chart (C chart, U chart, NP chart, P chart) should be employed to assess the process stability? Please provide examples to support your answer.

 

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To check the stability of process for Defective Data, we use NP chart (subgroup size fixed) and P chart (subgroup size variable) and for Defects Data, we use C chart (subgroup size fixed) and U chart (subgroup size variable). 

 

Based on the criticality of the defects i.e. minor, major and critical as in this case, Special Cause Tests also known as Nelson’s Rules for special cause are used along with the relevant control charts. Out of the 8 rules, the following first 4 are applied here due to it being a discrete dataset:

 

1.       1 point greater 3 std dev on either side of the center line – Indicates strongest evidence for lack of control and a special cause.

2.       9 points in a row on same side of the center line – Indicates shift in the process mean.

3.       6 points in a row, all increasing or all decreasing – Indicates a trend or gradual shift of mean.

4.       14 points in a row alternating up and down – Indicates a non-random pattern.

 

If it’s a minor defect, we may just want to use the 1^st test to understand the special cause. 

If it’s a major defect, then any one or two tests from the remainder 2^nd to 4^th along with the 1^st can be used depending on shifts, trends or patterns whichever is of interest to us.

If it’s a critical defect and we want all the warnings and alarms of special causes well in advance, then all 4 special causes tests are to be conducted.

 

Example:  In a typical publishing house, the content of several monthly and weekly magazines is evaluated by subject matter experts against various attributes that are critical to quality and acceptance by the customers.  The attributes are categorized into minor, major, and critical defects and checked for stability from time to time.

 

1).  Minor Defect –Punctuation Errors Per Page is considered as Minor Defects.  The publishing company might just want to know the special causes, if any, and would go ahead with the 1st special test along with the relevant control chart.

 

2).  Major Defect – Spelling Errors or Improper Verbiage per page is considered a Major Defect.  In this case, along with the Special Causes, the company may also want to know if there is any shift of the mean or if there are any trends or non-random patterns and might consider applying either one or two tests from 2^nd to 4^th along with the 1^st test depending on its area of interest along with the relevant control chart.

 

3).  Critical Defect – Any defects in the magazine that arise out of a content that lacks integrity (unverified numbers and information), promotes discrimination, is politically or racially motivated, have shades of blasphemy and have provocative verbiage is considered a Critical Defect by the publishing company and if not controlled may warrant scrapping of the entire weekly or monthly edition.  In such a case, the publishing company may want to use all the 4 special tests along with the relevant control chart so that it is aware of any unusual shifts, trends or patterns well in advance and can take necessary actions to eliminate such defects.

 

Defective data follows the binomial distribution ‘P’ chart to be used for monitoring and capability analysis. ‘P’ chart signifies the proportion of defective trends. NP chart is used when you have Defectives data with a Fixed Sample Size. P chart is used when you have Defectives data with a Variable Sample Size.

Defect data follow poison distribution, the Z goal will depend on how many defects be reduced to give DPMO and compute the required Zgoal. C chart is used when you have Defects data with a Fixed Sample Size. U chart is used when you have Defects data with a Variable Sample Size. In a U chart, the UCL and LCL will vary with changes in the sample size.

All three types of defects minor, major, and critical can be separately assessed for process stability, to get a sense of contribution from each of these classes on stability. Based on the criticality of these classes, decisions can be devised towards making the overall process stable, before exploring the capability of the process.

While a couple of participants have tried to answer the question, however no one has really gone in details of the specific situation given. Hence, there is no winner for this question.

 

In the situation given here, the team is collecting data on both defectives and defects and defects are also being classified into critical, major and minor. Let's consider an example - we are manufacturing cars. Examples of defectives and types of defects would be something as below

Defective car - a car which has defects

Critical defect - malfunctioning brakes

Major defect - the door does not close properly

Minor defect - scratch on the bonnet of the car

 

Stability of the process can be checked with any one of the parameters. From an overview perspective, I would use either a P or an NP chart to check for stability which means I would work with defectives.

 

In addition to this, I would pro-actively work with a C or a U chart for critical defects as there could be multiple critical defects in the same car.

 

By using these 2 charts I will be able to better control my process. 

 

Of course, if I have the resources and time, I would like to use C or a U chart even for major and minor defects, however resources and time is a rare luxury